Content-Type: multipart/mixed; boundary="-------------0207050404367" This is a multi-part message in MIME format. ---------------0207050404367 Content-Type: text/plain; name="02-294.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-294.keywords" Aharonov-Bohm effect,point-like magnetic field, scattering ---------------0207050404367 Content-Type: application/postscript; name="ABeffct-mp.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="ABeffct-mp.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.78 p1.4c Copyright 1996-99 ASCII Corp.(www-ptex@ascii.co.jp) %%based on dvipsk 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: ABeffct-mp.dvi %%Pages: 42 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR12 CMTI12 CMMIB10 CMR8 CMMI12 CMSY10 CMEX10 %%+ CMMI8 CMSY8 CMMI6 CMR6 LASY10 CMSY6 CMR10 CMTI10 CMBX10 Courier %%EndComments %DVIPSCommandLine: dvipsk -D600 -t a4size -P dl ABeffct-mp.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.07.05:1757 %%BeginProcSet: texc.pro %! 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346f35373ff64402dc41345148bce01c962954f693cc8087319b0b6ec7c6ba45 f8fe290f6ce8949b3d35dd31f8e7ca94f0b3a698089130c595d9e68f763fd268 34409a3770b549ebf25739877478961f35bcbff2155c44d0f57cd86b8913702c d9ac62030da35b69d50e01709fdfdc428111bce6ef76de29247019053f615e70 e1eca1f1611824504f0add691a8672081ebec98914c34addfdedf62e704cb022 a835bd251d94b2386e0c5c46ae377f73f13a72295d80fe9646631afd304845d2 eb23a4596b26fb70f695d8ff7ae2ae81815346a8056e1bc5406c743479e4e967 3ca28138ede3b17e6da1c33ecc37eea04fbd9731570066f29ecde6d61014f6c1 16094d3aeb4ba5c2d27e595c73c3b92ce7f8ef10a6af7a0c94de7f306f920386 c0bb3b17c4beb1df82f30a627b6d1eca1f56279e5e7b3fdc09b5b08ceb2d72fb ea8c831f72d6f887b01c36913f99450941d4ef0b35e0f6e8eb3af8194c856dd4 0ee089bf3b963f19455cf2a83e3fd28141398d89b12f4414b9cbfff52ac2bafa fcc31a624aecfd06de58a854206a370d75a7fb8e8a3b951d2f542886c517fbeb ed6a2e7626cf44b89c7d6d688a8a795753201265276e59a46ccaf50ecd6ff7a8 05cf1defc5f7874757829b5118129d0b6326f7df88069ee643149ccb1677a259 7b4d677abbf491f298cbf5ee9589e849dfd833af50b9f46379c80863c2b03e06 4f52f3fbe8c7a5f21702bd4d7796cfd5c7dbf8630a0a869452de2b4ec72c1a06 4f19022c61572d01da1f820cc2efb89b679ae45730b6b246a4ab7240ad5c81ed d5d7733b83077705471c0851883cccb984c5fc163661c50f0ae0c6919001db89 9a4af13c05fc2138f5b1e395efa0d5b61ecc2b789f2c184d400151d0273f62bc ae0949cadbb52c5b3fb58441507c2248c809b20d2f6e8b0aaf19a965 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 69 /E put dup 97 /a put dup 100 /d put dup 101 /e put dup 105 /i put dup 108 /l put dup 109 /m put dup 114 /r put dup 115 /s put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 7d8cd83bb8ac7aff4df36751f4f12aaaea2b6d7260c09a26e987c904003e0723 7dbcc4a8e4e85cd3259f40d3caf55c742cbb40ad0db1044c20a4f122a63f7b81 1d945bfa69662189ce4d089464d2ead9f6ed60b581b04114d5d45e97be27a576 35154e9b8464f2a0df18da855eb51b8f64d3054b0b2e84621f025a0776d16fed b988a43d2d64c32768dd106b9f541ae8e68ac0bb7399e16f4d4ba074b2152d0a 4e9b5bfc21bfa0d531e28165e518ffc054dd4ed0d74eca079d20e79670419f92 e03bcbfeecf3554d661596f6f29e12170804d15a250d917ffe7a8b6e8fa53047 1ed97ba56481589a65ca13619129f1e26affe6c22f0c38540f8ce37efb6e9e9b 60b51a5a9cb4454fd7c7f92f2f9437159687ab590f35b946a54491a7739c9269 e0f1fb48b129811c82edb3171cbd5105fe65906974db8a7da92f4f43dc7f6b36 6981146d86d23613a0b38d9d6191db9fea0172e982cb1cc50e382f69da1b377c 1be9407f88a2a761b56f398467a057f35d18c01cc377e0061822b94abb98feaf 33e32c9bc59416e65491cb08cd8de429deca10ec4765d20faea23f130f5226ac 4d27d24db0385cc31b8b3227812d2c2fd223d0b86eb936ff0bdc45a281c544fb d7798b4aa264d33ce1e3eed7c77fc4942637b524a072aaf76b4aa25c250c8496 d0787d1139a647e7165191dd7ef7d25d830220b8ba0e91b1019c1541cd052faa de1157d53f434b7002e64cc69c69c8fd1c82546655ca38fda41b1c205e915b27 e614b2ea7571f1029bebdc6f85e1c91da856a2491495d1f13f7ca105deab43b9 c2d3fa5565b0d5cada91192bd803cdd87896e69fe97d51b895ccd30ddc40c162 f22591886e6d4815c91afc97132bdb283c19ec54aa4f0e16a9ab343e2da839aa 40c0330e318dbfb47a725e41bdfeb3ad0ea1736f19f273d223331199bb10851a 6372835f4d83115e21e8d936fc9612c8e026ddafad4796c7ceb8b84f2fc05a97 ed8e85e7676d918eba191ff70e179a7c59df36e2b19db609b31b72dd9c06eaa0 8aa13bbbd9a9eeb7ac0c0722bb5bdf97cab8dcb192b81aa570b1c2f571bb884b 03eceb26237b39f51aa5f093bb731cff7935f924589cfc6f35b4be19e155add6 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27a54e2a9b6a2948f6577785f2f340a4f311e574c3ed7ef9a20504c61f80a6a7 ea1b5b8f5a6e70103da3a0daaf08aba4052cc98928dba03909111439a2541605 9fbebbf6d130d18f0e07e1dfe8d13f4097fc22ac546d32c6e4d0b81e5f8e2b08 a36b8b36e110e5ad899935bec912a021e5f6ea8a08e584eb8e1b539a21a62b9c 9564a961c17e823a6fe017a8386a800110c2db8fc7dd42c20bd63a5376ff4432 9ba5c141a2edd34a82cebb91d0afca10521a2624449a99222037ba8009e685c2 e4e914e44da1386c7b625a1774ec839a98238115a4645e60ccf67929ccf6f3bb 7568be9ca389636b3b581308c4c4470e6f498ca2102be2120228e05c65024a69 9edcc69b7e46502b1089b79041ebf8b028f91744614d93b97a3ce803669030b0 c28229be07ad81cc25e3d53af3a96474bcd9e752b1f56cb2564466c3730570b4 82f03fba2db33db7af798c2339fde85843fb446eca80cf638621a6e860f82b8c 6bf7c0c87e12a6be48c54d2d8f8d05e96c779cc801c78ce3acbb24454a6e675f a202160ee748dddd0f796c0917c5b2520e833401d3dc3e0e00adf450c321190f 0659e6c60aea475fed896529bf6d67000bbbd2ef7b787839ff3f5c938508e4b4 0ded39cb02d5f83a0b369b18e7cf42dc524b291fcf67b52eae4b84d0913071f0 1720ee135cc86af21f187695b51ed408eb3c7aaecee69d6573dbfae480228a1f 615cdd8b4741a34eeff52c7ce618e9d23adfaaf25962560d7f07874e33ff2167 65e28091c816b4702a9929f8962a6b1bee0f9a99b5c55c4cacc5663248087354 b65ea231f57a93b795d434cee1a46f4f162de0744f3f44df70c3091aa1ace6bb d0490698fb8476d1841d005f4248ca379c033db7df6c232f06ffeb6daac877be 517bdec3ec7af92a6775733f2f7714cedc074c3429eea9753642d5d3bfa962a1 227393ee99ced56f35f90196991fce85bf9c2d81ca343e661dbeb1517bbca03e 898d7beeca81e4ae0561989dcff885610237aa355a8bce5388ec43ceeae23d35 1ab71d155fdad95646f1db3b1b134a545d66860b3e6985de69fb28c096ade2c3 9af06a097d51203314acb448b320bc3b85f51bbebd5503d8b0a373d100cd949a 9062dffaa1592c26d4a59c140aeacc680bcccb3149cd58ae38cd941141cd4144 cfc90c434ab8797d3fc6ec3322606f47321bceeaf7f33952f3d41794fa1069ad 33d4e3f4f2835d3430da9f28423467bdb06d47be4f0317bd0956edd3693507b9 aed956c8cb533e81420bbb4de6e00401879acc1da6f38e12c07bbe9bc158ad85 303e0d9dc0275cd8be9b6ca36e628bc9517b5336ab094d4d2bb347b8835dc648 55d0bc8862d36ea57af461e171dc5015218d4cf961f6c5ff736916f6a0f77446 37f3a925aa6c967b2fbd6b2a5d7073c555a8f3bed374d4b20498fd0dec3d98d4 d73f4761d69399989c1c65fad63ea982c553e93930a5a91605ec5c8b9185b8ab 41bece0a551b58f79eab7d0978cffe4e94e88fadcbe25c13e883a9a34d5319e5 9393688b73bb4da0608403e53fcb27a755e50657b186493b09c61468d9f018c7 c466c31120dc49de2693e2997966bbaf27fdc91c8016585a553a15bbe1420e1e 37d0c6f51ef00ad650b50aa5234dea3ae8dadef88835373c3ba314c884aaf696 e44b40e2b6f92d2400b9fb20e78015f1e078160908ffd987acacb21e99f47b38 ff1a44b3ebd3cbfc01ffba8305342916068ed92760db21adc56ebefa2251e4b9 5f3b44edc6a91517174ec75181a42e1600dacf24fbf9142c4e14d201b527c242 e8ace9d861fd443dbe4e72d22e6d8d54d46b752231bbb4953a2a47a8b93d7362 846ad32018c30180c888a39060f99103f9cd6462ff1b371d6f50c97b1b948a18 c3458afd5c8428b77344092ae95ba0367ba6d0d83446b4a32381886ae2cd7de8 5f3be68a068455faea327de2 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 48 /zero put dup 51 /three put dup 53 /five put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 67 /C put dup 68 /D put dup 69 /E put dup 74 /J put dup 77 /M put dup 79 /O put dup 83 /S put dup 85 /U put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 107 /k put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 123 /endash put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 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d121bb7d6944c08af9ac15d95510a36b791d193edeaafe16263630c5c56aa148 a428b8309e55b103227addf7ed9e3fa2c40a0cad691fac43f9b76c57dff756a0 a1b5a9c0ff3fa64ea32e55a59341d032b1b2052d937d80274a832c3d9fd65aee d41d043860ae99e4275b6a6284acd5ee173ea97dad6c4150c47736ed9961f405 46fc6ae708547f8a1f438725d64aca3cb3760d86d544a62dfd5b1cb648f0c33d b1e81dc81634c3bfac93ecdeabce881a2f2b71f4a96704860b0d945e5071949b f1b13035a5ad831a9eb2a3f650d3d83b85045e4097f4ba2a82b024941babf5b8 b61e31615d10fc9d5db0e569e637724ae4719340e39d558c273bb52e3002547a 9a2096c1cb36bd6f57983c3983137f0b54e73541f50daf832443f66120507970 44cbe0607fdf04b90be5c722afdcf77c0282cd435ec99b54fedbd1b135b02cf4 65cd6bd22065abe2fa03a4bdc06d4aa65800b56ffad78bc02bfcd84fabbf8a98 5b4460ace874135d93e1195a7fd0f5e8107a524998c61c6e20237c39bf92edbb 9ae52c2ea5fbd716949b7fca0f2cc9f93f6c062b029bbca246a667f0bfaf6c15 7c0e153d4aa0179dbff67b90f8c7bd7d0c85b074ebc07992415216278cacb3e3 b09a2776905cd56a4558fdeaea323f9005ea3b58cd15761fd6fb477de9685780 5637310c0edee8d65fe0515c405160aaf013b774209a5030f18182092a8b1bf1 c24e80efc41be2f9e92b1eab4fe02406d040dc08e212735b729f57eca4cae929 7504d339219c258428757731582df4c27a8f24622455ab42f23bd0684f697eaa 6b23db5e4fae06d8096d93fdf9b30ddc35f6bc96b7f945e065ae7cbba243babd 0f982bb70241351d07a1eb80b753e4185a57fa5dec692a7c7d79180a20d848c3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e2851973f31a3280c08220536dd2c2de1ffd15fc739091fb7cd5fb9bba2be a5ab0785843300a48f080377b45809107ea6c4e3b0bf4e928ef65d468a19dc1d 34a8be67669f93aa7ca73e2eda716c26be7f59bd96bede57fab460fb9288d0d3 c2fe8705148aee59a4ed0c8b88807058fd33434b44b99b0c53023559fd91fb48 f27902cb06dfe7d2195b36568eb6200c4585c10804b3aba9add5046e370ce410 d49de558233033d079c01e7738e6c96c90bdfaa7549aab3d503536fc16a0be8d 527704627186e9c74c1ac67027ef0c0f20933f92057a41445000cd375450881e 6ad50d543b7bdc29ebf3c3022c7aac385214df9ab1d57f4140b7fa3185a6d28b fd73c67cad22f1536cb1fc19bf9589257a873252a282c6d7de6f0cc5aee1d3a9 ddfa006541aff6253b810e0ba18bcb7152d1937196 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LASY10 %!PS-AdobeFont-1.1: LASY10 1.00 %%CreationDate: 1992 Oct 23 20:19:17 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (LASY10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /LASY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 50 /a50 put readonly def /FontBBox{-19 -192 944 683}readonly def /UniqueID 5011949 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192e3f6620e5383410 9c674a944e5ff85290c767088ede1e6835bf2aaf7a0e947193d98442808fc3dd 148069ab44a71076493a05cbf836aeb3dd5c78829d1482b3c40c2f4cf5fdd0be c3c3c1e08cd5d21db9363551e5ea23a95a928a532e09d2b59879067059a5974e 4912c690ee71858bbf009a75913237a9ab9eb9d8d683ea3fe066fb2ecd3df7b5 c7cb950bdefac7931a3501dd1dd59c10d45f8f91ff07c7c41361e1fafb605c38 0431bdf3b1e44d21d351cf80d8dc6fbb5131fb8ad1a0e9a9a5fdea6432ec1d59 bee32029965fb5c141768d6f2c624b2dae5c9ede58cb4f522099a96749094f15 07e9a6b977ebc86c877b8c4a0758b69dca966be63e606c8efde1f65b295997e5 1205bef471d087f51dc9ff816ef9f6a4a23226f9305feba8da8baa909e515d85 b60901cd8e958e0c94d2a64c1d9510e66d37d18fdf08c5408032c63ae7a667bd 1ca377a9eab6b0bfd434ccc71b779a6cbab2183016bddbc05f171719794bf19d 0118b9e708296d876e7ebd011b0d49e51b56e10bae4b5f2d07b16e0c83df55ab 42cf85da87350d752cd4522682b02f82c49d08a2e0d47d58374443a63831e432 c48f945cc5e42d807ba86cf3e7b3b09f636c17360c5c9bd7717f7e4909e8bb4a 7efb7a580cc9357613467b64fd0161dc026602cc382bdc1779ce8ebc0587f172 654aff1ed908166f3755ccdc64a183e50dc8ff8b9d8ea9ab556615ce390b4660 1749955a3ac5f7c061d6b9948677ca68373ee7c6738abdd0856c90a91d904c91 914f3ba09a3a8b54fa319b1ba9bbd7441b69f0431716a4156816329b7e09b57f 495591d0d9c9049cd0475c7d2b75a8105b99f34816c75f82922b2ff19f835843 adf237dbe7d8fe6c10f1a7886b55baabf55cb33784653da0ac3b49692b348e26 0e2995ae562bf8fce2a4754886dfaac090986bb50eeff294d171eff1b12356d2 e67a7040f2ac7eaa0fde3cce8808b041589918d213923d556f42dbf5c27a062b 4885c544d36fb68419aa660bc55824a647ee56d3a4f4c48ee9b6168c721b54fc e8c202833282c38447a03eebad4a0098fabff640b27298f9e63dbca777a37849 d70d0ae5436463a8d8272bfbab7dee85243e4046f8af3fb02dfbf7fc9fd59837 9b3af8cb2faf3a58d7aed120e3c05f5fc69074b299057f821eab 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523d98f2e44ef37ad46 282d7a587974734c2b1e24d8418fba0841578cb551332e6f777773f1b3155cda 5c13080030cd6402a22174611509221f2b3ac19fb60920218837144746f81792 43cd14528d48c032d279f6d8a87d2eb484f1b977e07c9f343d925c4e29440e4d 7fa894f7b3aed4f35967cf0754f375a178c830bf375ed5712c0598dda2182320 99fd8a45277a5d36139c90411cdf1b382d711f4c8011df724a07333c5421040c 06c6bd0c5bfb17cc2aa404c135fece394c5e77f735945b7dee71367ddb6c0e18 57d9eff272051cf196ea6b066d9ce7babfe387d9119d18a5e39a309f31a783c3 0df3e61b5fbca7d2ec0c81e76c4bd5d8ee71005814bff982fc50a47d68cb3864 afc1374db9f708ca964ab5fbb144195867aeb5679ebc7cd179cf2930a39e1e00 b069c5bb808e8f4d6fa76809a9b3bb2a51a92550895a2a003652db9b243d8723 b9fe67a8d1a395cbc82edb2b90760601d9b1c26ce4b2d388b7d5a8bf869970c6 320d2f8234ccd2571fa9d7433e0417995c96e118c665c769d36d8b03d294abd7 3309d0a515d5fc31b1cf350d9faf137e37dfae10d57a43db97e66885d8c6908d 41488814b6dcdcdbb38918c83faf349fd40dc4e07daf673cf9d7c3fa153bd121 fcb3423df6f5d6b96d935cd21f51a6db90a69d3211bfc35ed53227587c8e1899 eb1fd43dd853f77b5b5ab84efc9b05dd1038041806725f2a1c3099ddcee61546 9c612945cf9f915039ee8aa22d37dac60edab48dc37b33952706d0e6fdc43502 64e4b82ca26b6a98b9a56c829a4eb43f4de9b78c198dcafc06e701f349102838 b104edbc1c87632a08884e8f48cf84ed92b884d3fb4ed825be625905eaccd6b3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 97 /a put dup 98 /b put dup 100 /d put dup 106 /j put dup 109 /m put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 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6cc97fa47ffdd7d897fb6bdd5572e35d34e7e1cb5e7273a4ffd86525323ace4a 84e1297028c2bd5469baa2e75d19360c2c9042139d5e7dd4390a6a3935424711 de21910126d750ae279916ceb71da3591d60dc62db333c5021e2c1cd61ade51e 9395804fa8f124b194547de13ddc8ce157d5d0de6ed3fdd7744b6a550a86e512 cdd4cee97ace14169328308a476280d5bccbb36e0110f1e188d96d94a49eb194 155b324ee22215f101561468f9552bc16c241ec3ae03927f3393a3dd510a4437 b17bd2762e9b7078cb1269444e2692c2e7ead20698f7445c844d4b04e16a7275 a579bfbdd0e7b1f9e4305452d926a1e807aad8e8b34b483388faf7373ecde364 d1052bc91352cb94d1fb383a981d43f1046d7edd841f09cfde2910fa38ab67a7 f8d10a243cf3b2ae31d743b82e44f808b6f44083cc0037927008ed1eaa0d04a4 3fb31cc422c20a108ebe5fe5a9f000896da7e3f269541391775b23bc65f22ea5 9b4cd3d5ca7e3848fc79bc7cb542078a406559338802d1a373a5e37ea2f2510d a5df9e0f0b2c207740fcdeda17bfd8768ab9184f2062a184be5615c8c02da862 e5a57dfffb5e437b09567c86b3c96118519e9cdd7253c66655203aa17f5b1042 87a57a07b205d8a77836d0df8b926dc86fa60279db8b208903b746bf9057998e 5c259b0e1883fd5d320532b0ff76219c73a7778db64020e59ec982b6a3fd5e17 10f6eb0850076700e82700f20561e22d7ae1e219052c5f62e024b9dfb7a54caf 21385619bfa600a84c132f8ac41904ac35f7e46cc715c55fc021b17763536f8d 9911daf9b48d31eec56b8c2609d28a6564ef2d91acc730e7b9e9797bd194f2e0 c8888f67e7030d0ef97c6cee17f24dfc7a400e5a582f70f92b7215f03e67c79a 4826d6e4165e9a32525320ebd525c26bcf930a7810e88050a93849e5d32d1871 6950098aabe16259ee4ee5a5b26c650ecd717ecfcb13169386e7900682400479 15cc778ff2da06b3dd86c15b04b46de660bc7cc703a81c3708edd9b8f9041c3e 61faa0fa66b84772a5036b022658b5ac467c70f3e16cf303f63394a50c4d4908 0bee78b4d78ea386068f4ae8157da25be5b488ea70388f7b58481269377cc105 43d1538e5626adf4cdf7ea3b287c4acd08b37b99aa274fb58abf90e56d8e3bae 372d0de6c81ba39aafb7da93e3a94018ddb0461c300fd6b751838fa18000b42b 6d5913fac664e71f7fb631fa63613420781c6c3f87cb876c4048aeae317bdf3a 3f23291b89551ca04a059b88b6772e216cf3d2e18f4efac228fedf71ae1ad0e0 93305422f89985ec3241e3488184e9872e75a0334e2bc5e28ea17f3dc73d587e c462545afd36e3729174e608747c027e787ddf4ae4a6f6137b6b83e6e8a51d60 1c0c02f72b79f05fe4d55f997c2e1862356b83268be2581f43b28000ca82f92d 1e9083e6c495ceb5e316fe8039cd156ece0a084a069463d7f0a24123abe8e372 b6995bf4e279b54aa53911e04d5880bf80315f7288c554420ad4566e51b12a66 54f1f4e89415c4ac83e8e1b42e514a6b324c2a48b974d50760a5600f33cf5cb6 69bbc75063d8f83c52a2198e2e62a56cbe7412e0597748b8c90466c9fd135b93 88311defff13a66782e82d544fdc860b178011de37f6ebd5ec5c1e99148b0acb ecac33571fac83396f8400fc6673e6a0c1272d267f0f579ef2140adcc258fdbf bf341a5dd0b725d8ec9449efca368ebf79deb8838e388cebd8aa38855e7e59d7 8ad8ff78ebd91acdce37d698d0dba983458c73b599a1d1c73eff7fcd82f103fe bd912f6f10877efa34f3a5c5c6f3080a6ddf1141c02ca771ec60ca113e3fa946 17ddf9e78a00af8e6a551a19a080b017c2a2e941110a8d43e31c5a9ecda79725 090ab669b8020b3a97f9491d9d74bc2dc8b6ec1cf1b4e5d7 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 33 /arrowright put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a 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7d800df8a7780cb2010589d8ab7ddfe444eb76e6edd01b6a6d636f60454e4f6e 0ed03431438fc7faeda34ae05f246e60fde46e9a3efb84bbd13f92f39b89f89d 9b9d5eccf340a5eec0f75cf7593d86c72b0bb27befbc1211ac8b4a4aabdf4f42 97d8d66864ee72a9c8101fdd0f740e1f33a3a65168604326bc419a44afda4fb7 c5e20c8538d717cee1783c158216c0fbe65ccd450043e601a9da4146ea12822c 4da3ca6fab12229d1132e1120b768687173e5475be084227880e6ca5115e1144 dca2214b85aaf74d569386832fb51a1c65b6409301c9b02346cca7bda332ce3f 408ec6cc3ea98952cbec81bcfdf760622f331e4e09a85b6ebadeccab145acbc0 5b9d4c243fe390924d17d5db4883b23d492ef68ca790dba8b931ea217f33d4d4 d14804374d135d606ae6c9b6e688a43444cd925c6cc6f117c853bc594e21b1ec 8229740fa2d45f7b6d5190b859294905b1b323ee9c8e260edff34f9dc588dcdb 3841682e752a7a83fd1f551d2f049191276870016f59b241d5f0f45ca2c2bf3b 62faeb078f9a9e43c97f01f2bee36c3ff099f62901c72aaa01a5503b4f09fb0f 4ff7a1f47f279cd2cf33e107c900a282d3c60e350d6a4f0c2973e0b12f2db02a 8e557027283d34160db52306b2a7f5471e1ac26f3f1825349a975a1ef8fc2bda a1697bc6a4f7ec449f1090750f8d3b83c0d8a7fbcb6490ae1324c9200dce315e 3210874d2bc30affe78be41abf82e2aec711c45848fd472575206a7e53fe1da5 8b02e7b35880569cc9698d3faac0cdb5b9774bc0307e8fc3824627f4f55ea8bf 07e5697ee219b26aa6d8f7dd19d41435f429690624d78dd9337efb51edf585ca e552b1fa26ad5b29b7005363295d4d8d7c5986b25955a32a689b2af19d50cfd1 6bf87aeb693f52a2faaa10c1427ced8758e5da8e68b50d0e4dc1266771ba8077 02201550eaaaa6077b36f02ec66f95a944b48495e932e1dbb5ba7b8c9e92a765 ea459434662da3c9965920a032350b52564118e6c5bbf13ec1ca9cd898d87db7 5cb47a6a1c86e80fc052e40673f4c70833143a05b06a66280fb19f65263ec9f5 974d4b99e87c9a8a3fff88bdf58773f4086b2a231307b8a3c11327d989c08196 d0d4ad71183426e951c06ed5f08a71b363e1413e7b070f027481a3533831f98e 15500b1496bf3c6bb2063d0fd5dfb5e9ba8148b5678a102911dc69b00f5d715a 9a1275bfcca639dd969def42cba49cdb6a64c0f3a684716467c45f121147300c 6a6298dfe23c3aede92757fe3cf42eb015e59a59941bd36d9c1592999e9759a6 f4c9f3d172f2affdfb937cb9a3891e6d42f51b56d0865bf73f81d555c42e9307 58bb46d692d3d5970f0b126ee9e899352455b41102236b154fd075d064a853d2 e9fb0a539052c76d2fb3ef98ec19a9dff4c3ecf7849a9a282bb839ffc6f66f91 c423f5143f264bfc92377403c4e9659af5668681dfd334b0584cc96651385f50 1bcda3393d4841b3a7a27f96025914cea0641d58b0366e902b3d80fc60fdc1da a1fee5c0fab33d0d18766f6e3fb4f47e30ef565eb0cced91e96122966cecf62e 3d7a184e036cbfe1a25201755b380884a55cf891bd8a02ceec237cbb9fc6a497 07411e0b95338c2b4a184b936dcdbbcd3458136095c9c91bcdce0b0fa38251c5 6fff2658596b0712f20c0285eaced22851660ffbfe567ff56d770697e14174f9 dd390a8eb9fbdde260ad7d6b293dce20b1612496d9f7cf50da30e2f2d939830d 50cd4fef788562fc3000909ffc1581324bea570a6233d71e7afff311df8abf38 9ee4297ff3f77081278960b24bf0a1f4267602cc8a7ba499f73001e322082665 1bcb1e4e3906ec41e401aaf341103d78f0c333dea8af6dd142492cb01f006095 752cdb5ebf1eee435ef0356b9995f8e1c5e55cbc794a29185366ab872a1d366a 689347dc52eb1376edb6705826f5361273e86af3e960c91e6fb145fc4713eb2a 059589186977b47b7f64255703ec11d9f7fabddb6c12f92a62115e9002b58629 3d3122942b25e8d73839b441d3bc12bf28ff570d80b1424a221e77b4d031849f 75a13d22b7071ae9e960a17c001b5e21bcf6ca2a24dbabb86874b61cad52d234 e263e8d5fb594c120f7d1f7ea01260c9a48cec3c8ca8db5491101b7f666d5720 4bcd0f0c69be89b33d41a97280c751cd05c6f19867b3d46aa6c180a7957a926a e2d548dc780abcbac62c78153636246a30e954c31c79a28af39d825c4db6257f 78fa3b2abe8dd0a1dfc3102dee07fa7e2fe87259a723ba6ca9247f09aeedb550 cabbfb1d9e8f260ed2d49e5ae0ddc5bdc45fad07a59d452c339439e8e1c9dc7f 6ccb861aff0e73e0196b02a584c1a920d8581279d9eec00127a86a73effacb79 b2476aa64c311b089e4d8132497daf9035bf860ef97d0885daef1ef06a3d0889 9419d6e5420be36ba436059d470be519 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 69 /E put dup 76 /L put dup 78 /N put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 113 /q put dup 115 /s put dup 116 /t put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 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3233fb27802b1ca4094a826cc4e6eb3df5824b5c07c564f491ec0b1098e24d6f 7f8a4c6ed042e79130fec9610bb266f8893e81b25e6e2bd7d3bc946991e47944 9a83ebb4453c8c047f71f79781d96572ce37edeb9a586738b85cdc5eeca97a3f edd98561f09786f05cf89509700a2dbcc73e8dace10bc67eef3cf5bac56f5016 e1cf0901f2c761aa49a7c9ce84207433ff396f3c733faed450878604ed4e0b2c 22376aa0a3bf734a37ec7b6620cf13e986588413f8c4f94b1f0fe0851734e8a3 e663436a64070dbc1d050b7b24b660c81d9ce6e7e3de8f60415f251d7ed73cc6 4e6146f7bd338147158ed73738d3183e9fc6546244fe6ddb7aa0ddd6484804c7 42aa026842febd7e3fe8c87544b7d6791144d1bf8a059e1ea1a2b21959601fb6 534c53e4d63fa4a3de0a4827a99136ed899d0bdac87ba8cec3228e8649aed5f7 3af219da67836a6b96e4685e0c26796b0202e4402e166b558a74bfb611b64806 f9caa841c0d049867c2caf5bd54d509660010803a462a09ebede5a2df629bd4d 54b3c6b10be7469e6b7f3b032d38ae7458fc12453d328019edd8208ff5853e92 fcbd01745b58c11900b105ff746cf48fad6d26b67f420b5af7386055a1fc06a4 ac7b67a1615c2975a23ab612c576470f881ae593b6e4bad3d3ed25986d09f0a0 57b5f72f2d1ced45ad90655d97e527080cad2d9089663565b6a80bea948fbe64 2cef76a2ce31429e70169cd5aa59b0056e38c89ef775e1c7e3412cd1d701e104 f6a675bc00b2d288f3f060af457ac405a10de2b332ab279088049e60579d7aaf 7d8de4f3a4eda70a4965ccdd9112410ce3325ce06d935563a7ddfc8b2ed82bf3 2d04fb7a01ce56f110370aeb7cdde1862151a529895cfb688b9f3215fafa86d3 69aeb6c171671f7e57811d91e455b4ec7ed22fc6f38d0c12fda2c0fad8c90eec 7641240549ad78011054aa145b36d002cabefae053efa1d531b21be3bec4dce1 c093b2ca13a84f8d5c0b07e3a3a156ebfa7828f93f5fc0b5582f0aa21d6299ae dc71e3bf127ea7256bf95b10649036d5fda7c3daee136e6536b6f3baf430eec7 8818449bce124633d92954b2b13e81e71afab789 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 80 /summationtext put dup 81 /producttext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 98 /hatwide put dup 100 /hatwidest put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 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2cb64444e62cd71d739ff93287fad249cd5d1c275d59a42a8079e6dc011a51bd 3b3fa20c24d44cb7fcccccedc05ff269c05a8cc8de86642f6b4eb5d7f032cc2d e7357ad55fb3a51d36d5b2cf64784ed8e0ae35f9210f0e726761808d2311b70b 32913ed82a5481d002b852089c4212b67cdc913363ebd371854329da54da9f80 98d0b6e75e8b6bcb14df449e7aaf80bc59b5ec205afd6b39df033edb4c851abb 657ba203eb0028f23ce1f88135cfd74571c49a13acb8704239200aee23b464d3 e3ab8b315d0264e93977acdd06bdc1a4b6de8c2b2fd3f45cd1a5e96389b0de97 2d87a53bfeff0a2a9c7baab7ae2e9407b24f8f9df1316dbdac093f238ae65ef2 9fea6793577cdbf6e33faee3c4ee87c0b3ccf4a06b4258dedcbaf2bad089d7e3 3bf234a1a3315b59a69a6a4ec0abe02ba803ec168938c49b97a55670cfead944 e005a6a78f40281930bd0289cd2686fb47ff3f8d6a9477aaf187fc5adfb54e1f 3d28be2a6ccb6811b786d2b821f0d48820a738cfb709bff18ae06b2368872583 c1c2baed9036c7b81049dddcf61a3782f8a403bdff112012b2def5e5942fd219 5345962d94634dad49ede56123d72af734b15008096c2e7dce3f6a261a28e38d 5ed183664bc793232969c96341890162c3987317d4e442eff402165135c61a7b ad02ace0a4ae51348de214941416f57c6bc55b4ccdabb4982d6ba86a39b1d0cf 24cb1f8e416efe4b4eb9b8261ba1cdeb35398f503d478dba3f2769a326f2c587 4b8880c7e6d23763afb9454128f6cc4dd00cb7fd30bf41ba477bbb06d5d22fb3 0f1ba0846c219f0dfc328f6a673e4c961fb8457fb6ce973c69b1f21fd343856d a0f5d2390096f2f30406ae4b0e9780b781bfa65cc2d1ec1dad33dc3e2bae06e0 cfebfa2437883a1d98bf5337cee825e6eb5a8467bbc78b89a10ff2fcfa7c7bbd 0bd61371b05d2665f8cd77ed6e8854a6fc0b415efa53f447d42be14b351a1c6f 991d4318db6c56af498a40327c1d21abe9fba81449cae419b30ab23238109dd1 691ac0cbb08983b8f51ef9ff7334dab727a21b22c2b10fea939abed0afa571b2 14ca1f2b79e8cf743cefb29681c0f41419e12302c763e7e0f6a1aa23f01d2760 f262368bce62381c93033c16e0922b1d997a9c1c0bd3da0c6361509ec6368b1b 9a3489b6611029a5ea96e39920308a8b04dedfdf7798f8a52f9f5d8ad6fdba30 3c5d7879f4a742839adc7a01ee6a44ebbd71ffedbc2edfc93914ce 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 28 /lessmuch put dup 29 /greatermuch put dup 33 /arrowright put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 68 /D put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c43002591893a571bbe4dd05506a93c40f517d06cb123975ca3614a4e4dad 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1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put dup 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 99 /c put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 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921b1b05d80968561ad15c8f55cc4298a1f017ddc2144f62435b7f50b25a2243 0b8fcbbddee6bc070f922e9c6dee169128f7411e8ed99ca41b07688d8f88b7b0 4b887b2653139cbf75fac2abf0c0570f744c5b29d96a57628ef190f069cf6d0a ce737bebfb73d69cf5e97f87c91eb49d6652a2d6486483855ebfcae5a737fc49 feb7cc1204c23384b4189c8957947277661a35f0a800d00242194d52b563dfa0 3a96f90376c77bcc5c4f6dd175b50a0073e54046408cf6d3b04c1c040300262b 4d1d4dd9c1113c019d417c9674ffca110797b709a3e72a2a1cced042e919b4fc b3f9ff998f5a9638232a7de9ac385791a60f4d7ab4f8fd8141ea988eced34103 26fa22e04cd170b1d5447bbf8ed21cd87e1f51ec7da59d617c709b4df3061e3d 29cd4414d026aa6777136d8695ae936ace9f130fff604f144c685c3edb8405f6 1d94c3a89ff509c66e4015d23c9134bb67a0e0c6d3ba2eab38411ec2383270e8 fcba8301aa8bc9c7349235e15f7f336d784ab09e750c2754fd41b7d0333c9286 5fe93b29589004fa2db78f648602ade2b97e967cb6c09a2e1ae8357315e7c333 fdc6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put dup 90 /Z put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueID 5087392 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d78041490e364babe4b85935b8c9c7758c2dbe253653c 892b1fc2c6a01103e0b8553f847bb38d8e4fcd563ebe51cb7d5f0877af29249d b61636618fb31eeb6cbb4ea4db687fd77ed1574da8c9f9d33b592ec0e38d798c 498a205cab252f7e2f1ddb82a38f331f917b8452af11b2b93e34c1ef55ee005c e8418dbcd0fb9d4d3fa8cb388ec91f16c8864913ad3fc8960d3c424650bdd12c 4db4049367faae97c660f00021f712e9eb6366b7ce74255ff62b72396ca43287 7c77fecdc53883427c90c1c3ff7bd46e472cea9bd72eef0e1be36abb3a50a7bf 6f5d460fa2fc81466014df9ee1e15365642c2de78706dfa740e035b4f28f290d 79b8ba16e5bca13fd9c3eb7eb54006ac2c1cf0bf363b3b69e923797a95b76515 073892c75cf733da7c07da8ed1a8d1ded902f784764c6df6fcd0fd28083d88c8 4c41aeaa6c2c2c1bb10219f4feaab75ee904f4314fc0b9de5e96054f2472ad86 42140315385400686cb07a0585d922ae4b1b25ae722edc6b4afe053560fc9ac9 20a1d2fb8d0921c52c9468d34dba9bed42e3a8308742d36186ed0a3b43f690a4 dca6bb2af8bd698fb303fd68df53edc5e01912cf007dd31ca7481ce844be1258 7002d4aafb204a8075fc6df86f22249d61dd840e7ef87362d72e35f4e8ece044 95ae41ee5c02d6aafaad37141935867a8770fbd9e9ea71e77d3c935c53100566 039eb96ba3821b284b42a0e2ac4ad3181ff029ce1394c31e7694b2e7f47d34c4 190a2ec05ecb43774baeceb345230f68a967b91883e3b184d030c1183d707d1f 2cda85d6de979350243ede31995d77233c2ee1e2b00c53ee0c0fea0c527c706e 114259f991939e5a79d0eb4ef82df7fb0f7434be3b242b840f1c0dee6aa1a98c 20f395e9b93d121bb1e0e420aaaf34ecc31289bea097a288ffbc9dc85f95b752 f4561d817fa7ad9921e00b0ec4cb9ef1385d0cedcd674a913810fb5b58d15cc7 10ed4ba977cbaa4841834df2e86e19c70509d5d4b9e15fdf5a957a83e685dfaf 1199fc34abc5a53409cec391b5fdbd5de19fb06c034c37f077cb5660981ef88b b609e077e8b211db895d679da4b83592a40891484af62e71f1d2ee144f7cee2c 19219bec3a8255962c4bce48f44d0593e4bbbbee9b657233c5563e642cb0fe11 fea856e880e7ac63f383c0d95f080fcc861fcffba5cfc0a9a9048f634f8765f1 f7beb3dba1a8fcd4d6983f7f3dde8e8c1e759206f5e9e51eab9da1e426ec79f0 57c5e3ad365e0dd97e4cc97d7ed4c6a8e6ee2ab2ed4f1bd3cdaad50c4d0059cf a4fd86f3ce0df2d76f5a661718d562b0b35ab98b0f9f53fcf1a964a01fde18da 91316f0999ef643d870ba5430894e2fea44951ab239be692ad2650505de7310a ac0148f924cf2660dfd164b8271d608d0298cf071165792e76e8d7c9b0a68439 a95e5c88d12dca67a82e4fb614e9d7d98757cf22c72e4919b8f622f3aaa3a014 c4348a606538904bc38114756b9da5de2dd4efe778c36a2d8a30a7cc5dd0f4dd c451f3fee6311692f92706abeac74f0a756c0e543a222afe2e3c581bef40c973 7dec835503ccf9bd6f8fb6f9b2a37d437e6ab83c14e81cd4b659c3a8cb4355e1 b15512b1b0694f0631d17a9db4739804a0eabbfda151b5a6fcacfa76abafa571 879232512e1fb2d475ae1b41d079a08696b2f0eadbb4baaff2d525c746f4d196 c5edc1e024b0201c72063e0d7d512b0324c45fa32611f650a9ff966e4ee4a8d5 0516b007f75b4e2c9f5154e60b1e7b1a9f7da867317951a34d879055fa1e0670 abd5ac33f2191e7d2d1ea96bcee17ced07cd767167fc1af207fe 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 19 /acute put dup 44 /comma put dup 46 /period put dup 49 /one put dup 52 /four put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 123 /endash put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 87d31dc36e555668d9578b338402f8c259f6813b0b71e6cbd95e19c20ced8495 2559e47577e612a4d94de3c1b4c6c41a6a3fa9e2313457242de74c7e4c0d722b 3e224d18baa726369542682e9459b951b2ac638494880c42be4e2175a3c067e5 945bfc1a05d3de8c3e8ab97f80ab6000e1f78fc258b85d3c84b038d7d0f5be85 0d43fe03e26cdfbb41c36d14cb552e8447ca678efea1d275e85503123a2263b1 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 5 /Pi put dup 6 /Sigma put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 22 /macron put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 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5f5674631eccd2dab9cc265a4afc8b620753b56d606557b1c0714f04 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 73 /I put dup 76 /L put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 123 /endash put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea 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d8c6a9ba90080cbfe47fa898522025055d0c2387 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (ABeffct-mp.dvi) @start /Fa 134[ 55 3[ 58 41 41 43 1[ 58 52 1[ 87 1[ 55 32 29 58 2[ 48 1[ 46 1[ 51 32[ 81 17[ 29 35 45[{ } 18 90.9091 /CMBX10 rf /Fb 140[ 37 38 4[ 74 23 2[ 28 3[ 42 46 2[ 46 27[ 62 23[ 33 45[{ } 10 90.9091 /CMTI10 rf /Fc 132[ 45 1[ 48 2[ 48 51 35 36 36 1[ 51 45 51 76 1[ 48 1[ 25 51 1[ 28 40 1[ 40 1[ 45 11[ 68 1[ 51 3[ 71 1[ 83 2[ 47 4[ 62 69 66 8[ 25 45 45 45 1[ 45 1[ 45 2[ 45 3[ 25 44[{ } 34 90.9091 /CMR10 rf /Fd 207[ 18 47[ 48{ } 2 49.8132 /CMSY6 rf /Fe 205[ 74 50[{ } 1 99.6264 /LASY10 rf /Ff 204[ 30 30 30 49[{ } 3 49.8132 /CMR6 rf /Fg 146[ 54 2[ 25 5[ 32 1[ 27 34 97[{ } 5 49.8132 /CMMI6 rf /Fh 143[ 59 5[ 20 51[ 0 3[ 47 71 19 12[ 35 1[ 71 25[ 55 55 2[ 35 55 20 55{ } 14 66.4176 /CMSY8 rf /Fi 133[ 33 35 40 3[ 25 33 1[ 32 2[ 43 62 21 37 29 24 4[ 36 31 30 37 6[ 48 11[ 56 1[ 48 6[ 52 7[ 35 1[ 20 24[ 33 44 46 4[ 40 36 41 31 35 42 41 41 1[ 33 4[ 36 40 45 11[{ } 37 66.4176 /CMMI8 rf /Fj 155[ 120 1[ 46 7[ 46 1[ 120 6[ 78 88 60[ 61 61 50 50 16[{ } 10 83.022 /CMEX10 rf /Fk 141[ 83 1[ 83 1[ 50 2[ 50 28 39 39 50 50 9[ 66 66 22[ 77 13[ 0 3[ 66 100 9[ 77 5[ 100 3[ 100 100 1[ 77 1[ 77 2[ 77 77 11[ 77 77 77 3[ 77 28 77{ } 29 99.6264 /CMSY10 rf /Fl 133[ 45 48 55 70 47 56 35 46 44 43 49 47 58 85 29 51 40 33 56 47 48 45 51 42 41 51 6[ 67 57 81 92 57 1[ 57 60 74 77 63 75 78 94 66 83 54 1[ 81 77 63 72 81 70 74 73 51 1[ 76 49 76 27 27 18[ 64 4[ 46 61 63 61 2[ 42 55 50 55 43 48 59 57 2[ 45 48 43 1[ 43 51 55 62 11[{ } 76 99.6264 /CMMI12 rf /Fm 129[ 35 26[ 31 5[ 20 1[ 20 29[ 55 1[ 20 4[ 35 1[ 35 35 35 35 35 4[ 55 1[ 27 27 40[{ } 15 66.4176 /CMR8 rf /Fn 165[ 77 7[ 87 82[{ } 2 99.6264 /CMMIB10 rf /Fo 132[ 50 1[ 47 45 65 45 52 32 40 41 1[ 50 50 55 80 25 45 30 30 50 45 30 45 50 45 45 50 11[ 72 70 55 71 75 66 1[ 72 87 61 75 51 38 72 1[ 64 66 74 70 1[ 72 6[ 30 5[ 50 2[ 50 2[ 30 1[ 30 24[ 50 6[ 55 60 11[{ } 51 99.6264 /CMTI12 rf /Fp 128[ 49 49 2[ 49 43 51 51 70 51 54 38 38 38 51 54 49 54 81 27 51 30 27 54 49 30 43 54 43 54 49 2[ 49 27 1[ 27 1[ 73 73 100 73 1[ 70 54 72 1[ 66 76 73 89 61 76 1[ 35 73 77 64 66 75 70 69 73 3[ 76 1[ 27 27 49 49 49 49 49 49 49 49 49 49 1[ 27 33 27 76 1[ 38 38 17[ 49 7[ 81 54 54 57 4[ 70 73 3[ 81 61{ } 82 99.6264 /CMR12 rf /Fq 134[ 59 59 1[ 59 62 44 44 46 1[ 62 56 62 93 31 59 1[ 31 62 56 34 51 62 50 62 54 12[ 78 62 84 1[ 77 3[ 67 2[ 42 2[ 70 2[ 81 1[ 85 6[ 31 56 1[ 56 56 56 56 56 56 56 56 1[ 31 33[ 62 65 11[{ } 44 99.6264 /CMBX12 rf /Fr 138[ 65 46 46 46 2[ 59 65 98 3[ 33 65 2[ 52 65 2[ 59 12[ 85 10[ 42 88 25[ 33 46[{ } 16 119.552 /CMR12 rf /Fs 132[ 81 1[ 85 2[ 85 1[ 63 64 66 2[ 81 90 134 45 85 1[ 45 90 81 49 74 90 72 90 78 13[ 90 2[ 110 2[ 153 6[ 101 106 1[ 117 115 122 53[ 94 11[{ } 29 143.462 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop Fs 466 708 a(Aharono) l(v{Bohm) p 1707 708 a(E\013ect) p 2169 708 a(in) p 2358 708 a(Scattering) 323 844 y(b) l(y) p 547 844 a(a) p 679 844 a(Chain) p 1152 844 a(of) p 1336 844 a(P) l(oin) l(t{lik) l(e) p 2094 844 a(Magnetic) p 2802 844 a(Fields) p Fr 918 1086 a(Hiroshi) p 1325 1086 a(T.) p 1481 1086 a(Ito) p 1666 1086 a(and) p 1894 1086 a(Hideo) p 2229 1086 a(T) p 2304 1086 a(am) m(ura) p Fq 146 1395 a(Abstract) p Fp 672 1395 a(According) p 1139 1395 a(to) p 1262 1395 a(the) p 1434 1395 a(Aharono) m(v{Bohm) p 2187 1395 a(e\013ect,) p 2476 1395 a(magnetic) p 2897 1395 a(p) 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a(for) p 149 407 a(the) p 317 407 a(magnetic) p 735 407 a(Sc) m(hr\177) p 921 407 a(odinger) p 1269 407 a(op) s(erator) p 1662 407 a(with) p 1884 407 a(v) m(ector) p 2177 407 a(p) s(oten) m(tial) p Fl 2589 407 a(A) p Fp(\() p Fl(x) p Fp(\)) p 2821 407 a(=) p 2925 407 a(\() p Fl(a) p Fm 3014 422 a(1) p Fp 3053 407 a(\() p Fl(x) p Fp(\)) p Fl(;) p 3228 407 a(a) p Fm 3279 422 a(2) p Fp 3319 407 a(\() p Fl(x) p Fp(\)\)) p 3516 407 a(:) p Fn 0 527 a(R) p Fm 87 485 a(2) p Fk 154 527 a(!) p Fn 282 527 a(R) p Fm 369 485 a(2) p Fp 409 527 a(.) p 479 527 a(The) p 679 527 a(magnetic) p 1097 527 a(\014eld) p Fl 1308 527 a(b) p Fp(\() p Fl(x) p Fp(\)) p 1513 527 a(is) p 1612 527 a(de\014ned) p 1948 527 a(as) p Fl 1238 747 a(b) p Fp 1307 747 a(=) p Fk 1411 747 a(r) p 1516 747 a(\002) p Fl 1616 747 a(A) p Fp 1717 747 a(=) p Fl 1820 747 a(@) p Fm 1871 762 a(1) p Fl 1911 747 a(a) p Fm 1962 762 a(2) p Fk 2024 747 a(\000) p Fl 2123 747 a(@) p Fm 2174 762 a(2) p Fl 2214 747 a(a) p Fm 2265 762 a(1) p Fp 0 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a(de\014ned) p 846 5209 a(b) m(y) p 981 5209 a(\(1.2\).) p 1252 5209 a(The) p 1453 5209 a(\014rst) p 1654 5209 a(main) p 1898 5209 a(theorem) p 2277 5209 a(is) p 2375 5209 a(form) m(ulated) p 2869 5209 a(as) p 2988 5209 a(follo) m(ws.) 1747 5753 y(3) p 90 rotate dyy eop %%Page: 4 4 4 3 bop Fq 0 407 a(Theorem) p 475 407 a(1.1) p Fo 667 407 a(L) p 723 407 a(et) p 829 407 a(the) p 985 407 a(notation) p 1367 407 a(b) p 1407 407 a(e) p 1480 407 a(as) p 1598 407 a(ab) p 1688 407 a(ove.) p 1900 407 a(Assume) p Fp 2258 407 a(\(1) p Fl(:) p Fp(3\)) p Fo 2487 407 a(and) p Fp 2670 407 a(\(1) p Fl(:) p Fp(4\)) p Fo(.) p 2943 407 a(If) p Fl 3039 407 a(!) p Fk 3131 407 a(6) p Fp(=) 3252 381 y(^) p Fl 3235 407 a(d) p Fi 3286 422 a(j) t(k) p Fo 3389 407 a(and) p Fp 8 538 a(~) p Fl 0 538 a(!) p Fk 92 538 a(6) p Fp(=) 213 512 y(^) p Fl 196 538 a(d) p Fi 247 553 a(j) t(k) p Fo 351 538 a(for) p 501 538 a(al) p 581 538 a(l) p 636 538 a(p) p 681 538 a(airs) p Fp 871 538 a(\() p Fl(j;) p 993 538 a(k) p Fp 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1405 5504 a(:) p Fk 1460 5504 a(j) p Fl(x) p Fk 1565 5504 a(\000) p Fl 1665 5504 a(d) p Fi 1716 5519 a(j) p Fk 1752 5504 a(j) p Fl 1807 5504 a(<) p 1911 5504 a(C) p 1988 5504 a(d) p Fi 2039 5463 a(\033) p Fk 2086 5504 a(g) p Fl(;) p Fp 2277 5504 a(1) p Fk 2353 5504 a(\024) p Fl 2458 5504 a(j) p Fk 2532 5504 a(\024) p Fl 2637 5504 a(N) p 2720 5504 a(;) p Fp 3294 5504 a(\(1.12\)) 1747 5753 y(5) p 90 rotate dyy eop %%Page: 6 6 6 5 bop Fp 0 407 a(with) p Fl 222 407 a(C) p 327 407 a(>) p Fp 430 407 a(1.) p 550 407 a(The) p 750 407 a(pro) s(of) p 1005 407 a(of) p 1116 407 a(the) p 1284 407 a(main) p 1528 407 a(theorems) p 1946 407 a(is) p 2044 407 a(based) p 2315 407 a(on) p 2451 407 a(the) p 2619 407 a(resolv) m(en) m(t) p 3028 407 a(estimate) p Fk 1023 610 a(k) p Fl(s) p Fi 1119 625 a(j) p Fl 1156 610 a(R) p Fp 1231 610 a(\() p Fl(E) p Fk 1369 610 a(\006) p Fl 1468 610 a(i) p Fp(0;) p Fl 1594 610 a(H) p Fi 1675 625 a(d) p Fp 1715 610 a(\)) p Fl(s) p Fi 1799 625 a(k) p Fk 1842 610 a(k) p Fp 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eop %%Page: 7 7 7 6 bop Fp 0 407 a(can) p 179 407 a(b) s(e) p 312 407 a(de\014ned) p 648 407 a(as) p 767 407 a(a) p 849 407 a(unitary) p 1193 407 a(op) s(erator.) p 1624 407 a(Let) p Fl 788 582 a(') p Fm 852 597 a(0) p Fp 891 582 a(\() p Fl(x) p Fp(;) p Fl 1028 582 a(\025;) p 1129 582 a(!) p Fp 1194 582 a(\)) p 1259 582 a(=) p 1362 582 a(exp) q(\() p Fl(i) p Fk 1582 493 a(p) p 1666 493 57 4 v Fl 1666 582 a(\025) p 1739 582 a(x) p Fk 1817 582 a(\001) p Fl 1866 582 a(!) p Fp 1931 582 a(\)) p Fl(;) p 2110 582 a(\025) p 2195 582 a(>) p Fp 2298 582 a(0) p Fl(;) p 2437 582 a(!) p Fk 2529 582 a(2) p Fl 2623 582 a(S) p Fm 2689 541 a(1) p Fl 2728 582 a(;) p Fp 0 757 a(b) s(e) p 130 757 a(the) p 295 757 a(generalized) p 797 757 a(eigenfunction) p 1393 757 a(of) p 1501 757 a(the) p 1667 757 a(free) p 1851 757 a(Hamiltonian) p Fl 2409 757 a(H) p Fm 2490 772 a(0) p Fp 2557 757 a(=) p Fk 2660 757 a(\000) p Fp(\001,) p 2877 757 a(where) p 3156 757 a(the) p 3321 757 a(nota-) 0 878 y(tion) p Fk 201 878 a(\001) p Fp 261 878 a(denotes) p 614 878 a(the) p 782 878 a(scalar) p 1058 878 a(pro) s(duct) p 1424 878 a(in) p Fn 1538 878 a(R) p Fm 1625 835 a(2) p Fp 1665 878 a(.) p 1735 878 a(The) p 1936 878 a(unitary) p 2280 878 a(mapping) 183 1077 y(\() p Fl(F) p 298 1077 a(u) p Fp(\)) p 407 1077 a(\() p Fl(\025;) p 546 1077 a(!) p Fp 611 1077 a(\)) p 676 1077 a(=) p 780 1077 a(2) p Fh 829 1036 a(\000) p Fm(1) p Fi(=) p Fm(2) p Fp 993 1077 a(\(2) p Fl(\031) p Fp 1139 1077 a(\)) p Fh 1177 1036 a(\000) p Fm(1) p Fj 1288 960 a(Z) p Fp 1403 1077 a(\026) p Fl 1387 1077 a(') p Fm 1451 1092 a(0) p Fp 1491 1077 a(\() p Fl(x) p Fp(;) p Fl 1628 1077 a(\025;) p 1729 1077 a(!) p Fp 1794 1077 a(\)) p Fl(u) p Fp(\() p Fl(x) p Fp(\)) p Fl 2036 1077 a(dx) p Fp 2168 1077 a(:) p Fl 2223 1077 a(L) p Fm 2289 1036 a(2) p Fk 2356 1077 a(!) p Fl 2483 1077 a(L) p Fm 2549 1036 a(2) p Fp 2589 1077 a(\(\(0) p Fl(;) p Fk 2758 1077 a(1) p Fp(\)) p Fk 2917 1077 a(\002) p Fl 3017 1077 a(S) p Fm 3083 1036 a(1) p Fp 3122 1077 a(\)) p 3343 1077 a(\(2.1\)) 0 1282 y(decomp) s(oses) p Fl 529 1282 a(S) p Fp 595 1282 a(\() p Fl(H) p Fi 714 1297 a(\013) p Fl 764 1282 a(;) p 808 1282 a(H) p Fm 889 1297 a(0) p Fp 927 1282 a(\)) p 998 1282 a(in) m(to) p 1196 1282 a(the) p 1364 1282 a(direct) p 1640 1282 a(in) m(tegral) p Fl 629 1490 a(S) p Fp 695 1490 a(\() p Fl(H) p Fi 814 1505 a(\013) p Fl 863 1490 a(;) p 907 1490 a(H) p Fm 988 1505 a(0) p Fp 1027 1490 a(\)) p Fk 1093 1490 a(') p Fl 1198 1490 a(F) p 1275 1490 a(S) p Fp 1341 1490 a(\() p Fl(H) p Fi 1460 1505 a(\013) p Fl 1509 1490 a(;) p 1553 1490 a(H) p Fm 1634 1505 a(0) p Fp 1673 1490 a(\)) p Fl(F) p Fh 1788 1449 a(\003) p Fp 1854 1490 a(=) p Fj 1958 1373 a(Z) p Fh 2041 1399 a(1) p Fm 2004 1561 a(0) p Fk 2132 1490 a(\010) p Fl 2226 1490 a(S) p Fp 2292 1490 a(\() p Fl(\025) p Fp(;) p Fl 2431 1490 a(H) p Fi 2512 1505 a(\013) p Fl 2561 1490 a(;) p 2605 1490 a(H) p Fm 2686 1505 a(0) p Fp 2725 1490 a(\)) p Fl 2780 1490 a(d\025;) p Fp 0 1703 a(where) p 288 1703 a(the) p 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p 144 5167 a(ha) m(v) m(e) 547 5287 y(exp) q(\() p Fk(\000) p Fl(i\013) q(\015) p Fp 963 5287 a(\() p Fl(x) p Fp(;) p Fl 1100 5287 a(!) p Fp 1165 5287 a(\)\)) p Fl(H) p Fi 1322 5302 a(\013) p Fp 1387 5287 a(exp) q(\() p Fl(i\013) q(\015) p Fp 1726 5287 a(\() p Fl(x) p Fp(;) p Fl 1863 5287 a(!) p Fp 1928 5287 a(\)\)) p 2031 5287 a(=) p Fl 2135 5287 a(H) p Fp 2224 5287 a(\() p Fl(A) p Fi 2335 5302 a(\013) p Fk 2406 5287 a(\000) p Fl 2506 5287 a(\013) p Fk 2569 5287 a(r) p Fl(\015) p Fp 2708 5287 a(\)) p 2773 5287 a(=) p Fl 2876 5287 a(H) p Fm 2957 5302 a(0) p Fp 3343 5287 a(\(2.6\)) 0 5442 y(on) p 135 5442 a(\006\() p Fl(R) q(;) p 362 5442 a(!) t(;) p 471 5442 a(\016) p Fp 518 5442 a(\).) p 626 5442 a(The) p 827 5442 a(next) p 1046 5442 a(lemma) p 1360 5442 a(is) p 1458 5442 a(w) m(ell) p 1656 5442 a(kno) m(wn) p 1965 5442 a(\([10,) p 2187 5442 a(Theorem) p 2599 5442 a(IX.31]\).) 1747 5753 y(7) p 90 rotate dyy eop %%Page: 8 8 8 7 bop Fq 0 407 a(Lemma) p 397 407 a(2.1) p Fo 589 407 a(L) p 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a(Lemma) p 484 2101 a(2.1,) p 668 2101 a(and) p 858 2101 a(hence) p 1129 2101 a(w) m(e) p 1272 2101 a(ha) m(v) m(e) p 1497 2101 a(the) p 1665 2101 a(decomp) s(osition) p Fl 709 2305 a(W) p Fh 801 2320 a(\000) p Fp 860 2305 a(\() p Fl(H) p Fi 979 2320 a(\013) p Fl 1028 2305 a(;) p 1072 2305 a(H) p Fm 1153 2320 a(0) p Fp 1192 2305 a(\)) p Fl(\014) p Fm 1291 2264 a(2) p Fp 1358 2305 a(=) p Fl 1461 2305 a(W) p Fh 1553 2320 a(\000) p Fp 1613 2305 a(\() p Fl(H) p Fi 1732 2320 a(\013) p Fl 1781 2305 a(;) p 1825 2305 a(H) p Fm 1906 2320 a(0) p Fp 1945 2305 a(;) p Fl 1989 2305 a(J) p Fm 2043 2320 a(+) p Fp 2101 2305 a(\)) p Fl(W) p Fh 2231 2320 a(\000) p Fp 2291 2305 a(\() p Fl(H) p Fm 2410 2320 a(0) p Fl 2449 2305 a(;) p 2493 2305 a(H) p Fm 2574 2320 a(0) p Fp 2613 2305 a(;) p Fl 2657 2305 a(J) p Fh 2711 2320 a(\000) p Fp 2769 2305 a(\)) p Fl(;) p Fp 3343 2305 a(\(2.7\)) 0 2509 y(where) p Fl 294 2509 a(J) p Fh 348 2524 a(\006) p Fp 454 2509 a(=) p Fl 578 2509 a(e) p Fm 623 2524 a(0) p Fp 679 2509 a(exp) q(\() p Fk(\006) p Fl 944 2509 a(i\013) q(\015) p Fp 1096 2509 a(\() p Fl(x) p Fp(;) p Fl 1233 2509 a(!) p Fp 1298 2509 a(\)\)) p Fl(\014) p Fp 1435 2509 a(.) p 1539 2509 a(The) p 1751 2509 a(existence) p 2178 2509 a(of) p Fl 2301 2509 a(W) p Fh 2393 2524 a(\000) p Fp 2452 2509 a(\() p Fl(H) p Fm 2571 2524 a(0) p Fl 2611 2509 a(;) p 2655 2509 a(H) p Fm 2736 2524 a(0) p Fp 2775 2509 a(;) p Fl 2819 2509 a(J) p Fh 2873 2524 a(\000) p Fp 2931 2509 a(\)) p 3013 2509 a(follo) m(ws) p 3345 2509 a(from) 0 2629 y(Lemma) p 355 2629 a(2.1,) p 547 2629 a(while) p 808 2629 a(the) p 983 2629 a(existence) p 1405 2629 a(of) p Fl 1522 2629 a(W) p Fh 1614 2644 a(\000) p Fp 1673 2629 a(\() p Fl(H) p Fi 1792 2644 a(\013) p Fl 1842 2629 a(;) p 1886 2629 a(H) p Fm 1967 2644 a(0) p Fp 2006 2629 a(;) p Fl 2050 2629 a(J) p Fm 2104 2644 a(+) p Fp 2162 2629 a(\)) p 2239 2629 a(is) p 2344 2629 a(v) m(eri\014ed) p 2692 2629 a(b) m(y) p 2834 2629 a(\(2.6\).) p 3124 2629 a(The) p 3331 2629 a(same) 0 2750 y(argumen) m(t) p 436 2750 a(applies) p 762 2750 a(to) p 881 2750 a(\014nal) p 1098 2750 a(direction) p 1512 2750 a(~) p Fl 1504 2750 a(!) p Fp 1569 2750 a(.) p 1639 2750 a(W) p 1731 2750 a(e) p 1807 2750 a(de\014ne) 1267 2927 y(~) p Fl 1253 2954 a(\014) p Fp 1314 2954 a(\() p Fl(\030) p Fp 1400 2954 a(\)) p 1465 2954 a(=) p Fl 1568 2954 a(\037) p Fp(\() p Fk(j) p Fl(\030) p Fk 1764 2954 a(\000) 1864 2865 y(p) p 1947 2865 79 4 v Fl 1947 2954 a(E) p Fp 2033 2954 a(~) p Fl 2025 2954 a(!) p Fk 2089 2954 a(j) p Fl(=\016) p Fm 2213 2912 a(2) p Fp 2252 2954 a(\)) 0 3157 y(and) p 190 3157 a(w) m(e) p 333 3157 a(tak) m(e) p 545 3157 a(a) p 626 3157 a(function) p 1012 3157 a(~) p Fl 1008 3157 a(e) p Fm 1053 3172 a(0) p Fk 1120 3157 a(2) p Fl 1214 3157 a(C) p Fh 1291 3121 a(1) p Fp 1366 3157 a(\() p Fn(R) p Fm 1491 3115 a(2) p Fp 1531 3157 a(\)) p 1601 3157 a(suc) m(h) p 1821 3157 a(that) 645 3361 y(supp) p 866 3361 a(~) p Fl 862 3361 a(e) p Fm 907 3376 a(0) p Fk 974 3361 a(\032) p Fp 1080 3361 a(\006\() p Fl(R) q(;) p Fk 1307 3361 a(\000) p Fp 1392 3361 a(~) p Fl 1384 3361 a(!) t(;) p 1493 3361 a(\016) p Fp 1540 3361 a(\)) p Fl(;) p Fp 1820 3361 a(~) p Fl 1816 3361 a(e) p Fm 1861 3376 a(0) p Fp 1928 3361 a(=) p 2032 3361 a(1) p 2127 3361 a(on) p 2277 3361 a(\006\(2) p Fl(R) q(;) p Fk 2553 3361 a(\000) p Fp 2638 3361 a(~) p Fl 2630 3361 a(!) s(;) p Fp 2738 3361 a(2) p Fl(\016) p Fp 2834 3361 a(\)) p Fl(:) p Fp 3343 3361 a(\(2.8\)) 0 3565 y(If) p 98 3565 a(w) m(e) p 241 3565 a(set) 417 3540 y(~) p Fl 393 3565 a(J) p Fh 447 3580 a(\006) p Fp 534 3565 a(=) p 641 3565 a(~) p Fl 638 3565 a(e) p Fm 683 3580 a(0) p Fp 739 3565 a(exp) q(\() p Fk(\006) p Fl(i\013) q(\015) p Fp 1155 3565 a(\() p Fl(x) p Fp(;) p Fk 1292 3565 a(\000) p Fp 1377 3565 a(~) p Fl 1369 3565 a(!) p Fp 1434 3565 a(\)\)) 1524 3539 y(~) p Fl 1510 3565 a(\014) p Fp 1571 3565 a(,) p 1630 3565 a(then) p 1852 3565 a(w) m(e) p 1996 3565 a(obtain) p Fl 709 3769 a(W) p Fm 801 3784 a(+) p Fp 860 3769 a(\() p Fl(H) p Fi 979 3784 a(\013) p Fl 1028 3769 a(;) p 1072 3769 a(H) p Fm 1153 3784 a(0) p Fp 1192 3769 a(\)) 1244 3742 y(~) p Fl 1230 3769 a(\014) p Fm 1291 3728 a(2) p Fp 1358 3769 a(=) p Fl 1461 3769 a(W) p Fm 1553 3784 a(+) p Fp 1613 3769 a(\() p Fl(H) p Fi 1732 3784 a(\013) p Fl 1781 3769 a(;) p 1825 3769 a(H) p Fm 1906 3784 a(0) p Fp 1945 3769 a(;) 2012 3743 y(~) p Fl 1989 3769 a(J) p Fm 2043 3784 a(+) p Fp 2101 3769 a(\)) p Fl(W) p Fm 2231 3784 a(+) p Fp 2291 3769 a(\() p Fl(H) p Fm 2410 3784 a(0) p Fl 2449 3769 a(;) p 2493 3769 a(H) p Fm 2574 3784 a(0) p Fp 2613 3769 a(;) 2680 3743 y(~) p Fl 2657 3769 a(J) p Fh 2711 3784 a(\000) p Fp 2769 3769 a(\)) p Fl(:) p Fp 3343 3769 a(\(2.9\)) 0 3972 y(W) p 92 3972 a(e) p 168 3972 a(com) m(bine) p 550 3972 a(\(2.7\)) p 783 3972 a(and) p 973 3972 a(\(2.9\)) p 1206 3972 a(to) p 1325 3972 a(obtain) p 1629 3972 a(that) 361 4150 y(~) p Fl 347 4176 a(\014) p Fm 408 4135 a(2) p Fl 447 4176 a(S) p Fp 513 4176 a(\() p Fl(H) p Fi 632 4191 a(\013) p Fl 681 4176 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4511 a(e) p 3127 4511 a(denote) p 3440 4511 a(b) m(y) p Fl 0 4631 a(S) p Fm 60 4646 a(0) p Fp 99 4631 a(\() p Fl(\022) p Fh 185 4595 a(0) p Fl 209 4631 a(;) p 253 4631 a(\022) p Fp 301 4631 a(;) p Fl 345 4631 a(\025) p Fp(\)) p 482 4631 a(the) p 661 4631 a(k) m(ernel) p 959 4631 a(of) p 1080 4631 a(\014bre) p Fl 1313 4631 a(S) p Fm 1373 4646 a(0) p Fp 1413 4631 a(\() p Fl(\025) p Fp(;) p Fl 1552 4631 a(H) p Fi 1633 4646 a(\013) p Fl 1682 4631 a(;) p 1726 4631 a(H) p Fm 1807 4646 a(0) p Fp 1846 4631 a(\)) p 1929 4631 a(:) p Fl 2002 4631 a(L) p Fm 2068 4595 a(2) p Fp 2108 4631 a(\() p Fl(S) p Fm 2212 4595 a(1) p Fp 2251 4631 a(\)) p Fk 2335 4631 a(!) p Fl 2480 4631 a(L) p Fm 2546 4595 a(2) p Fp 2586 4631 a(\() p Fl(S) p Fm 2690 4595 a(1) p Fp 2729 4631 a(\).) p 2869 4631 a(By) p 3033 4631 a(Lemma) p 3392 4631 a(2.1,) p Fl 0 4752 a(W) p Fh 92 4767 a(\000) p Fp 151 4752 a(\() p Fl(H) p Fm 270 4767 a(0) p Fl 309 4752 a(;) p 353 4752 a(H) p Fm 434 4767 a(0) p Fp 473 4752 a(;) p Fl 517 4752 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5504 a(\025\022) p Fp 2699 5504 a(\)) p Fk 2760 5504 a(\002) p Fl 2859 5504 a(:) p Fp 1747 5753 a(8) p 90 rotate dyy eop %%Page: 9 9 9 8 bop Fp 0 407 a(Since) p Fl 255 407 a(\014) p Fp 316 407 a(\() p Fk 354 323 a(p) p 436 323 79 4 v Fl 436 407 a(E) p 514 407 a(!) p Fp 579 407 a(\)) p 644 407 a(=) 762 381 y(~) p Fl 748 407 a(\014) p Fp 808 407 a(\() p Fk 846 323 a(p) p 929 323 V Fl 929 407 a(E) p Fp 1015 407 a(~) p Fl 1007 407 a(!) p Fp 1072 407 a(\)) p 1137 407 a(=) p 1241 407 a(1) p 1322 407 a(and) p Fl 1512 407 a(\015) p Fp 1568 407 a(\() p Fk(\000) p Fl(!) p Fp 1748 407 a(;) p Fl 1792 407 a(!) p Fp 1857 407 a(\)) p 1921 407 a(=) p Fl 2025 407 a(\015) p Fp 2081 407 a(\() p 2127 407 a(~) p Fl 2119 407 a(!) p Fp 2183 407 a(;) p Fk 2227 407 a(\000) p Fp 2312 407 a(~) p Fl 2304 407 a(!) p Fp 2369 407 a(\)) p 2434 407 a(=) p Fl 2538 407 a(\031) p Fp 2597 407 a(,) p 2656 407 a(w) m(e) p 2800 407 a(ha) m(v) m(e) p Fl 1253 627 a(S) p Fp 1319 627 a(\() p 1365 627 a(~) p Fl 1357 627 a(!) t(;) 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a(\035) p Fp 1363 2138 a(1) p 1453 2138 a(with) p Fk 1684 2138 a(j) p Fp 1718 2138 a(^) p Fl 1712 2138 a(x) p Fk 1795 2138 a(\000) p Fl 1900 2138 a(!) p Fk 1965 2138 a(j) p Fl 2034 2138 a(<) p 2152 2138 a(\016) p Fp 2240 2138 a(and) p 2438 2138 a(since) p Fl 2685 2138 a(\014) p Fp 2746 2138 a(\() p Fl(\030) p Fp 2832 2138 a(\)) p 2910 2138 a(has) p 3093 2138 a(supp) s(ort) p 3462 2138 a(in) p Fk 0 2258 a(fj) p Fl(\030) p Fk 149 2258 a(\000) 251 2174 y(p) p 334 2174 V Fl 334 2258 a(E) p 412 2258 a(!) p Fk 477 2258 a(j) p Fl 536 2258 a(<) p Fp 644 2258 a(2) p Fl(\016) p Fm 740 2222 a(2) p Fk 780 2258 a(g) p Fp 865 2258 a(only) p 1038 2258 a(,) p 1101 2258 a(it) p 1202 2258 a(follo) m(ws) p 1525 2258 a(from) p 1758 2258 a(Lemma) p 2109 2258 a(2.1) p 2269 2258 a(that) p Fl 2483 2258 a(W) p Fm 2575 2273 a(+) p Fp 2634 2258 a(\() p Fl(H) p Fi 2753 2273 a(\013) p Fl 2803 2258 a(;) p 2847 2258 a(H) p Fm 2928 2273 a(0) p Fp 2967 2258 a(;) p Fl 3011 2258 a(J) p Fm 3065 2273 a(+) p Fp 3123 2258 a(\)) p 3194 2258 a(=) p 3302 2258 a(0) p 3386 2258 a(and) 0 2379 y(hence) p Fl 679 2499 a(W) p Fh 771 2514 a(\000) p Fp 831 2499 a(\() p Fl(H) p Fi 950 2514 a(\013) p Fl 999 2499 a(;) p 1043 2499 a(H) p Fm 1124 2514 a(0) p Fp 1163 2499 a(;) p Fl 1207 2499 a(J) p Fm 1261 2514 a(+) p Fp 1319 2499 a(\)) p 1385 2499 a(=) p Fk 1489 2499 a(\000) p Fl(i) p Fj 1632 2382 a(Z) p Fp 1732 2499 a(exp) q(\() p Fl(itH) p Fi 2068 2514 a(\013) p Fp 2118 2499 a(\)) p Fl(T) p Fp 2243 2499 a(exp) q(\() p Fk(\000) p Fl(itH) p Fm 2656 2514 a(0) p Fp 2696 2499 a(\)) p Fl 2751 2499 a(dt:) p Fp 0 2698 a(If) p 98 2698 a(w) m(e) p 241 2698 a(mak) m(e) p 496 2698 a(use) p 664 2698 a(of) p 775 2698 a(this) p 966 2698 a(relation,) p 1350 2698 a(then) p 1573 2698 a(w) m(e) p 1716 2698 a(obtain) p Fl 357 2918 a(S) p Fm 417 2933 a(0) p Fp 457 2918 a(\() p Fl(\025) p Fp(;) p Fl 596 2918 a(H) p Fi 677 2933 a(\013) p Fl 726 2918 a(;) p 770 2918 a(H) p Fm 851 2933 a(0) p Fp 890 2918 a(\)) p 955 2918 a(=) p 1059 2918 a(2) p Fl(\031) t(iF) p Fp 1277 2918 a(\() p Fl(\025) p Fp(\)) p Fj 1427 2821 a(\020) p Fk 1475 2918 a(\000) p Fp 1576 2893 a(~) p Fl 1552 2918 a(J) p Fh 1615 2877 a(\003) p Fm 1606 2942 a(+) p Fl 1666 2918 a(T) p Fp 1759 2918 a(+) 1876 2893 y(~) p Fl 1857 2918 a(T) p Fh 1928 2877 a(\003) p Fl 1967 2918 a(R) p Fp 2042 2918 a(\() p Fl(\025) p Fp 2159 2918 a(+) p Fl 2257 2918 a(i) p Fp(0;) p Fl 2383 2918 a(H) p Fi 2464 2933 a(\013) p Fp 2513 2918 a(\)) p Fl(T) p Fj 2622 2821 a(\021) p Fl 2688 2918 a(F) p Fh 2765 2877 a(\003) p Fp 2804 2918 a(\() p Fl(\025) p Fp(\)) p 3294 2918 a(\(2.12\)) 0 3150 y(in) p 113 3150 a(exactly) p 449 3150 a(the) p 617 3150 a(same) p 861 3150 a(w) m(a) m(y) p 1058 3150 a(as) p 1178 3150 a([6,) p 1313 3150 a(Theorem) p 1725 3150 a(3.3]) p 1909 3150 a(\(see) p 2104 3150 a(also) p 2299 3150 a([12,) p 2483 3150 a(Section) p 2824 3150 a(7]\),) p 2998 3150 a(where) p Fl 3279 3150 a(F) p Fp 3356 3150 a(\() p Fl(\025) p Fp(\)) p 3516 3150 a(:) p Fl 0 3271 a(L) p Fm 66 3234 a(2) p Fi 66 3295 a(s) p Fp 106 3271 a(\() p Fn(R) p Fm 231 3229 a(2) p Fp 271 3271 a(\)) p Fk 336 3271 a(!) p Fl 463 3271 a(L) p Fm 529 3234 a(2) p Fp 569 3271 a(\() p Fl(S) p Fm 673 3234 a(1) p Fp 712 3271 a(\)) p Fl(;) p 827 3271 a(s) p 900 3271 a(>) p Fp 1004 3271 a(1) p Fl(=) p Fp(2,) p 1210 3271 a(is) p 1308 3271 a(the) p 1476 3271 a(trace) p 1720 3271 a(op) s(erator) p 2113 3271 a(de\014ned) p 2449 3271 a(b) m(y) 1158 3491 y(\() p Fl(F) p Fp 1273 3491 a(\() p Fl(\025) p Fp(\)) p Fl(u) p Fp(\)\() p Fl(\022) p Fp 1586 3491 a(\)) p 1650 3491 a(=) p 1754 3491 a(\() p Fl(F) p 1869 3491 a(u) p Fp(\)\() p Fl(\026;) p 2104 3491 a(\022) p Fp 2152 3491 a(\)) p Fk(j) p Fi 2218 3506 a(\026) p Fm(=) p Fi(\025) p Fl 2359 3491 a(:) p Fp 0 3711 a(Th) m(us) p 247 3711 a(it) p 345 3711 a(follo) m(ws) p 665 3711 a(from) p 895 3711 a(\(2.11\)) p 1177 3711 a(and) p 1367 3711 a(\(2.12\)) p 1649 3711 a(that) p Fl 332 3931 a(f) p Fi 380 3946 a(\013) p Fp 430 3931 a(\() p Fl(!) p Fk 560 3931 a(!) p Fp 695 3931 a(~) p Fl 687 3931 a(!) p Fp 751 3931 a(;) p Fl 795 3931 a(E) p Fp 873 3931 a(\)) p 994 3931 a(=) p Fk 1153 3931 a(\000) p Fp(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 1459 3931 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1654 3931 a(\)\() p Fl(T) p 1801 3931 a(') p Fm 1865 3946 a(0) p Fp 1904 3931 a(\() p Fl(!) t(;) p 2051 3931 a(E) p Fp 2129 3931 a(\)) p Fl(;) p Fp 2233 3905 a(~) p Fl 2211 3931 a(J) p Fm 2265 3946 a(+) p Fl 2322 3931 a(') p Fm 2386 3946 a(0) p Fp 2426 3931 a(\() p 2472 3931 a(~) p Fl 2464 3931 a(!) s(;) p 2572 3931 a(E) p Fp 2650 3931 a(\)\)) 994 4076 y(+) p 1153 4076 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 1382 4076 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1577 4076 a(\)\() p Fl(R) p Fp 1728 4076 a(\() p Fl(E) p Fp 1866 4076 a(+) p Fl 1964 4076 a(i) p Fp(0;) p Fl 2090 4076 a(H) p Fi 2171 4091 a(\013) p Fp 2220 4076 a(\)) p Fl(T) p 2329 4076 a(') p Fm 2393 4091 a(0) p Fp 2432 4076 a(\() p Fl(!) t(;) p 2579 4076 a(E) p Fp 2657 4076 a(\)) p Fl(;) p Fp 2756 4051 a(~) p Fl 2739 4076 a(T) p 2808 4076 a(') p Fm 2872 4091 a(0) p Fp 2911 4076 a(\() p 2957 4076 a(~) p Fl 2949 4076 a(!) t(;) p 3058 4076 a(E) p Fp 3136 4076 a(\)\)) p 3294 4076 a(\(2.13\)) 0 4296 y(for) p Fl 152 4296 a(!) p Fk 248 4296 a(6) p Fp(=) p 364 4296 a(~) p Fl 356 4296 a(!) p Fp 421 4296 a(,) p 484 4296 a(where) p 768 4296 a(w) m(e) p 914 4296 a(denote) p 1231 4296 a(b) m(y) p 1370 4296 a(\() p Fl 1456 4296 a(;) p Fp 1549 4296 a(\)) p 1622 4296 a(the) p Fl 1793 4296 a(L) p Fm 1859 4260 a(2) p Fp 1934 4296 a(scalar) p 2213 4296 a(pro) s(duct) p 2582 4296 a(and) p 2774 4296 a(write) p Fl 3026 4296 a(') p Fm 3090 4311 a(0) p Fp 3130 4296 a(\() p Fl(!) t(;) p 3277 4296 a(E) p Fp 3355 4296 a(\)) p 3427 4296 a(for) p Fl 0 4416 a(') p Fm 64 4431 a(0) p Fp 103 4416 a(\() p Fl(x) p Fp(;) p Fl 240 4416 a(!) t(;) p 349 4416 a(E) p Fp 427 4416 a(\)) p 492 4416 a(=) p 596 4416 a(exp) q(\() p Fl(i) p Fk 816 4332 a(p) p 899 4332 V Fl 899 4416 a(E) p 977 4416 a(x) p Fk 1055 4416 a(\001) p Fl 1104 4416 a(!) p Fp 1169 4416 a(\).) 146 4587 y(W) p 238 4587 a(e) p 324 4587 a(no) m(w) p 537 4587 a(\014x) p Fl 685 4587 a(\033) n(;) p Fp 825 4587 a(0) p Fl 918 4587 a(<) p 1038 4587 a(\033) p Fk 1141 4587 a(\034) p Fp 1285 4587 a(1,) p 1405 4587 a(small) p 1670 4587 a(enough) p 2016 4587 a(and) p 2216 4587 a(tak) m(e) p Fl 2437 4587 a(R) p Fp 2556 4587 a(=) p Fl 2676 4587 a(d) p Fi 2727 4550 a(\033) p Fl 2774 4587 a(;) p 2860 4587 a(d) p Fk 2955 4587 a(\035) p Fp 3099 4587 a(1,) p 3219 4587 a(in) p 3343 4587 a(\(2.4\)) 0 4707 y(and) p 194 4707 a(\(2.8\).) p 479 4707 a(W) p 571 4707 a(e) p 651 4707 a(ma) m(y) p 867 4707 a(assume) p 1209 4707 a(that) p Fl 1425 4707 a(e) p Fm 1470 4722 a(0) p Fp 1546 4707 a(ob) s(eys) p Fl 1822 4707 a(@) p Fi 1878 4671 a(\014) 1873 4732 y(x) p Fl 1926 4707 a(e) p Fm 1971 4722 a(0) p Fp 2011 4707 a(\() p Fl(x) p Fp(\)) p 2178 4707 a(=) p Fl 2289 4707 a(O) p Fp 2367 4707 a(\() p Fk(j) p Fl(x) p Fk(j) p Fh 2516 4671 a(\000j) p Fi(\014) p Fh 2634 4671 a(j) p Fp 2656 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a(and) 23 5043 y(~) p Fl 0 5068 a(J) p Fm 54 5083 a(+) p Fp 113 5068 a(\() p Fl(x;) p 250 5068 a(\030) p Fp 298 5068 a(\)) p 372 5068 a(do) s(es) p 595 5068 a(not) p 773 5068 a(in) m(tersect) p 1170 5068 a(with) p 1396 5068 a(eac) m(h) p 1619 5068 a(other.) p 1923 5068 a(Hence) p 2216 5068 a(the) p 2388 5068 a(\014rst) p 2593 5068 a(term) p 2830 5068 a(on) p 2969 5068 a(the) p 3141 5068 a(righ) m(t) p 3380 5068 a(side) 0 5188 y(of) p 111 5188 a(\(2.13\)) p 393 5188 a(ob) s(eys) 797 5408 y(\() p Fl(T) p 906 5408 a(') p Fm 970 5423 a(0) p Fp 1009 5408 a(\() p Fl(!) t(;) p 1156 5408 a(E) p Fp 1234 5408 a(\)) p Fl(;) p Fp 1338 5383 a(~) p Fl 1316 5408 a(J) p Fm 1370 5423 a(+) p Fl 1427 5408 a(') p Fm 1491 5423 a(0) p Fp 1531 5408 a(\() p 1577 5408 a(~) p Fl 1569 5408 a(!) s(;) p 1677 5408 a(E) p Fp 1755 5408 a(\)\)) p 1858 5408 a(=) p Fl 1962 5408 a(O) p Fp 2040 5408 a(\() p Fl(d) p Fh 2129 5367 a(\000) p Fi(L) p Fp 2235 5408 a(\)) p Fl(;) p 2414 5408 a(d) p Fk 2492 5408 a(!) p 2620 5408 a(1) p Fl(;) p Fp 1747 5753 a(9) p 90 rotate dyy eop %%Page: 10 10 10 9 bop Fp 0 407 a(for) p 149 407 a(an) m(y) p Fl 333 407 a(L) p Fk 427 407 a(\035) p Fp 555 407 a(1,) p 663 407 a(and) p 853 407 a(w) m(e) p 996 407 a(ha) m(v) m(e) p Fl 103 626 a(f) p Fi 151 641 a(\013) p Fp 201 626 a(\() p Fl(!) p Fk 331 626 a(!) p Fp 466 626 a(~) p Fl 458 626 a(!) p Fp 523 626 a(;) p Fl 567 626 a(E) p Fp 645 626 a(\)) p 710 626 a(=) p 813 626 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 1042 626 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1237 626 a(\)\() p Fl(R) p Fp 1388 626 a(\() p Fl(E) p Fp 1526 626 a(+) p Fl 1624 626 a(i) p Fp(0;) p Fl 1750 626 a(H) p Fi 1831 641 a(\013) p Fp 1880 626 a(\)) p Fl(T) p 1989 626 a(') p Fm 2053 641 a(0) p Fp 2092 626 a(\() p Fl(!) t(;) p 2239 626 a(E) p Fp 2317 626 a(\)) p Fl(;) p Fp 2417 601 a(~) p Fl 2399 626 a(T) p 2469 626 a(') p Fm 2533 641 a(0) p Fp 2572 626 a(\() p 2618 626 a(~) p Fl 2610 626 a(!) s(;) p 2718 626 a(E) p Fp 2796 626 a(\)\)) p 2894 626 a(+) p Fl 2992 626 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a(supp) s(ort) p 703 1500 a(in) p 817 1500 a(the) p 985 1500 a(outgoing) p 1386 1500 a(region) 386 1720 y(supp) p Fl 604 1720 a(T) p Fh 661 1735 a(1) p Fk 763 1720 a(\032) p 868 1720 a(f) p Fp(\() p Fl(x;) p 1055 1720 a(\030) p Fp 1103 1720 a(\)) p 1168 1720 a(:) p Fk 1223 1720 a(j) p Fl(x) p Fk(j) p Fl 1362 1720 a(>) p Fp 1465 1720 a(2) p Fl(d) p Fi 1565 1678 a(\033) p Fl 1611 1720 a(;) p Fk 1702 1720 a(j) p Fl(\030) p Fk 1799 1720 a(\000) 1898 1631 y(p) p 1981 1631 79 4 v Fl 1981 1720 a(E) p 2060 1720 a(!) p Fk 2125 1720 a(j) p Fl 2179 1720 a(<) p Fp 2283 1720 a(2) p Fl(\016) p Fm 2379 1678 a(2) p Fl 2418 1720 a(;) p Fp 2514 1720 a(^) p Fl 2508 1720 a(x) p Fk 2586 1720 a(\001) p Fp 2646 1693 a(^) p Fl 2635 1720 a(\030) p 2711 1720 a(>) p Fp 2814 1720 a(1) p Fk 2885 1720 a(\000) p Fp 2985 1720 a(3) p Fl(\016) p Fk 3081 1720 a(g) p Fl(:) p Fp 0 1939 a(The) p 208 1939 a(classical) p 591 1939 a(particle) p 951 1939 a(starting) p 1322 1939 a(from) p 1560 1939 a(\() p Fl(x;) p 1697 1939 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2212 5278 a(1) p Fp 2329 5263 a(and) p Fl 2527 5263 a(R) p Fp 2602 5263 a(\() p Fl(E) p Fk 2747 5263 a(\000) p Fl 2852 5263 a(i) p Fp(0;) p Fl 2978 5263 a(H) p Fi 3059 5278 a(\013) p Fp 3108 5263 a(\)) 3165 5238 y(~) p Fl 3146 5263 a(T) p Fh 3203 5278 a(1) p Fp 3278 5263 a(.) p 3375 5263 a(The) 0 5384 y(appro) m(ximations) p 694 5384 a(tak) m(e) p 910 5384 a(the) p 1082 5384 a(forms) p 1356 5384 a(\(3.19\)) p 1642 5384 a(and) p 1837 5384 a(\(3.20\)) p 2123 5384 a(in) p 2242 5384 a(the) p 2414 5384 a(next) p 2639 5384 a(section.) p 3016 5384 a(W) p 3108 5384 a(e) p 3189 5384 a(rep) s(eat) p 3495 5384 a(a) 0 5504 y(similar) p 320 5504 a(argumen) m(t) p 757 5504 a(in) p 870 5504 a(the) p 1038 5504 a(pro) s(of) p 1293 5504 a(of) p 1404 5504 a(Theorem) p 1816 5504 a(1.1.) 1723 5753 y(10) p 90 rotate dyy eop %%Page: 11 11 11 10 bop Fq 146 407 a(3.) p 271 407 a(Auxiliary) p 767 407 a(op) s(erators) p 1267 407 a(and) p 1483 407 a(appro) m(ximation) p 2230 407 a(to) p 2367 407 a(resolv) m(en) 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2646 4150 a(X) p Fm 2735 4109 a(+) p Fi 2727 4175 a(am;L) p Fj 2899 4054 a(\021) p Fh 2948 4077 a(\003) p Fl 3004 4150 a(;) p Fp 0 4365 a(where) p Fl 282 4365 a(X) p Fm 371 4324 a(+) p Fi 363 4389 a(am;L) p Fp 534 4365 a(\() p Fl(x;) p 671 4365 a(\030) p Fp 719 4365 a(\)) p 789 4365 a(has) p 963 4365 a(supp) s(ort) p 1324 4365 a(in) p 1438 4365 a(\(3.15\)) p 1720 4365 a(and) p 1910 4365 a(ob) s(eys) p 2181 4365 a(\(3.21\).) 146 4528 y(An) p 302 4528 a(appro) m(ximation) p 947 4528 a(for) p Fl 1092 4528 a(R) p Fp 1167 4528 a(\() p Fl(E) p Fk 1296 4528 a(\006) p Fl 1386 4528 a(i) p Fp(0;) p Fl 1512 4528 a(H) p Fi 1593 4543 a(a) p Fp 1634 4528 a(\)) p Fl(X) p Fh 1761 4492 a(1) p Fi 1753 4553 a(am) p Fp 1885 4528 a(is) p 1979 4528 a(constructed) p 2500 4528 a(in) p 2609 4528 a(the) p 2773 4528 a(same) p 3013 4528 a(w) m(a) m(y) p 3206 4528 a(as) p 3321 4528 a(para-) 0 4649 y(metrices) p 385 4649 a(for) p 534 4649 a(elliptic) p 854 4649 a(op) s(erators.) p 1323 4649 a(The) p 1524 4649 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5463 a(1) p Fi 1460 5529 a(am) p Fp 1592 5504 a(=) p Fl 1695 5504 a(X) p Fh 1784 5463 a(1) p Fi 1776 5529 a(am;L) p Fp 1970 5504 a(+) p Fl 2068 5504 a(R) p Fp 2143 5504 a(\() p Fl(E) p Fp 2281 5504 a(+) p Fl 2379 5504 a(i) p Fp(0;) p Fl 2505 5504 a(H) p Fi 2586 5519 a(a) p Fp 2628 5504 a(\)) t(~) p Fl 2666 5504 a(r) p Fi 2710 5519 a(L) p Fp 3294 5504 a(\(3.24\)) 1723 5753 y(14) p 90 rotate dyy eop %%Page: 15 15 15 14 bop Fp 0 407 a(for) p 144 407 a(some) p 383 407 a(pseudo) s(di\013eren) m(tial) p 1162 407 a(op) s(erator) p Fl 1550 407 a(X) p Fh 1639 371 a(1) p Fi 1631 431 a(am;L) p Fp 1802 407 a(\() p Fl(x;) p 1939 407 a(D) p Fi 2020 422 a(x) p Fp 2064 407 a(\),) p 2158 407 a(where) p Fl 2435 407 a(X) p Fh 2524 371 a(1) p Fi 2516 431 a(am;L) p Fp 2687 407 a(\() p Fl(x;) p 2824 407 a(\030) p Fp 2872 407 a(\)) p 2937 407 a(has) p 3106 407 a(supp) s(ort) p 3462 407 a(in) 0 527 y(\(3.23\)) p 271 527 a(and) p 450 527 a(ob) s(eys) p 711 527 a(\(3.21\).) p 1028 527 a(The) p 1218 527 a(appro) 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Fl 2782 5504 a(;) p 2826 5504 a(\022) s(;) p Fp 2918 5504 a(1) p Fl(=) p Fp(3\)) 1723 5753 y(15) p 90 rotate dyy eop %%Page: 16 16 16 15 bop Fp 0 430 a(and) p 195 430 a(that) p Fk 412 430 a(j) p Fl(@) p Fi 496 394 a(\014) 491 455 y(x) p Fp 552 430 a(~) p Fl 544 430 a(p) p Fi 593 445 a(j) p Fp 629 430 a(\() p Fl(x) p Fp(\)) p Fk(j) p 825 430 a(\024) p Fl 940 430 a(C) p Fi 1010 445 a(\014) p Fj 1073 334 a(\020) p Fk 1123 430 a(j) p Fl(x) p Fk 1228 430 a(\000) p Fl 1328 430 a(d) p Fi 1379 445 a(j) p Fk 1415 430 a(j) p Fp 1465 430 a(+) p Fl 1563 430 a(d) p Fm 1614 394 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fj 1821 334 a(\021) p Fh 1870 357 a(\000j) p Fi(\014) p Fh 1988 357 a(j) p Fp 2012 430 a(.) p 2099 430 a(W) p 2191 430 a(e) p 2272 430 a(set) p Fl 2430 430 a(p) p Fi 2479 445 a(a) p Fp 2520 430 a(\() p Fl(x) p Fp(\)) p 2689 430 a(=) p Fj 2801 364 a(Q) p Fi 2880 451 a(j) p Fh 2913 451 a(2) p Fi(a) p Fp 3026 430 a(~) p Fl 3018 430 a(p) p Fi 3067 445 a(j) p Fp 3103 430 a(\() p Fl(x) p Fp(\).) p 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1141 4873 a(for) p 1290 4873 a(the) p 1458 4873 a(m) m(ultiplication) p 2084 4873 a(op) s(erator) p Fl 1329 5091 a(r) p Fh 1373 5106 a(\006) p Fi(\027) p Fp 1499 5091 a(=) p 1602 5091 a(\() p Fk(j) p Fl(x) p Fk(j) p Fm 1751 5050 a(2) p Fp 1813 5091 a(+) p Fl 1911 5091 a(d) p Fm 1962 5050 a(2) p Fp 2001 5091 a(\)) p Fh 2039 5050 a(\007) p Fi(\027) p Fk 2137 5091 a(\002) p Fp 3343 5091 a(\(4.2\)) 0 5309 y(with) p Fl 222 5309 a(\027) p Fk 305 5309 a(\035) p Fp 432 5309 a(1.) p 551 5309 a(The) p 752 5309 a(pro) s(of) p 1007 5309 a(is) p 1105 5309 a(based) p 1377 5309 a(on) p 1512 5309 a(the) p 1680 5309 a(follo) m(wing) p 2092 5309 a(theorem) p 2472 5309 a(on) p 2607 5309 a(the) p 2775 5309 a(resolv) m(en) m(t) p 3185 5309 a(estimate) 0 5430 y(for) p Fl 149 5430 a(H) p Fi 230 5445 a(a) p Fp 299 5430 a(=) p Fl 403 5430 a(H) p Fp 492 5430 a(\() p Fl(A) p Fi 603 5445 a(a) p Fp 644 5430 a(\)) p 714 5430 a(de\014ned) p 1050 5430 a(b) m(y) p 1186 5430 a(\(3.1\)) p 1419 5430 a(for) p 1568 5430 a(subset) p Fl 1867 5430 a(a) p Fk 1946 5430 a(\032) p 2051 5430 a(f) p Fp(1) p Fl(;) p Fp 2194 5430 a(2) p Fl(;) p 2287 5430 a(:) p 2331 5430 a(:) p 2375 5430 a(:) p 2417 5430 a(;) p 2461 5430 a(N) p Fk 2549 5430 a(g) p Fp(.) 1723 5753 y(16) p 90 rotate dyy eop %%Page: 17 17 17 16 bop Fq 0 407 a(Theorem) p 475 407 a(4.1) p Fo 667 407 a(Assume) p Fp 1031 407 a(\(1) p Fl(:) p Fp(3\)) p Fo 1266 407 a(that) p Fp 1466 407 a(\(1) p Fl(:) p Fp(4\)) p Fo(.) p 1741 407 a(Set) p Fl 540 611 a(s) p Fi 586 626 a(j) p Fm 619 626 a(1) p Fp 658 611 a(\() p Fl(x) p Fp(\)) p 817 611 a(=) p Fl 921 611 a(s) p Fi 967 626 a(j) p Fp 1003 611 a(\() p Fl(x) p Fp(\)) p Fk(h) p Fl(x) p Fk 1251 611 a(\000) p Fl 1350 611 a(d) p Fi 1401 626 a(j) p Fk 1437 611 a(i) p Fh 1476 570 a(\000) p Fm(1) p Fi(=) p Fm(2) p Fl 1641 611 a(;) p 1884 611 a(b) p Fi 1925 626 a(j) p Fm 1958 626 a(1) p Fp 1997 611 a(\() p Fl(x) p Fp(\)) p 2156 611 a(=) p Fl 2260 611 a(b) p Fi 2301 626 a(j) p Fp 2338 611 a(\() p Fl(x) p Fp(\)) p Fk(h) 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1598 2307 a(a) p Fp 1639 2292 a(\)) p Fl(s) p Fi 1723 2307 a(k) p Fm 1762 2307 a(1) p Fk 1801 2292 a(k) p Fp 1934 2292 a(=) p Fl 2092 2292 a(O) p Fp 2170 2292 a(\() p Fl(d) p Fh 2259 2251 a(\000) p Fm(1) p Fi(=) p Fm(2+) p Fi(c\033) p Fp 2551 2292 a(\)) p 3343 2292 a(\(4.7\)) p Fo 0 2496 a(for) p Fl 156 2496 a(j) p Fk 229 2496 a(6) p Fp(=) p Fl 333 2496 a(k) p Fo 387 2496 a(.) p Fp 146 2752 a(The) p 349 2752 a(resolv) m(en) m(t) p 760 2752 a(estimate) p 1153 2752 a(\(1.13\)) p 1437 2752 a(is) p 1537 2752 a(obtained) p 1940 2752 a(as) p 2061 2752 a(an) p 2199 2752 a(immediate) p 2677 2752 a(consequence) p 3230 2752 a(of) p 3343 2752 a(\(4.7\)) 0 2872 y(in) p 112 2872 a(the) p 278 2872 a(ab) s(o) m(v) m(e) p 553 2872 a(theorem.) p 969 2872 a(W) p 1061 2872 a(e) p 1135 2872 a(pro) s(ceed) p 1494 2872 a(to) p 1611 2872 a(the) p 1777 2872 a(pro) s(of) p 2030 2872 a(of) p 2139 2872 a(Theorem) p 2549 2872 a(1.1,) p 2732 2872 a(accepting) p 3164 2872 a(Theorem) 0 2992 y(4.1) p 157 2992 a(as) p 277 2992 a(pro) m(v) m(ed.) p 632 2992 a(The) p 832 2992 a(pro) s(of) p 1087 2992 a(is) p 1185 2992 a(done) p 1418 2992 a(in) p 1532 2992 a(the) p 1700 2992 a(next) p 1920 2992 a(section.) p Fo 0 3158 a(Pr) p 102 3158 a(o) p 147 3158 a(of) p 264 3158 a(of) p 380 3158 a(The) p 540 3158 a(or) p 626 3158 a(em) p 787 3158 a(1.1.) p Fp 1044 3158 a(The) p 1247 3158 a(scattering) p 1699 3158 a(amplitude) p Fl 2162 3158 a(f) p Fi 2210 3173 a(d) p Fp 2282 3158 a(=) p Fl 2390 3158 a(f) p Fi 2438 3173 a(d) p Fp 2478 3158 a(\() p Fl(!) p Fk 2612 3158 a(!) p Fp 2751 3158 a(~) p Fl 2743 3158 a(!) p Fp 2807 3158 a(;) p Fl 2851 3158 a(E) p Fp 2929 3158 a(\)) p 3002 3158 a(is) p 3102 3158 a(de\014ned) p 3440 3158 a(b) m(y) 0 3278 y(\(2.2\)) p 226 3278 a(through) p 588 3278 a(the) p 749 3278 a(scattering) p 1193 3278 a(k) m(ernel.) p 1516 3278 a(W) p 1608 3278 a(e) p 1677 3278 a(follo) m(w) p 1952 3278 a(the) p 2113 3278 a(argumen) m(t) p 2542 3278 a(in) p 2649 3278 a(section) p 2968 3278 a(2) p 3043 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Fl(\016) p Fp 2820 4132 a(\)) p Fl(;) p Fp 610 4277 a(supp) p 831 4277 a(~) p Fl 827 4277 a(e) p Fm 872 4292 a(0) p Fk 940 4277 a(\032) p Fp 1045 4277 a(\006\() p Fl(d) p Fi 1204 4236 a(\033) p Fl 1251 4277 a(;) p Fk 1295 4277 a(\000) p Fp 1380 4277 a(~) p Fl 1372 4277 a(!) s(;) p 1480 4277 a(\016) p Fp 1527 4277 a(\)) p Fl(;) p Fp 1859 4277 a(~) p Fl 1855 4277 a(e) p Fm 1900 4292 a(0) p Fp 1968 4277 a(=) p 2071 4277 a(1) p 2167 4277 a(on) p 2316 4277 a(\006\(2) p Fl(d) p Fi 2524 4236 a(\033) p Fl 2571 4277 a(;) p Fk 2615 4277 a(\000) p Fp 2700 4277 a(~) p Fl 2692 4277 a(!) s(;) p Fp 2800 4277 a(2) p Fl(\016) p Fp 2896 4277 a(\)) 0 4481 y(with) p Fl 226 4481 a(d) p Fp 311 4481 a(=) p 421 4481 a(min) p Fk 617 4481 a(j) p Fl(d) p Fi 696 4496 a(j) t(k) p Fk 770 4481 a(j) p 832 4481 a(\035) p Fp 966 4481 a(1,) p 1080 4481 a(where) p 1365 4481 a(the) p 1537 4481 a(notation) p 1931 4481 a(\006\() p Fl(R) q(;) p 2158 4481 a(!) t(;) p 2267 4481 a(\016) p Fp 2314 4481 a(\)) p 2388 4481 a(is) p 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p Fi 588 4755 a(d) p Fp 629 4740 a(\)) p Fl(\014) p Fp 760 4740 a(and) 973 4714 y(~) p Fl 949 4740 a(J) p Fm 1003 4755 a(+) p Fp 1090 4740 a(=) p 1197 4740 a(~) p Fl 1194 4740 a(e) p Fp 1272 4740 a(exp) q(\() p Fl(i) p Fp 1500 4713 a(~) p Fl 1492 4740 a(\022) p Fi 1537 4755 a(d) p Fp 1578 4740 a(\)) 1630 4713 y(~) p Fl 1616 4740 a(\014) p Fp 1677 4740 a(,) p 1736 4740 a(where) p Fl 2018 4740 a(\014) p Fp 2106 4740 a(=) p Fl 2210 4740 a(\014) p Fp 2271 4740 a(\() p Fl(D) p Fi 2390 4755 a(x) p Fp 2433 4740 a(\)) p Fl(;) p Fp 2562 4713 a(~) p Fl 2548 4740 a(\014) p Fp 2636 4740 a(=) 2753 4713 y(~) p Fl 2739 4740 a(\014) p Fp 2800 4740 a(\() p Fl(D) p Fi 2919 4755 a(x) p Fp 2963 4740 a(\)) p 3033 4740 a(and) p Fl 575 5018 a(\022) p Fi 620 5033 a(d) p Fp 661 5018 a(\() p Fl(x) p Fp(\)) p 820 5018 a(=) p Fi 953 4910 a(N) p Fj 925 4935 a(X) p Fi 924 5117 a(j) p Fm 957 5117 a(=1) p Fl 1063 5018 a(\013) p Fi 1125 5033 a(j) p Fl 1161 5018 a(\015) p Fp 1217 5018 a(\() p Fl(x) p Fk 1333 5018 a(\000) p Fl 1432 5018 a(d) p Fi 1483 5033 a(j) p Fp 1520 5018 a(;) p Fl 1564 5018 a(!) p Fp 1629 5018 a(\)) p Fl(;) p Fp 1912 4992 a(~) p Fl 1904 5018 a(\022) p Fi 1949 5033 a(d) p Fp 2018 5018 a(=) p Fi 2151 4910 a(N) p Fj 2123 4935 a(X) p Fi 2122 5117 a(j) p Fm 2155 5117 a(=1) p Fl 2261 5018 a(\013) p Fi 2323 5033 a(j) p Fl 2359 5018 a(\015) p Fp 2415 5018 a(\() p Fl(x) p Fk 2531 5018 a(\000) p Fl 2630 5018 a(d) p Fi 2681 5033 a(j) p Fp 2718 5018 a(;) p Fk 2762 5018 a(\000) p Fp 2847 5018 a(~) p Fl 2839 5018 a(!) p Fp 2903 5018 a(\)) p Fl(:) p Fp 0 5300 a(W) p 92 5300 a(e) p 168 5300 a(can) p 347 5300 a(calculate) p Fl 422 5504 a(T) p Fp 520 5504 a(=) p Fl 624 5504 a(H) p Fi 705 5519 a(d) p Fl 745 5504 a(J) p Fm 799 5519 a(+) p Fk 880 5504 a(\000) p Fl 980 5504 a(J) p Fm 1034 5519 a(+) p Fl 1093 5504 a(H) p Fm 1174 5519 a(0) p Fp 1241 5504 a(=) p 1344 5504 a(exp) q(\() p Fl(i\022) p Fi 1609 5519 a(d) p Fp 1651 5504 a(\)[) p Fl(H) p Fm 1797 5519 a(0) p Fl 1836 5504 a(;) p 1880 5504 a(e) p Fp(]) p Fl(\014) p 2013 5504 a(;) p Fp 2270 5479 a(~) p Fl 2251 5504 a(T) p Fp 2350 5504 a(=) p 2453 5504 a(exp) q(\() p Fl(i) p Fp 2681 5478 a(~) p Fl 2673 5504 a(\022) p Fi 2718 5519 a(d) p Fp 2759 5504 a(\)[) p Fl(H) p Fm 2905 5519 a(0) p Fl 2945 5504 a(;) p Fp 2992 5504 a(~) p Fl 2989 5504 a(e) p Fp(]) 3075 5478 y(~) p Fl 3061 5504 a(\014) p Fp 1723 5753 a(17) p 90 rotate dyy eop %%Page: 18 18 18 17 bop Fp 0 407 a(b) m(y) p 135 407 a(making) p 480 407 a(use) p 648 407 a(of) p 759 407 a(relation) p 1117 407 a(\(2.6\),) p 1377 407 a(and) p 1567 407 a(w) m(e) p 1710 407 a(obtain) p Fl 491 627 a(f) p Fi 539 642 a(d) p Fp 607 627 a(=) p 711 627 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 940 627 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1135 627 a(\)\() p Fl(R) p Fp 1286 627 a(\() p Fl(E) p Fp 1424 627 a(+) p Fl 1522 627 a(i) p Fp(0;) p Fl 1648 627 a(H) p Fi 1729 642 a(d) p Fp 1769 627 a(\)) p Fl(T) p 1878 627 a(') p Fm 1942 642 a(0) p Fp 1981 627 a(\() p Fl(!) t(;) p 2128 627 a(E) p Fp 2206 627 a(\)) p Fl(;) p Fp 2305 602 a(~) p Fl 2288 627 a(T) p 2357 627 a(') p Fm 2421 642 a(0) p Fp 2460 627 a(\() p 2506 627 a(~) p Fl 2498 627 a(!) t(;) p 2607 627 a(E) p Fp 2685 627 a(\)\)) p 2782 627 a(+) p Fl 2880 627 a(o) p Fp(\(1\)) p 3343 627 a(\(4.8\)) 0 847 y(b) m(y) p 135 847 a(rep) s(eating) p 566 847 a(the) p 734 847 a(same) p 979 847 a(argumen) m(t) p 1415 847 a(as) p 1535 847 a(used) p 1758 847 a(to) p 1877 847 a(deriv) m(e) p 2164 847 a(\(2.14\).) p 2484 847 a(W) p 2576 847 a(e) p 2652 847 a(set) p Fl 664 1141 a(\037) p Fi 725 1156 a(j) p Fp 762 1141 a(\() p Fl(x) p Fp(\)) p 921 1141 a(=) p Fl 1024 1141 a(\037) p Fp(\() p Fk(j) p Fl(x) p Fk 1229 1141 a(\000) p Fl 1328 1141 a(d) p Fi 1379 1156 a(j) p Fk 1416 1141 a(j) p Fl(=) p Fp(2) p Fl(d) p Fi 1593 1100 a(\033) p Fp 1638 1141 a(\)) p Fl(;) p 1915 1141 a(\037) p Fh 1976 1156 a(1) p Fp 2051 1141 a(\() p Fl(x) p Fp(\)) p 2210 1141 a(=) p 2313 1141 a(1) p Fk 2384 1141 a(\000) p Fi 2514 1033 a(N) p Fj 2485 1058 a(X) p Fi 2484 1241 a(j) p Fm 2517 1241 a(=1) p Fl 2623 1141 a(\037) p Fi 2684 1156 a(j) p Fp 2721 1141 a(\() p Fl(x) p Fp(\)) p Fl(:) p Fp 0 1439 a(If) p Fl 98 1439 a(k) p Fk 179 1439 a(6) p Fp(=) p Fl 283 1439 a(j) p Fp 329 1439 a(,) p 388 1439 a(then) p Fl 611 1439 a(e) p Fi 656 1454 a(k) p Fp 726 1439 a(=) p 830 1439 a(1) p 911 1439 a(on) p 1046 1439 a(supp) p Fl 1264 1439 a(\037) p Fi 1325 1454 a(j) p Fp 1362 1439 a(,) p 1421 1439 a(and) p 1611 1439 a(w) m(e) p 1755 1439 a(can) p 1934 1439 a(decomp) s(ose) p Fl 2425 1439 a(T) p Fp 2528 1439 a(in) m(to) p 2726 1439 a(the) p 2894 1439 a(sum) p Fl 1352 1736 a(T) p Fp 1451 1736 a(=) p Fi 1584 1628 a(N) p Fj 1556 1653 a(X) p Fi 1554 1836 a(j) p Fm 1587 1836 a(=1) p Fp 1693 1736 a(\() p Fl(T) p Fi 1788 1751 a(j) p Fp 1847 1736 a(+) p Fl 1945 1736 a(T) p Fi 2002 1751 a(j) p Fh 2035 1751 a(1) p Fp 2109 1736 a(\)) p Fl 2164 1736 a(;) p Fp 0 2039 a(where) p Fl 282 2039 a(T) p Fi 339 2054 a(j) p Fp 403 2039 a(=) p Fl 507 2039 a(\037) p Fi 568 2054 a(j) p Fp 621 2039 a(exp) q(\() p Fl(i\022) p Fi 886 2054 a(d) p Fp 927 2039 a(\)[) p Fl(H) p Fm 1073 2054 a(0) p Fl 1112 2039 a(;) p 1156 2039 a(e) p Fi 1201 2054 a(j) p Fp 1238 2039 a(]) p Fl(\014) p Fp 1358 2039 a(and) p Fl 764 2259 a(T) p Fi 821 2274 a(j) p Fh 854 2274 a(1) p Fp 956 2259 a(=) p Fl 1059 2259 a(\037) p Fh 1120 2274 a(1) p Fp 1212 2259 a(exp) q(\() p Fl(i\022) p Fi 1477 2274 a(d) p Fp 1518 2259 a(\)) p Fl(e) p Fm 1601 2274 a(1) p Fl 1657 2259 a(:) p 1701 2259 a(:) p 1745 2259 a(:) p 1788 2259 a(e) p Fi 1833 2274 a(j) p Fh 1866 2274 a(\000) p Fm(1) p Fp 1960 2259 a([) p Fl(H) p Fm 2068 2274 a(0) p Fl 2107 2259 a(;) p 2151 2259 a(e) p Fi 2196 2274 a(j) p Fp 2233 2259 a(]) p Fl(e) p Fi 2305 2274 a(j) p Fm 2338 2274 a(+1) p Fl 2448 2259 a(:) p 2492 2259 a(:) p 2536 2259 a(:) p 2579 2259 a(e) p Fi 2624 2274 a(N) p Fl 2692 2259 a(\014) p 2753 2259 a(:) p Fp 0 2495 a(Similarly) p 423 2495 a(w) m(e) p 575 2495 a(decomp) s(ose) 1093 2470 y(~) p Fl 1074 2495 a(T) p Fp 1185 2495 a(in) m(to) 1410 2470 y(~) p Fl 1391 2495 a(T) p Fp 1503 2495 a(=) p Fj 1621 2428 a(P) p Fi 1708 2455 a(N) 1708 2519 y(j) p Fm 1741 2519 a(=1) p Fj 1852 2399 a(\020) p Fp 1920 2470 a(~) p Fl 1901 2495 a(T) p Fi 1958 2510 a(j) p Fp 2017 2495 a(+) 2134 2470 y(~) p Fl 2115 2495 a(T) p Fi 2172 2510 a(j) p Fh 2205 2510 a(1) p Fj 2279 2399 a(\021) p Fp 2329 2495 a(.) p 2424 2495 a(The) p 2633 2495 a(sym) m(b) s(ol) p Fl 2974 2495 a(T) p Fi 3031 2510 a(j) p Fh 3064 2510 a(1) p Fp 3139 2495 a(\() p Fl(x;) p 3276 2495 a(\030) p Fp 3324 2495 a(\)) p 3402 2495 a(has) 0 2615 y(supp) s(ort) p 361 2615 a(in) p 475 2615 a(the) p 643 2615 a(outgoing) p 1044 2615 a(region) 123 2844 y(supp) p Fl 341 2844 a(T) p Fi 398 2859 a(j) p Fh 431 2859 a(1) p Fk 533 2844 a(\032) p 638 2844 a(f) p Fp(\() p Fl(x;) p 825 2844 a(\030) p Fp 873 2844 a(\)) p 938 2844 a(:) p Fk 992 2844 a(j) p Fl(x) p Fk 1098 2844 a(\000) p Fl 1197 2844 a(d) p Fi 1248 2859 a(j) p Fk 1284 2844 a(j) p Fl 1340 2844 a(>) p Fp 1443 2844 a(2) p Fl(d) p Fi 1543 2803 a(\033) p Fl 1590 2844 a(;) p Fk 1680 2844 a(j) p Fl(\030) p Fk 1777 2844 a(\000) 1877 2755 y(p) p 1960 2755 79 4 v Fl 1960 2844 a(E) p 2038 2844 a(!) p Fk 2103 2844 a(j) p Fl 2157 2844 a(<) p Fp 2261 2844 a(2) p Fl(\016) p Fm 2357 2803 a(2) p Fl 2396 2844 a(;) p Fj 2597 2805 a(d) p Fp 2486 2844 a(\() p Fl(x) p Fk 2602 2844 a(\000) p Fl 2701 2844 a(d) p Fi 2752 2859 a(j) p Fp 2789 2844 a(\)) p Fk 2849 2844 a(\001) p Fp 2909 2817 a(^) p Fl 2899 2844 a(\030) p 2974 2844 a(>) p Fp 3077 2844 a(1) p Fk 3148 2844 a(\000) p Fp 3248 2844 a(3) p Fl(\016) p Fk 3344 2844 a(g) p Fl(;) p Fp 0 3064 a(while) 274 3039 y(~) p Fl 255 3064 a(T) p Fi 312 3079 a(j) p Fh 345 3079 a(1) p Fp 419 3064 a(\() p Fl(x;) p 556 3064 a(\030) p Fp 604 3064 a(\)) p 674 3064 a(has) p 848 3064 a(supp) s(ort) p 1209 3064 a(in) p 1323 3064 a(the) p 1491 3064 a(incoming) p 1908 3064 a(region) 85 3301 y(supp) 322 3276 y(~) p Fl 303 3301 a(T) p Fi 360 3316 a(j) p Fh 393 3316 a(1) p Fk 495 3301 a(\032) p 600 3301 a(f) p Fp(\() p Fl(x;) p 787 3301 a(\030) p Fp 835 3301 a(\)) p 900 3301 a(:) p Fk 954 3301 a(j) p Fl(x) p Fk 1060 3301 a(\000) p Fl 1159 3301 a(d) p Fi 1210 3316 a(j) p Fk 1247 3301 a(j) p Fl 1302 3301 a(>) p Fp 1405 3301 a(2) p Fl(d) p Fi 1505 3260 a(\033) p Fl 1552 3301 a(;) p Fk 1642 3301 a(j) p Fl(\030) p Fk 1739 3301 a(\000) 1839 3212 y(p) p 1922 3212 V Fl 1922 3301 a(E) p Fp 2008 3301 a(~) p Fl 2000 3301 a(!) p Fk 2064 3301 a(j) p Fl 2120 3301 a(<) p Fp 2223 3301 a(2) p Fl(\016) p Fm 2319 3260 a(2) p Fl 2358 3301 a(;) p Fj 2559 3262 a(d) p Fp 2448 3301 a(\() p Fl(x) p Fk 2564 3301 a(\000) p Fl 2664 3301 a(d) p Fi 2715 3316 a(j) p Fp 2751 3301 a(\)) p Fk 2811 3301 a(\001) p Fp 2871 3274 a(^) p Fl 2861 3301 a(\030) p 2936 3301 a(<) p Fk 3039 3301 a(\000) p Fp(1) p 3188 3301 a(+) p 3286 3301 a(3) p Fl(\016) p Fk 3382 3301 a(g) p Fl(:) p Fp 0 3532 a(W) p 92 3532 a(e) p 175 3532 a(no) m(w) p 385 3532 a(use) p 560 3532 a(the) p 735 3532 a(assumption) p 1258 3532 a(that) p Fl 1476 3532 a(!) p Fk 1580 3532 a(6) p Fp(=) 1712 3506 y(^) p Fl 1695 3532 a(d) p Fi 1746 3547 a(j) t(k) p Fp 1860 3532 a(and) p 2064 3532 a(~) p Fl 2057 3532 a(!) p Fk 2160 3532 a(6) p Fp(=) 2293 3506 y(^) p Fl 2276 3532 a(d) p Fi 2327 3547 a(j) t(k) p Fp 2401 3532 a(.) p 2492 3532 a(This) p 2722 3532 a(assumption) p 3245 3532 a(implies) 0 3652 y(that) p 212 3652 a(the) p 380 3652 a(outgoing) p 781 3652 a(classical) p 1157 3652 a(particle) p 1509 3652 a(starting) p 1874 3652 a(from) p 2104 3652 a(supp) p Fl 2322 3652 a(T) p Fi 2379 3667 a(j) p Fh 2412 3667 a(1) p Fp 2519 3652 a(at) p Fl 2639 3652 a(t) p Fp 2702 3652 a(=) p 2806 3652 a(0) p 2888 3652 a(passes) p 3183 3652 a(far) p 3332 3652 a(a) m(w) m(a) m(y) 0 3773 y(from) p 242 3773 a(all) p 389 3773 a(the) p 568 3773 a(cen) m(ters) p Fl 908 3773 a(d) p Fi 959 3788 a(k) p Fp 1045 3773 a(for) p Fl 1206 3773 a(t) p 1288 3773 a(>) p Fp 1411 3773 a(0) p 1504 3773 a(and) p 1705 3773 a(mo) m(v) m(es) p 2007 3773 a(lik) m(e) p 2197 3773 a(the) p 2377 3773 a(free) p 2575 3773 a(particle.) p 3000 3773 a(This) p 3234 3773 a(enables) 0 3893 y(us) p 127 3893 a(to) p 249 3893 a(construct) p 680 3893 a(an) p 818 3893 a(appro) m(ximation) p 1470 3893 a(to) p Fl 1592 3893 a(R) p Fp 1667 3893 a(\() p Fl(E) p Fp 1807 3893 a(+) p Fl 1906 3893 a(i) p Fp(0;) p Fl 2032 3893 a(H) p Fi 2113 3908 a(d) p Fp 2153 3893 a(\)) p Fl(T) p Fi 2248 3908 a(j) p Fh 2281 3908 a(1) p Fp 2390 3893 a(in) p 2507 3893 a(a) p 2590 3893 a(form) p 2823 3893 a(similar) p 3145 3893 a(to) p 3267 3893 a(\(3.19\).) 0 4014 y(Similarly) p 425 4014 a(the) p 603 4014 a(incoming) p 1030 4014 a(particle) p 1392 4014 a(starting) p 1766 4014 a(from) p 2007 4014 a(supp) 2243 3988 y(~) p Fl 2224 4014 a(T) p Fi 2281 4029 a(j) p Fh 2314 4029 a(1) p Fp 2431 4014 a(do) s(es) p 2661 4014 a(not) p 2845 4014 a(pass) p 3067 4014 a(around) p 3408 4014 a(the) 0 4134 y(cen) m(ters) p 324 4134 a(for) p Fl 469 4134 a(t) p 532 4134 a(<) p Fp 635 4134 a(0,) p 740 4134 a(and) p Fl 925 4134 a(R) p Fp 1000 4134 a(\() p Fl(E) p Fk 1130 4134 a(\000) p Fl 1220 4134 a(i) p Fp(0;) p Fl 1346 4134 a(H) p Fi 1427 4149 a(d) p Fp 1468 4134 a(\)) 1525 4109 y(~) p Fl 1506 4134 a(T) p Fi 1563 4149 a(j) p Fh 1596 4149 a(1) p Fp 1698 4134 a(can) p 1872 4134 a(b) s(e) p 2001 4134 a(appro) m(ximated) p 2614 4134 a(as) p 2730 4134 a(in) p 2839 4134 a(\(3.20\).) p 3157 4134 a(Since) p 3408 4134 a(the) 0 4254 y(outgoing) p 398 4254 a(and) p 584 4254 a(incoming) p 998 4254 a(particles) p 1385 4254 a(do) p 1517 4254 a(not) p 1687 4254 a(tak) m(e) p 1895 4254 a(momen) m(tum) p 2404 4254 a(around) p Fk 2731 4170 a(p) p 2814 4170 V Fl 2814 4254 a(E) p Fp 2900 4254 a(~) p Fl 2892 4254 a(!) p Fp 2986 4254 a(and) p Fk 3172 4170 a(p) p 3255 4170 V Fl 3255 4254 a(E) p 3333 4254 a(!) p Fp 3427 4254 a(for) p Fl 0 4375 a(t) p 63 4375 a(>) p Fp 166 4375 a(0) p 248 4375 a(and) p Fl 437 4375 a(t) p 500 4375 a(<) p Fp 604 4375 a(0) p 685 4375 a(resp) s(ectiv) m (ely) p 1173 4375 a(,) p 1236 4375 a(w) m(e) p 1379 4375 a(obtain) p 1683 4375 a(b) m(y) p 1818 4375 a(Theorem) p 2230 4375 a(4.1) p 2387 4375 a(that) 573 4570 y(~) p Fl 554 4595 a(T) p Fh 625 4554 a(\003) p Fi 611 4619 a(k) p Fl 664 4595 a(R) p Fp 739 4595 a(\() p Fl(E) p Fp 877 4595 a(+) p Fl 975 4595 a(i) p Fp(0;) p Fl 1101 4595 a(H) p Fi 1182 4610 a(d) p Fp 1222 4595 a(\)) p Fl(T) p Fi 1317 4610 a(j) p Fh 1350 4610 a(1) p Fp 1452 4595 a(=) p 1560 4595 a(~) p Fl 1555 4595 a(r) p Fi 1599 4610 a(L) p Fl 1651 4595 a(;) p 1890 4595 a(T) p Fh 1961 4554 a(\003) p Fi 1947 4619 a(k) p Fl 2000 4595 a(R) p Fp 2075 4595 a(\() p Fl(E) p Fk 2214 4595 a(\000) p Fl 2313 4595 a(i) p Fp(0;) p Fl 2439 4595 a(H) p Fi 2520 4610 a(d) p Fp 2560 4595 a(\)) 2617 4570 y(~) p Fl 2598 4595 a(T) p Fi 2655 4610 a(j) p Fh 2688 4610 a(1) p Fp 2790 4595 a(=) p 2898 4595 a(~) p Fl 2894 4595 a(r) p Fi 2938 4610 a(L) p Fp 3343 4595 a(\(4.9\)) 0 4815 y(for) p 149 4815 a(an) m(y) p Fl 333 4815 a(L) p Fk 427 4815 a(\035) p Fp 554 4815 a(1,) p 663 4815 a(where) p 949 4815 a(~) p Fl 944 4815 a(r) p Fi 988 4830 a(L) p Fp 1068 4815 a(:) p Fl 1123 4815 a(L) p Fm 1189 4779 a(2) p Fk 1256 4815 a(!) p Fl 1383 4815 a(L) p Fm 1449 4779 a(2) p Fp 1522 4815 a(has) p 1695 4815 a(the) p 1863 4815 a(prop) s(ert) m(y) p 2261 4815 a(\(3.17\).) p 2581 4815 a(W) p 2673 4815 a(e) p 2749 4815 a(can) p 2927 4815 a(also) p 3123 4815 a(sho) m(w) p 3364 4815 a(that) 1212 5010 y(~) p Fl 1193 5035 a(T) p Fh 1264 4994 a(\003) p Fi 1250 5059 a(k) p Fh 1289 5059 a(1) p Fl 1363 5035 a(R) p Fp 1438 5035 a(\() p Fl(E) p Fp 1576 5035 a(+) p Fl 1674 5035 a(i) p Fp(0;) p Fl 1800 5035 a(H) p Fi 1881 5050 a(d) p Fp 1921 5035 a(\)) p Fl(T) p Fi 2016 5050 a(j) p Fh 2049 5050 a(1) p Fp 2151 5035 a(=) p 2259 5035 a(~) p Fl 2255 5035 a(r) p Fi 2299 5050 a(L) p Fp 3294 5035 a(\(4.10\)) 0 5255 y(and) p 190 5255 a(hence) p 461 5255 a(w) m(e) p 604 5255 a(ha) m(v) m(e) 716 5475 y(\() p Fl(R) p Fp 829 5475 a(\() p Fl(E) p Fp 967 5475 a(+) p Fl 1065 5475 a(i) p Fp(0;) p Fl 1191 5475 a(H) p Fi 1272 5490 a(d) p Fp 1312 5475 a(\)) p Fl(T) p Fi 1407 5490 a(j) p Fh 1440 5490 a(1) p Fl 1515 5475 a(') p Fm 1579 5490 a(0) p Fp 1618 5475 a(\() p Fl(!) t(;) p 1765 5475 a(E) p Fp 1843 5475 a(\)) p Fl(;) p Fp 1943 5450 a(~) p Fl 1925 5475 a(T) p Fi 1982 5490 a(k) p Fh 2021 5490 a(1) p Fl 2094 5475 a(') p Fm 2158 5490 a(0) p Fp 2197 5475 a(\() p 2243 5475 a(~) p Fl 2235 5475 a(!) t(;) p 2344 5475 a(E) p Fp 2422 5475 a(\)\)) p 2525 5475 a(=) p Fl 2628 5475 a(o) p Fp(\(1\)) p Fl(:) p Fp 3294 5475 a(\(4.11\)) 1723 5753 y(18) p 90 rotate dyy eop %%Page: 19 19 19 18 bop Fp 0 407 a(The) p 202 407 a(rigorous) p 577 407 a(pro) s(of) p 833 407 a(of) p 946 407 a(\(4.9\)) p 1180 407 a(and) p 1371 407 a(\(4.10\)) p 1654 407 a(requires) p 2021 407 a(the) p 2191 407 a(lemma) p 2506 407 a(b) s(elo) m(w) p 2784 407 a(\(Lemma) p 3171 407 a(4.1\).) p 3408 407 a(W) p 3500 407 a(e) 0 527 y(pro) m(v) m(e) p 266 527 a(them) p 518 527 a(after) p 751 527 a(completing) p 1253 527 a(the) p 1424 527 a(pro) s(of) p 1681 527 a(of) p 1796 527 a(the) p 1966 527 a(theorem.) p 2393 527 a(If) p 2493 527 a(w) m(e) p 2640 527 a(use) p 2811 527 a(\(4.7\)) p 3047 527 a(in) p 3164 527 a(Theorem) 0 648 y(4.1,) p 184 648 a(then) 800 768 y(\() p Fl(R) p Fp 913 768 a(\() p Fl(E) p Fp 1051 768 a(+) p Fl 1149 768 a(i) p Fp(0;) p Fl 1275 768 a(H) p Fi 1356 783 a(d) p Fp 1397 768 a(\)) p Fl(T) p Fi 1492 783 a(j) p Fl 1528 768 a(') p Fm 1592 783 a(0) p Fp 1631 768 a(\() p Fl(!) t(;) p 1778 768 a(E) p Fp 1856 768 a(\)) p Fl(;) p Fp 1956 743 a(~) p Fl 1938 768 a(T) p Fi 1995 783 a(k) p Fl 2037 768 a(') p Fm 2101 783 a(0) p Fp 2140 768 a(\() p 2186 768 a(~) p Fl 2178 768 a(!) t(;) p 2287 768 a(E) p Fp 2365 768 a(\)\)) p 2468 768 a(=) p Fl 2571 768 a(o) p Fp(\(1\)) 0 931 y(for) p Fl 149 931 a(j) p Fk 223 931 a(6) p Fp(=) p Fl 326 931 a(k) p Fp 380 931 a(,) p 440 931 a(and) p 630 931 a(hence) p 901 931 a(it) p 998 931 a(follo) m(ws) p 1318 931 a(from) p 1549 931 a(\(4.8\)) p 1782 931 a(that) p Fl 385 1200 a(f) p Fi 433 1215 a(d) p Fp 501 1200 a(=) p 605 1200 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 834 1200 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1029 1200 a(\)) p Fi 1113 1093 a(N) p Fj 1084 1117 a(X) p Fi 1083 1300 a(j) p Fm 1116 1300 a(=1) p Fp 1206 1200 a(\() p Fl(R) p Fp 1319 1200 a(\() p Fl(E) p Fp 1457 1200 a(+) p Fl 1555 1200 a(i) p Fp(0;) p Fl 1681 1200 a(H) p Fi 1762 1215 a(d) p Fp 1802 1200 a(\)) p Fl(T) p Fi 1897 1215 a(j) p Fl 1933 1200 a(') p Fm 1997 1215 a(0) p Fp 2037 1200 a(\() p Fl(!) t(;) p 2184 1200 a(E) p Fp 2262 1200 a(\)) p Fl(;) p Fp 2362 1175 a(~) p Fl 2344 1200 a(T) p Fi 2401 1215 a(j) p Fl 2436 1200 a(') p Fm 2500 1215 a(0) p Fp 2539 1200 a(\() p 2585 1200 a(~) p Fl 2577 1200 a(!) t(;) p 2686 1200 a(E) p Fp 2764 1200 a(\)\)) p 2861 1200 a(+) p Fl 2959 1200 a(o) p Fp(\(1\)) p Fl(:) p Fp 0 1478 a(Let) p Fl 175 1478 a(H) p Fi 256 1493 a(j) p Fp 320 1478 a(=) p Fl 423 1478 a(H) p Fp 512 1478 a(\() p Fl(A) p Fi 623 1493 a(j) p Fp 659 1478 a(\)) p 730 1478 a(b) s(e) p 863 1478 a(as) p 982 1478 a(in) p 1096 1478 a(\(1.6\).) p 1367 1478 a(W) p 1459 1478 a(e) p 1535 1478 a(claim) p 1795 1478 a(that) p Fk 649 1673 a(k) p Fl(s) p Fi 745 1688 a(j) p Fp 798 1673 a(\() p Fl(R) p Fp 911 1673 a(\() p Fl(E) p Fk 1049 1673 a(\006) p Fl 1149 1673 a(i) p Fp(0;) p Fl 1275 1673 a(H) p Fi 1356 1688 a(d) p Fp 1396 1673 a(\)) p Fk 1456 1673 a(\000) p Fl 1556 1673 a(R) p Fp 1631 1673 a(\() p Fl(E) p Fk 1769 1673 a(\006) p Fl 1869 1673 a(i) p Fp(0;) p Fl 1995 1673 a(H) p Fi 2076 1688 a(j) p Fp 2112 1673 a(\)\)) p Fl 2204 1673 a(s) p Fi 2250 1688 a(j) p Fk 2287 1673 a(k) p Fp 2364 1673 a(=) p Fl 2468 1673 a(O) p Fp 2546 1673 a(\() p Fl(d) p Fh 2635 1632 a(\000) p Fm(1+) p Fi(c\033) p Fp 2856 1673 a(\)) p 3294 1673 a(\(4.12\)) 0 1867 y(for) p 152 1867 a(some) p Fl 399 1867 a(c) p 474 1867 a(>) p Fp 582 1867 a(0.) p 710 1867 a(This) p 936 1867 a(is) p 1037 1867 a(also) p 1235 1867 a(v) m(eri\014ed) p 1580 1867 a(after) p 1813 1867 a(the) p 1984 1867 a(completion) p 2485 1867 a(of) p 2599 1867 a(the) p 2770 1867 a(pro) s(of.) p 3072 1867 a(The) p 3275 1867 a(b) s(ound) 0 1988 y(yields) p Fl 387 2251 a(f) p Fi 435 2266 a(d) p Fp 503 2251 a(=) p 607 2251 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 836 2251 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1031 2251 a(\)) p Fi 1115 2143 a(N) p Fj 1086 2168 a(X) p Fi 1085 2350 a(j) p Fm 1118 2350 a(=1) p Fp 1208 2251 a(\() p Fl(R) p Fp 1321 2251 a(\() p Fl(E) p Fp 1459 2251 a(+) p Fl 1557 2251 a(i) p Fp(0;) p Fl 1683 2251 a(H) p Fi 1764 2266 a(j) p Fp 1800 2251 a(\)) p Fl(T) p Fi 1895 2266 a(j) p Fl 1931 2251 a(') p Fm 1995 2266 a(0) p Fp 2035 2251 a(\() p Fl(!) t(;) p 2182 2251 a(E) p Fp 2260 2251 a(\)) p Fl(;) p Fp 2360 2226 a(~) p Fl 2342 2251 a(T) p Fi 2399 2266 a(j) p Fl 2434 2251 a(') p Fm 2498 2266 a(0) p Fp 2537 2251 a(\() p 2583 2251 a(~) p Fl 2575 2251 a(!) t(;) p 2684 2251 a(E) p Fp 2762 2251 a(\)\)) p 2859 2251 a(+) p Fl 2958 2251 a(o) p Fp(\(1\)) p Fl(:) p Fp 0 2523 a(If) p Fl 98 2523 a(k) p Fk 179 2523 a(6) p 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3496 a(O) p Fp 3021 3496 a(\() p Fl(d) p Fh 3110 3455 a(\000) p Fm(1+) p Fi(\033) p Fp 3301 3496 a(\)) p Fl(:) p Fp 0 3691 a(Th) m(us) p 247 3691 a(Lemma) p 595 3691 a(2.2) p 752 3691 a(completes) p 1203 3691 a(the) p 1371 3691 a(pro) s(of.) p Fe 1663 3691 a(2) p Fp 146 3854 a(W) p 238 3854 a(e) p 312 3854 a(pro) s(ceed) p 669 3854 a(to) p 786 3854 a(the) p 951 3854 a(pro) s(of) p 1203 3854 a(of) p 1311 3854 a(\(4.9\),) p 1569 3854 a(\(4.10\)) p 1848 3854 a(and) p 2035 3854 a(\(4.12\)) p 2314 3854 a(whic) m(h) p 2590 3854 a(remain) p 2913 3854 a(unpro) m(v) m(ed.) p 3375 3854 a(The) 0 3974 y(pro) s(of) p 257 3974 a(of) p 370 3974 a(\(4.9\)) p 605 3974 a(and) p 797 3974 a(\(4.10\)) p 1081 3974 a(uses) p 1290 3974 a(the) p 1461 3974 a(follo) m(wing) p 1875 3974 a(lemma.) p 2233 3974 a(The) p 2436 3974 a(lemma) p 2753 3974 a(is) p 2853 3974 a(a) p 2936 3974 a(sp) s(ecial) p 3256 3974 a(case) p 3465 3974 a(of) 0 4095 y([5,) p 135 4095 a(Theorem) p 547 4095 a(1].) p Fq 0 4336 a(Lemma) p 397 4336 a(4.1) p Fo 589 4336 a(L) p 645 4336 a(et) p Fl 757 4336 a(g) p Fh 804 4351 a(\006) p Fp 863 4336 a(\() p Fl(x) p Fp(\)) p Fo 1029 4336 a(and) p Fl 1219 4336 a(f) p Fh 1267 4351 a(\006) p Fp 1326 4336 a(\() p Fl(\030) p Fp 1412 4336 a(\)) p Fo 1484 4336 a(b) p 1524 4336 a(e) p 1603 4336 a(smo) p 1768 4336 a(oth) p 1935 4336 a(b) p 1975 4336 a(ounde) p 2222 4336 a(d) p 2306 4336 a(functions) p 2729 4336 a(such) p 2951 4336 a(that) p Fp 678 4531 a(supp) p Fl 896 4531 a(g) p Fh 943 4546 a(\006) p Fk 1029 4531 a(\032) p 1135 4531 a(fj) p Fl(x) p Fk(j) p Fl 1323 4531 a(>) p 1426 4531 a(c) p Fk(g) p Fl(;) p Fp 1761 4531 a(supp) p Fl 1979 4531 a(f) p Fh 2027 4546 a(\006) p Fk 2114 4531 a(\032) p 2219 4531 a(f) p Fp(1) p Fl(=c) p 2436 4531 a(<) p Fk 2539 4531 a(j) p Fl(\030) p Fk 2615 4531 a(j) p Fl 2670 4531 a(<) p 2773 4531 a(c) p Fk(g) p Fo 0 4726 a(for) p 156 4726 a(some) p Fl 405 4726 a(c) p 474 4726 a(>) p Fp 578 4726 a(1) p Fo(.) p 701 4726 a(Assume) p 1065 4726 a(that) p 1265 4726 a(ther) p 1428 4726 a(e) p 1507 4726 a(exists) p Fl 1774 4726 a(\026;) p Fp 1911 4726 a(0) p Fl 1988 4726 a(<) p 2091 4726 a(\026) p 2177 4726 a(<) p Fp 2281 4726 a(1) p Fo(,) p 2395 4726 a(such) p 2616 4726 a(that) p Fk 870 4920 a(\006) p Fp 953 4920 a(^) p Fl 947 4920 a(x) p Fk 1025 4920 a(\001) p Fp 1085 4894 a(^) p Fl 1074 4920 a(\030) p 1149 4920 a(>) p Fk 1253 4920 a(\000) p Fl(\026;) p Fp 1533 4920 a(\() p Fl(x;) p 1670 4920 a(\030) p Fp 1718 4920 a(\)) p Fk 1783 4920 a(2) p Fp 1877 4920 a(supp) p Fl 2094 4920 a(g) p Fh 2141 4935 a(\006) p Fk 2222 4920 a(\002) p Fp 2322 4920 a(supp) p Fl 2540 4920 a(f) p Fh 2588 4935 a(\006) p Fl 2647 4920 a(:) p Fo 0 5115 a(If) p Fl 102 5115 a(\027) p Fk 184 5115 a(\035) p Fp 312 5115 a(1) p Fo(,) p 425 5115 a(then) p Fl 642 5115 a(R) p Fp 717 5115 a(\() p Fl(E) p Fk 855 5115 a(\006) p Fl 955 5115 a(i) p Fp(0;) p Fl 1081 5115 a(H) p Fm 1162 5130 a(0) p Fp 1201 5115 a(\)) p Fo 1274 5115 a(satis\014es) p Fk 266 5309 a(k) p Fl(r) p Fi 360 5325 a(\027) t(=) p Fm(2) p Fl 474 5309 a(R) p Fp 549 5309 a(\() p Fl(E) p Fp 687 5309 a(+) p Fl 785 5309 a(i) p Fp(0;) p Fl 911 5309 a(H) p Fm 992 5324 a(0) p Fp 1031 5309 a(\)) p Fl(f) p Fm 1117 5324 a(+) p Fl 1176 5309 a(g) p Fm 1223 5324 a(+) p Fl 1282 5309 a(r) p Fh 1326 5325 a(\000) p Fi(\027) t(=) p Fm(3) p Fk 1494 5309 a(k) p Fp 1566 5309 a(+) p Fk 1664 5309 a(k) p Fl(r) p Fi 1758 5325 a(\027) t(=) p Fm(2) p Fl 1872 5309 a(R) p Fp 1947 5309 a(\() p Fl(E) p Fk 2085 5309 a(\000) p Fl 2185 5309 a(i) p Fp(0;) p Fl 2311 5309 a(H) p Fm 2392 5324 a(0) p Fp 2431 5309 a(\)) p Fl(f) p Fh 2517 5324 a(\000) p Fl 2576 5309 a(g) p Fh 2623 5324 a(\000) p Fl 2682 5309 a(r) p Fh 2726 5325 a(\000) p Fi(\027) t(=) p Fm(3) p Fk 2894 5309 a(k) p Fp 2972 5309 a(=) p Fl 3075 5309 a(O) p Fp 3153 5309 a(\(1\)) p Fo 0 5504 a(as) p Fl 125 5504 a(d) p Fk 203 5504 a(!) p 330 5504 a(1) p Fo(,) p 495 5504 a(wher) p 691 5504 a(e) p Fl 770 5504 a(f) p Fh 818 5519 a(\006) p Fp 905 5504 a(=) p Fl 1008 5504 a(f) p Fh 1056 5519 a(\006) p Fp 1115 5504 a(\() p Fl(D) p Fi 1234 5519 a(x) p Fp 1278 5504 a(\)) p Fo(.) p Fp 1723 5753 a(19) p 90 rotate dyy eop %%Page: 20 20 20 19 bop Fo 146 407 a(Pr) p 248 407 a(o) p 293 407 a(of.) p Fp 501 407 a(W) p 593 407 a(e) p 668 407 a(pro) m(v) m(e) p 931 407 a(the) p 1099 407 a(lemma) p 1414 407 a(for) p Fl 1563 407 a(R) p Fp 1638 407 a(\() p Fl(E) p Fp 1776 407 a(+) p Fl 1874 407 a(i) p Fp(0;) p Fl 2000 407 a(H) p Fm 2081 422 a(0) p Fp 2120 407 a(\)) p 2190 407 a(only) p 2363 407 a(.) p 2434 407 a(Set) p Fl 1067 627 a(G) p Fp(\() p Fl(t) p Fp(\)) p 1282 627 a(=) p Fl 1386 627 a(r) p Fi 1430 642 a(\027) t(=) p Fm(2) p Fp 1560 627 a(exp) q(\() p Fk(\000) p Fl(itH) p Fm 1973 642 a(0) p Fp 2013 627 a(\)) p Fl(f) p Fm 2099 642 a(+) p Fl 2158 627 a(g) p Fm 2205 642 a(+) p Fl 2264 627 a(r) p Fh 2308 642 a(\000) p Fi(\027) t(=) p Fm(3) p Fp 0 847 a(for) p Fl 149 847 a(t) p 212 847 a(>) p Fp 315 847 a(0.) p 435 847 a(Then) p Fl 760 1077 a(r) p Fi 804 1092 a(\027) t(=) p Fm(2) p Fl 918 1077 a(R) p Fp 993 1077 a(\() p Fl(E) p Fp 1131 1077 a(+) p Fl 1229 1077 a(i) p Fp(0;) p Fl 1355 1077 a(H) p Fm 1436 1092 a(0) p Fp 1475 1077 a(\)) p Fl(f) p Fm 1561 1092 a(+) p Fl 1620 1077 a(g) p Fm 1667 1092 a(+) p Fl 1726 1077 a(r) p Fh 1770 1092 a(\000) p Fi(\027) t(=) p Fm(3) p Fp 1966 1077 a(=) p Fl 2070 1077 a(i) p Fj 2137 960 a(Z) p Fh 2220 986 a(1) p Fm 2183 1148 a(0) p Fl 2311 1077 a(e) p Fi 2356 1036 a(itE) p Fl 2465 1077 a(G) p Fp(\() p Fl(t) p Fp(\)) p Fl 2670 1077 a(dt:) p Fp 0 1331 a(The) p 201 1331 a(op) s(erator) p Fl 593 1331 a(G) p Fp(\() p Fl(t) p Fp(\)) p 814 1331 a(has) p 988 1331 a(the) p 1156 1331 a(k) m(ernel) p Fl 365 1588 a(G) p Fp(\() p Fl(t;) p 559 1588 a(x;) p 658 1588 a(y) p Fp 710 1588 a(\)) p 775 1588 a(=) p 878 1588 a(\(2) p Fl(\031) p Fp 1024 1588 a(\)) p Fh 1062 1547 a(\000) p Fm(2) p Fl 1156 1588 a(r) p Fi 1200 1604 a(\027) t(=) p Fm(2) p Fp 1314 1588 a(\() p Fl(x) p Fp(\)) p Fj 1462 1467 a(\022) 1523 1471 y(Z) p Fl 1622 1588 a(e) p 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1850 a(;) p 2589 1850 a(y) p Fp 2641 1850 a(\)) p Fk(j) p 2754 1850 a(\025) p Fl 2880 1850 a(c) p Fp 2939 1850 a(\() p Fl 2976 1850 a(t) p Fp 3034 1850 a(+) p Fk 3132 1850 a(j) p Fl(y) p Fk 3212 1850 a(j) p Fp(\)) p 3321 1850 a(when) 0 1970 y(\() p Fl(y) t(;) p 134 1970 a(\030) p Fp 182 1970 a(\)) p Fk 246 1970 a(2) p Fp 340 1970 a(supp) p Fl 558 1970 a(g) p Fm 605 1985 a(+) p Fk 685 1970 a(\002) p Fp 785 1970 a(supp) p Fl 1003 1970 a(f) p Fm 1051 1985 a(+) p Fp 1110 1970 a(.) p 1180 1970 a(If) p Fl 1278 1970 a(\027) p Fk 1360 1970 a(\035) p Fp 1487 1970 a(1,) p 1596 1970 a(then) p 1818 1970 a(partial) p 2132 1970 a(in) m(tegration) p 2628 1970 a(yields) p Fk 806 2190 a(j) p Fl(G) p Fp(\() p Fl(t;) p 1028 2190 a(x;) p 1127 2190 a(y) p Fp 1179 2190 a(\)) p Fk(j) p 1271 2190 a(\024) p Fl 1376 2190 a(c) p Fp 1435 2190 a(\() p Fl 1472 2190 a(t) p Fp 1530 2190 a(+) p 1628 2190 a(1\)) p Fh 1715 2142 a(\000) p Fm(2) p Fp 1825 2190 a(\() p Fk(j) p Fl(x) p Fk(j) p Fp 1996 2190 a(+) p 2094 2190 a(1\)) p Fh 2181 2142 a(\000) p Fm(2) p Fp 2292 2190 a(\() p Fk(j) p Fl(y) p Fk 2410 2190 a(j) p Fp 2459 2190 a(+) p 2557 2190 a(1\)) p Fh 2643 2142 a(\000) p Fm(2) p Fp 0 2410 a(uniformly) p 444 2410 a(in) p Fl 558 2410 a(d) p Fk 637 2410 a(\035) p Fp 764 2410 a(1.) p 883 2410 a(This) p 1106 2410 a(pro) m(v) m(es) p 1407 2410 a(the) p 1575 2410 a(lemma.) p Fe 1927 2410 a(2) p Fp 146 2581 a(W) p 238 2581 a(e) p 322 2581 a(shall) p 557 2581 a(pro) m(v) m(e) p 828 2581 a(\(4.9\).) p 1121 2581 a(As) p 1273 2581 a(stated) p 1573 2581 a(ab) s(o) m(v) m(e,) p 1886 2581 a(the) p 2061 2581 a(outgoing) p 2470 2581 a(classical) p 2852 2581 a(particle) p 3212 2581 a(starting) 0 2701 y(from) p 240 2701 a(supp) p Fl 458 2701 a(T) p Fi 515 2716 a(j) p Fh 548 2716 a(1) p Fp 665 2701 a(at) p Fl 794 2701 a(t) p Fp 874 2701 a(=) p 995 2701 a(0) p 1086 2701 a(mo) m(v) m(es) p 1387 2701 a(lik) m(e) p 1576 2701 a(the) p 1754 2701 a(free) p 1951 2701 a(particle) p 2313 2701 a(and) p 2513 2701 a(do) p 2659 2701 a(not) p 2842 2701 a(tak) m(e) p 3064 2701 a(momen) m(tum) 0 2821 y(around) p Fk 339 2737 a(p) p 422 2737 79 4 v Fl 422 2821 a(E) p Fp 508 2821 a(~) p Fl 500 2821 a(!) p Fp 606 2821 a(for) p Fl 764 2821 a(t) p 842 2821 a(>) p Fp 960 2821 a(0.) p 1106 2821 a(Let) p Fl 1290 2821 a(\014) p Fm 1345 2836 a(1) p Fp 1384 2821 a(\() p Fl(\030) p Fp 1470 2821 a(\)) p 1549 2821 a(b) s(e) p 1690 2821 a(a) p 1781 2821 a(smo) s(oth) p 2134 2821 a(sym) m(b) s(ol) p 2477 2821 a(suc) m(h) p 2706 2821 a(that) p 2926 2821 a(it) p 3032 2821 a(has) p 3215 2821 a(supp) s(ort) 0 2942 y(around) p Fk 331 2858 a(p) p 414 2858 V Fl 414 2942 a(E) p 492 2942 a(!) p Fp 588 2942 a(and) p Fl 778 2942 a(\014) p Fm 833 2957 a(1) p Fp 873 2942 a(\() p Fl(\030) p Fp 959 2942 a(\)) p Fl(\014) p Fp 1058 2942 a(\() p Fl(\030) p Fp 1144 2942 a(\)) p 1208 2942 a(=) p Fl 1311 2942 a(\014) p Fp 1372 2942 a(\() p Fl(\030) p Fp 1458 2942 a(\).) p 1565 2942 a(W) p 1657 2942 a(e) p 1733 2942 a(write) p Fl 1983 2942 a(\014) p Fm 2038 2957 a(1) p Fp 2110 2942 a(for) p Fl 2259 2942 a(\014) p Fm 2314 2957 a(1) p Fp 2353 2942 a(\() p Fl(D) p Fi 2472 2957 a(x) p Fp 2516 2942 a(\).) p 2624 2942 a(Then) p 2879 2942 a(w) m(e) p 3023 2942 a(ha) m(v) m(e) 255 3137 y(~) p Fl 236 3162 a(T) p Fh 307 3121 a(\003) p Fi 293 3186 a(k) p Fl 346 3162 a(R) p Fp 421 3162 a(\() p Fl(E) p Fp 559 3162 a(+) p Fl 657 3162 a(i) p Fp(0;) p Fl 783 3162 a(H) p Fi 864 3177 a(d) p Fp 904 3162 a(\)) p Fl(T) p Fi 999 3177 a(j) p Fh 1032 3177 a(1) p Fp 1134 3162 a(=) p 1242 3162 a(~) p Fl 1238 3162 a(r) p Fi 1282 3177 a(L) p Fl 1334 3162 a(R) p Fp 1409 3162 a(\() p Fl(E) p Fp 1547 3162 a(+) p Fl 1645 3162 a(i) p Fp(0;) p Fl 1771 3162 a(H) p Fm 1852 3177 a(0) p Fp 1891 3162 a(\)) p Fl(\014) p Fm 1984 3177 a(1) p Fl 2023 3162 a(e) p Fh 2068 3121 a(\000) p Fi(i\022) p Fg 2180 3133 a(d) p Fl 2221 3162 a(T) p Fi 2278 3177 a(j) p Fh 2311 3177 a(1) p Fp 2407 3162 a(+) 2524 3137 y(~) p Fl 2505 3162 a(T) p Fh 2576 3121 a(\003) p Fi 2562 3186 a(k) p Fl 2615 3162 a(R) p Fp 2690 3162 a(\() p Fl(E) p Fp 2828 3162 a(+) p Fl 2926 3162 a(i) p Fp(0;) p Fl 3052 3162 a(H) p Fi 3133 3177 a(d) p Fp 3174 3162 a(\)) t(~) p Fl 3212 3162 a(r) p Fi 3256 3177 a(L) p Fp 0 3382 a(b) m(y) p 148 3382 a(\(3.19\).) p 505 3382 a(W) p 597 3382 a(e) p 685 3382 a(use) p 866 3382 a(Lemma) p 1226 3382 a(4.1) p 1396 3382 a(for) p 1557 3382 a(the) p 1738 3382 a(\014rst) p 1951 3382 a(op) s(erator) p 2356 3382 a(on) p 2504 3382 a(the) p 2685 3382 a(righ) m(t) p 2933 3382 a(side) p 3141 3382 a(and) p 3343 3382 a(\(4.4\)) 0 3502 y(in) p 124 3502 a(Theorem) p 545 3502 a(4.1) p 712 3502 a(for) p 871 3502 a(the) p 1049 3502 a(second) p 1374 3502 a(one) p 1562 3502 a(to) p 1691 3502 a(obtain) p 2005 3502 a(that) 2245 3477 y(~) p Fl 2226 3502 a(T) p Fh 2297 3466 a(\003) p Fi 2283 3527 a(k) p Fl 2336 3502 a(R) p Fp 2411 3502 a(\() p Fl(E) p Fp 2556 3502 a(+) p Fl 2660 3502 a(i) p Fp(0;) p Fl 2786 3502 a(H) p Fi 2867 3517 a(d) p Fp 2907 3502 a(\)) p Fl(T) p Fi 3002 3517 a(j) p Fh 3035 3517 a(1) p Fp 3154 3502 a(=) p 3279 3502 a(~) p Fl 3274 3502 a(r) p Fi 3318 3517 a(L) p Fp 3370 3502 a(.) p 3470 3502 a(A) 0 3623 y(similar) p 327 3623 a(argumen) m(t) p 769 3623 a(applies) p 1101 3623 a(to) p Fl 1227 3623 a(T) p Fh 1298 3586 a(\003) p Fi 1284 3647 a(k) p Fl 1337 3623 a(R) p Fp 1412 3623 a(\() p Fl(E) p Fk 1555 3623 a(\000) p Fl 1659 3623 a(i) p Fp(0;) p Fl 1785 3623 a(H) p Fi 1866 3638 a(d) p Fp 1906 3623 a(\)) 1963 3597 y(~) p Fl 1944 3623 a(T) p Fi 2001 3638 a(j) p Fh 2034 3638 a(1) p Fp 2108 3623 a(,) p 2176 3623 a(and) p 2372 3623 a(\(4.9\)) p 2611 3623 a(is) p 2716 3623 a(v) m(eri\014ed.) p 3114 3623 a(The) p 3321 3623 a(pro) s(of) 0 3743 y(of) p 110 3743 a(\(4.10\)) p 391 3743 a(is) p 488 3743 a(done) p 720 3743 a(in) p 833 3743 a(almost) p 1147 3743 a(the) p 1314 3743 a(same) p 1558 3743 a(w) m(a) m(y) p 1755 3743 a(as) p 1873 3743 a(\(4.9\).) p 2144 3743 a(W) p 2236 3743 a(e) p 2311 3743 a(construct) p 2739 3743 a(appro) m(ximations) p 3427 3743 a(for) p Fl 0 3863 a(R) p Fp 75 3863 a(\() p Fl(E) p Fp 215 3863 a(+) p Fl 314 3863 a(i) p Fp(0;) p Fl 440 3863 a(H) p Fi 521 3878 a(d) p Fp 561 3863 a(\)) p Fl(T) p Fi 656 3878 a(j) p Fh 689 3878 a(1) p Fp 798 3863 a(in) p 914 3863 a(the) p 1084 3863 a(form) p 1316 3863 a(\(3.19\)) p 1600 3863 a(and) p 1792 3863 a(for) p Fl 1943 3863 a(R) p Fp 2018 3863 a(\() p Fl(E) p Fk 2158 3863 a(\000) p Fl 2259 3863 a(i) p Fp(0;) p Fl 2385 3863 a(H) p Fi 2466 3878 a(d) p Fp 2506 3863 a(\)) 2563 3838 y(~) p Fl 2544 3863 a(T) p Fi 2601 3878 a(k) p Fh 2640 3878 a(1) p Fp 2749 3863 a(in) p 2864 3863 a(the) p 3035 3863 a(form) p 3267 3863 a(\(3.20\).) 0 3984 y(Then) p 255 3984 a(w) m(e) p 398 3984 a(ha) m(v) m(e) 528 4178 y(~) p Fl 509 4204 a(T) p Fh 580 4163 a(\003) p Fi 566 4228 a(k) p Fh 605 4228 a(1) p Fl 679 4204 a(R) p Fp 754 4204 a(\() p Fl(E) p Fp 893 4204 a(+) p Fl 991 4204 a(i) p Fp(0;) p Fl 1117 4204 a(H) p Fi 1198 4219 a(d) p Fp 1238 4204 a(\)) p Fl(T) p Fi 1333 4219 a(j) p Fh 1366 4219 a(1) p Fp 1468 4204 a(=) p 1576 4204 a(~) p Fl 1571 4204 a(r) p Fi 1615 4219 a(L) p Fp 1689 4204 a(+) p Fj 1787 4107 a(\020) p Fl 1837 4204 a(R) p Fp 1912 4204 a(\() p Fl(E) p Fk 2050 4204 a(\000) p Fl 2150 4204 a(i) p Fp(0;) p Fl 2276 4204 a(H) p Fi 2357 4219 a(d) p Fp 2397 4204 a(\)) 2454 4178 y(~) p Fl 2435 4204 a(T) p Fi 2492 4219 a(k) p Fh 2531 4219 a(1) p Fj 2605 4107 a(\021) p Fh 2655 4130 a(\003) p Fp 2715 4204 a(~) p Fl 2711 4204 a(r) p Fi 2755 4219 a(L) p Fp 2835 4204 a(=) p 2943 4204 a(~) p Fl 2938 4204 a(r) p Fi 2982 4219 a(L) p Fp 0 4436 a(b) m(y) p 135 4436 a(making) p 480 4436 a(use) p 648 4436 a(of) p 759 4436 a(Lemma) p 1107 4436 a(4.1) p 1265 4436 a(and) p 1454 4436 a(of) p 1565 4436 a(\(4.3\)) p 1798 4436 a(in) p 1912 4436 a(Theorem) p 2324 4436 a(4.1.) 146 4606 y(W) p 238 4606 a(e) p 316 4606 a(mo) m(v) m(e) p 571 4606 a(to) p 692 4606 a(the) p 862 4606 a(pro) s(of) p 1119 4606 a(of) p 1232 4606 a(\(4.12\).) p 1558 4606 a(This) p 1783 4606 a(is) p 1883 4606 a(obtained) p 2287 4606 a(as) p 2409 4606 a(an) p 2546 4606 a(immediate) p 3025 4606 a(consequence) 0 4727 y(of) p 111 4727 a(the) p 279 4727 a(fact) p 471 4727 a(that) p Fk 330 4947 a(k) p Fl(s) p Fi 426 4962 a(j) p Fp 479 4947 a(\() p Fl(R) p Fp 592 4947 a(\() p Fl(E) p Fk 731 4947 a(\006) p Fl 830 4947 a(i) p Fp(0;) p Fl 956 4947 a(H) p Fi 1037 4962 a(a) p Fp 1078 4947 a(\)) p Fk 1138 4947 a(\000) p Fl 1238 4947 a(R) p Fp 1313 4947 a(\() p Fl(E) p Fk 1451 4947 a(\006) p Fl 1551 4947 a(i) p Fp(0;) p Fl 1677 4947 a(H) p Fi 1758 4962 a(j) p Fp 1794 4947 a(\)\)) p Fl 1886 4947 a(s) p Fi 1932 4962 a(j) p Fk 1969 4947 a(k) p Fp 2046 4947 a(=) p Fl 2150 4947 a(O) p Fp 2228 4947 a(\() p Fl(d) p Fh 2317 4906 a(\000) p Fm(1+) p Fi(c\033) p Fp 2538 4947 a(\)) p Fl(;) p 2717 4947 a(j) p Fk 2791 4947 a(2) p Fl 2885 4947 a(a;) p Fp 3294 4947 a(\(4.13\)) 0 5167 y(for) p 146 5167 a(some) p Fl 388 5167 a(c) p 457 5167 a(>) p Fp 561 5167 a(0) p 639 5167 a(indep) s(enden) m(t) p 1189 5167 a(of) p Fl 1297 5167 a(\033) p Fp 1356 5167 a(,) p 1414 5167 a(and) p 1600 5167 a(the) p 1766 5167 a(pro) s(of) p 2017 5167 a(of) p 2126 5167 a(this) p 2313 5167 a(fact) p 2502 5167 a(is) p 2598 5167 a(based) p 2866 5167 a(on) p 2999 5167 a(the) p 3164 5167 a(follo) m(wing) 0 5287 y(lemma.) 1723 5753 y(20) p 90 rotate dyy eop %%Page: 21 21 21 20 bop Fq 0 407 a(Lemma) p 397 407 a(4.2) p Fo 589 407 a(Assume) p 958 407 a(that) p Fl 1162 407 a(m) p Fk 1284 407 a(2) p Fl 1388 407 a(a) p Fo 1479 407 a(and) p Fl 1673 407 a(\022) p Fk 1758 407 a(2) p Fl 1861 407 a(S) p Fm 1927 371 a(1) p Fo 2006 407 a(ful\014l) p 2198 407 a(l) p Fp 2263 407 a(\(3) p Fl(:) p Fp(12\)) p Fo(.) p 2602 407 a(L) p 2658 407 a(et) p Fl 2775 407 a(X) p Fh 2864 371 a(\006) p Fi 2856 431 a(am) p Fp 2997 407 a(=) p Fl 3110 407 a(X) p Fh 3199 371 a(\006) p Fi 3191 431 a(am) p Fp 3295 407 a(\() p Fl(\022) p Fp 3381 407 a(\)) p Fo 3459 407 a(b) p 3499 407 a(e) 0 527 y(de\014ne) p 245 527 a(d) p 327 527 a(by) p Fp 452 527 a(\(3) p Fl(:) p Fp(14\)) p Fo 734 527 a(and) p 921 527 a(let) p Fl 1056 527 a(b) p Fi 1097 542 a(j) p Fp 1134 527 a(\() p Fl(x) p Fp(\)) p Fo 1298 527 a(b) p 1338 527 a(e) p 1416 527 a(the) p 1576 527 a(char) p 1757 527 a(acteristic) p 2179 527 a(function) p 2561 527 a(of) p Fl 2673 527 a(B) p Fi 2747 542 a(j) p Fo 2817 527 a(de\014ne) p 3062 527 a(d) p 3144 527 a(by) p Fp 3269 527 a(\(4) p Fl(:) p Fp(1\)) p Fo(.) p Fp 146 697 a(\(1\)) p Fo 306 697 a(Assume) p 670 697 a(that) p Fl 869 697 a(H) p Fi 950 712 a(a) p Fo 1026 697 a(satisfy) p Fp 1330 697 a(\(4) p Fl(:) p Fp(4\)) p Fo(.) p 1605 697 a(If) p Fk 718 917 a(j) p Fl(x) p Fk 824 917 a(\000) p Fl 923 917 a(y) p Fk 997 917 a(\000) p Fp 1096 917 a(2) p Fl(t\030) p Fk 1228 917 a(j) p 1283 917 a(\025) p Fl 1388 917 a(c) p 1447 917 a(d) p Fi 1498 876 a(\033) p Fl 1544 917 a(;) p Fp 1688 917 a(\() p Fl(y) t(;) p 1822 917 a(\030) p Fp 1870 917 a(\)) p Fk 1933 917 a(2) p Fp 2028 917 a(supp) p Fl 2245 917 a(X) p Fm 2334 876 a(+) p Fi 2326 942 a(am) p Fl 2430 917 a(;) p 2520 917 a(x) p Fk 2604 917 a(2) p Fl 2698 917 a(B) p Fi 2772 932 a(l) p Fl 2798 917 a(;) p Fo 0 1137 a(for) p Fl 156 1137 a(t) p 219 1137 a(>) p Fp 322 1137 a(0) p Fo(,) p 436 1137 a(then) p Fl 652 1137 a(b) p Fi 693 1152 a(l) p Fl 720 1137 a(R) p Fp 795 1137 a(\() p Fl(E) p Fp 933 1137 a(+) p Fl 1031 1137 a(i) p Fp(0;) p Fl 1157 1137 a(H) p Fi 1238 1152 a(a) p Fp 1279 1137 a(\)) p Fl(X) p Fm 1406 1101 a(+) p Fi 1398 1162 a(am) p Fp 1530 1137 a(=) p 1638 1137 a(~) p Fl 1633 1137 a(r) p Fi 1677 1152 a(L) p Fo 1764 1137 a(for) p 1920 1137 a(any) p Fl 2107 1137 a(L) p Fk 2201 1137 a(\035) p Fp 2328 1137 a(1) p Fo(,) p 2442 1137 a(and) p 2631 1137 a(if) p Fk 718 1357 a(j) p Fl(x) p Fk 824 1357 a(\000) p Fl 923 1357 a(y) p Fk 997 1357 a(\000) p Fp 1096 1357 a(2) p Fl(t\030) p Fk 1228 1357 a(j) p 1283 1357 a(\025) p Fl 1388 1357 a(c) p 1447 1357 a(d) p Fi 1498 1316 a(\033) p Fl 1544 1357 a(;) p Fp 1688 1357 a(\() p Fl(y) t(;) p 1822 1357 a(\030) p Fp 1870 1357 a(\)) p Fk 1933 1357 a(2) p Fp 2028 1357 a(supp) p Fl 2245 1357 a(X) p Fh 2334 1316 a(\000) p Fi 2326 1382 a(am) p Fl 2430 1357 a(;) p 2520 1357 a(x) p Fk 2604 1357 a(2) p Fl 2698 1357 a(B) p Fi 2772 1372 a(l) p Fl 2798 1357 a(;) p Fo 0 1577 a(for) p Fl 156 1577 a(t) p 219 1577 a(<) p Fp 322 1577 a(0) p Fo(,) p 436 1577 a(then) p Fl 652 1577 a(X) p Fh 741 1541 a(\000) p Fi 733 1602 a(am) p Fl 837 1577 a(R) p Fp 912 1577 a(\() p Fl(E) p Fp 1051 1577 a(+) p Fl 1149 1577 a(i) p Fp(0;) p Fl 1275 1577 a(H) p Fi 1356 1592 a(a) p Fp 1397 1577 a(\)) p Fl(b) p Fi 1476 1592 a(l) p Fp 1530 1577 a(=) p 1638 1577 a(~) p Fl 1633 1577 a(r) p Fi 1677 1592 a(L) p Fo 1730 1577 a(.) p Fp 146 1748 a(\(2\)) p Fo 308 1748 a(L) p 364 1748 a(et) p Fl 478 1748 a(b) p Fp 552 1748 a(=) p Fl 659 1748 a(a) p Fk 734 1748 a(n) p 808 1748 a(f) p Fl(m) p Fk(g) p Fo(.) p 1074 1748 a(Assume) p 1440 1748 a(that) p Fl 1641 1748 a(H) p Fi 1722 1763 a(b) p Fo 1794 1748 a(satisfy) p Fp 2100 1748 a(\(4) p Fl(:) p Fp(4\)) p Fo(.) p 2382 1748 a(Then) p Fp 2638 1748 a(\(1\)) p Fo 2799 1748 a(holds) p 3051 1748 a(true) p 3258 1748 a(for) p 3416 1748 a(the) 0 1868 y(auxiliary) p 405 1868 a(op) p 500 1868 a(er) p 581 1868 a(ator) p Fl 788 1868 a(K) p Fi 871 1883 a(am) p Fp 975 1868 a(\() p Fl(\022) p Fp 1061 1868 a(\)) p Fo 1134 1868 a(de\014ne) p 1379 1868 a(d) p 1463 1868 a(by) p Fp 1590 1868 a(\(3) p Fl(:) p Fp(6\)) p Fo(.) p Fp 146 2038 a(\(3\)) p Fo 311 2038 a(The) p 515 2038 a(same) p 768 2038 a(statements) p 1259 2038 a(as) p Fp 1388 2038 a(\(1\)) p Fo 1552 2038 a(and) p Fp 1746 2038 a(\(2\)) p Fo 1910 2038 a(r) p 1946 2038 a(emain) p 2245 2038 a(true) p 2455 2038 a(for) p Fl 2616 2038 a(Y) p Fh 2694 2002 a(\006) p Fi 2673 2063 a(am) p Fp 2813 2038 a(=) p Fl 2925 2038 a(Y) p Fh 3003 2002 a(\006) p Fi 2982 2063 a(am) p Fp 3086 2038 a(\() p Fl(\022) p Fp 3172 2038 a(\)) p Fo 3249 2038 a(de\014ne) p 3494 2038 a(d) 0 2159 y(by) p Fp 127 2159 a(\(3) p Fl(:) p Fp(25\)) p Fo(.) 0 2437 y(Pr) p 102 2437 a(o) p 147 2437 a(of.) p Fp 354 2437 a(W) p 446 2437 a(e) p 533 2437 a(sho) m(w) p 786 2437 a(\(1\)) p 954 2437 a(only) p 1127 2437 a(.) p 1231 2437 a(The) p 1443 2437 a(same) p 1698 2437 a(argumen) m(t) p 2145 2437 a(applies) p 2482 2437 a(to) p 2612 2437 a(the) p 2791 2437 a(other) p 3057 2437 a(statemen) m(ts.) 0 2557 y(In) p 128 2557 a(particular,) p 613 2557 a(\(2\)) p 776 2557 a(follo) m(ws) p 1103 2557 a(from) p 1340 2557 a(relation) p 1703 2557 a(\(3.30\).) p 2042 2557 a(The) p 2249 2557 a(op) s(erator) p Fl 2648 2557 a(R) p Fp 2723 2557 a(\() p Fl(E) p Fp 2865 2557 a(+) p Fl 2968 2557 a(i) p Fp(0;) p Fl 3094 2557 a(H) p Fi 3175 2572 a(a) p Fp 3216 2557 a(\)) p Fl(X) p Fm 3343 2521 a(+) p Fi 3335 2582 a(am) p Fp 3478 2557 a(is) 0 2677 y(appro) m(ximated) p 624 2677 a(b) m(y) p 765 2677 a(\(3.19\).) p 1102 2677 a(By) p 1261 2677 a(assumption,) p 1811 2677 a(the) p 1984 2677 a(free) p 2177 2677 a(particle) p 2535 2677 a(starting) p 2905 2677 a(from) p 3141 2677 a(supp) p Fl 3358 2677 a(X) p Fm 3447 2641 a(+) p Fi 3439 2702 a(am) p Fp 0 2798 a(do) s(es) p 220 2798 a(not) p 394 2798 a(pass) p 607 2798 a(o) m(v) m(er) p Fl 816 2798 a(B) p Fi 890 2813 a(l) p Fp 948 2798 a(for) p Fl 1098 2798 a(t) p 1161 2798 a(>) p Fp 1265 2798 a(0.) p 1385 2798 a(This,) p 1635 2798 a(together) p 2020 2798 a(with) p 2243 2798 a(\(4.4\),) p 2503 2798 a(yields) p 2778 2798 a(the) p 2946 2798 a(desired) p 3277 2798 a(result.) p Fe 0 2918 a(2) p Fp 146 3088 a(W) p 238 3088 a(e) p 314 3088 a(shall) p 542 3088 a(pro) m(v) m(e) p 805 3088 a(\(4.13\).) p 1125 3088 a(W) p 1217 3088 a(e) p 1293 3088 a(tak) m(e) p Fl 1504 3088 a(m) p Fk 1617 3088 a(2) p Fl 1711 3088 a(a;) p 1839 3088 a(m) p Fk 1952 3088 a(6) p Fp(=) p Fl 2055 3088 a(j) p Fp 2101 3088 a(,) p 2161 3088 a(so) p 2281 3088 a(as) p 2401 3088 a(to) p 2520 3088 a(satisfy) p Fk 1209 3308 a(j) p Fl(d) p Fi 1288 3323 a(j) t(m) p Fk 1387 3308 a(j) p Fp 1442 3308 a(=) p 1546 3308 a(max) p Fk 1744 3308 a(fj) p Fl(d) p Fi 1873 3323 a(j) t(k) p Fk 1947 3308 a(j) p Fp 2002 3308 a(:) p Fl 2057 3308 a(k) p Fk 2139 3308 a(2) p Fl 2233 3308 a(a) p Fk(g) p Fp 0 3528 a(for) p Fl 164 3528 a(j) p Fk 263 3528 a(2) p Fl 382 3528 a(a) p Fp 480 3528 a(\014xed,) p 762 3528 a(although) p Fl 1183 3528 a(m) p Fp 1315 3528 a(is) p 1428 3528 a(not) p 1616 3528 a(necessarily) p 2117 3528 a(determined) p 2642 3528 a(uniquely) p 2995 3528 a(.) p 3111 3528 a(W) p 3203 3528 a(e) p 3294 3528 a(de\014ne) p Fl 0 3649 a(K) p Fi 83 3664 a(am) p Fp 215 3649 a(=) p Fl 318 3649 a(K) p Fi 401 3664 a(am) p Fp 505 3649 a(\() p Fl(\022) p Fp 591 3649 a(\)) p 662 3649 a(b) m(y) p 797 3649 a(\(3.6\)) p 1030 3649 a(with) p Fl 1252 3649 a(\022) p Fp 1328 3649 a(=) 1448 3623 y(^) p Fl 1431 3649 a(d) p Fi 1482 3664 a(j) t(m) p Fp 1581 3649 a(.) p 1651 3649 a(Let) p Fl 1826 3649 a( ) p Fi 1889 3664 a(m) p Fp 1988 3649 a(b) s(e) p 2121 3649 a(de\014ned) p 2456 3649 a(b) m(y) p 2592 3649 a(\(3.8\).) p 2863 3649 a(Then) p Fl 3117 3649 a(s) p Fi 3163 3664 a(j) p Fl 3200 3649 a( ) p Fi 3263 3664 a(m) p Fp 3357 3649 a(=) p Fl 3461 3649 a(s) p Fi 3507 3664 a(j) p Fp 0 3769 a(and) p 190 3769 a(w) m(e) p 333 3769 a(ha) m(v) m(e) p Fl 86 3989 a(s) p Fi 132 4004 a(j) p Fp 185 3989 a(\() p Fl(R) p Fp 298 3989 a(\() p Fl(E) p Fp 436 3989 a(+) p Fl 534 3989 a(i) p Fp(0;) p Fl 660 3989 a(H) p Fi 741 4004 a(a) p Fp 782 3989 a(\)) p Fk 842 3989 a(\000) p Fl 942 3989 a(R) p Fp 1017 3989 a(\() p Fl(E) p Fp 1155 3989 a(+) p Fl 1253 3989 a(i) p Fp(0;) p Fl 1379 3989 a(K) p Fi 1462 4004 a(am) p Fp 1566 3989 a(\)\)) p Fl 1659 3989 a(s) p Fi 1705 4004 a(j) p Fp 1769 3989 a(=) p Fl 1872 3989 a(s) p Fi 1918 4004 a(j) p Fl 1955 3989 a(R) p Fp 2030 3989 a(\() p Fl(E) p Fp 2168 3989 a(+) p Fl 2266 3989 a(i) p Fp(0;) p Fl 2392 3989 a(H) p Fi 2473 4004 a(a) p Fp 2514 3989 a(\)) p Fl(V) p Fi 2609 4004 a(am) p Fl 2713 3989 a(R) p Fp 2788 3989 a(\() p Fl(E) p Fp 2926 3989 a(+) p Fl 3024 3989 a(i) p Fp(0;) p Fl 3150 3989 a(K) p Fi 3233 4004 a(am) p Fp 3337 3989 a(\)) p Fl(s) p Fi 3421 4004 a(j) p Fp 0 4220 a(b) m(y) p 129 4220 a(Lemma) p 471 4220 a(3.1.) p 664 4220 a(It) p 764 4220 a(follo) m(ws) p 1078 4220 a(from) p 1302 4220 a(\(1.3\)) p 1529 4220 a(and) p 1713 4220 a(\(1.4\)) p 1940 4220 a(that) p Fl 2145 4220 a(m) p Fk 2258 4220 a(2) p Fl 2352 4220 a(a) p Fp 2430 4220 a(and) p Fl 2613 4220 a(\022) p Fp 2689 4220 a(=) 2810 4194 y(^) p Fl 2792 4220 a(d) p Fi 2843 4235 a(j) t(m) p Fp 2968 4220 a(satisfy) p 3267 4220 a(\(3.12\).) 0 4341 y(W) p 92 4341 a(e) p 174 4341 a(decomp) s(ose) p Fl 671 4341 a(V) p Fi 728 4356 a(am) p Fp 870 4341 a(=) p Fl 984 4341 a(V) p Fi 1041 4356 a(am) p Fp 1145 4341 a(\() p Fl(\022) p Fp 1231 4341 a(\)) p 1308 4341 a(as) p 1433 4341 a(in) p 1553 4341 a(\(3.14\)) p 1841 4341 a(and) p 2037 4341 a(apply) p 2311 4341 a(Lemma) p 2666 4341 a(4.2) p 2829 4341 a(to) p 2954 4341 a(t) m(w) m(o) p 3144 4341 a(op) s(erators) p Fl 0 4461 a(s) p Fi 46 4476 a(j) p Fl 82 4461 a(R) p Fp 157 4461 a(\() p Fl(E) p Fp 297 4461 a(+) p Fl 396 4461 a(i) p Fp(0;) p 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a(4.1) p 1276 4702 a(that) p Fl 853 4922 a(s) p Fi 899 4937 a(j) p Fl 936 4922 a(R) p Fp 1011 4922 a(\() p Fl(E) p Fp 1149 4922 a(+) p Fl 1247 4922 a(i) p Fp(0;) p Fl 1373 4922 a(H) p Fi 1454 4937 a(a) p Fp 1495 4922 a(\)) p Fl(X) p Fh 1622 4881 a(\006) p Fi 1614 4947 a(am) p Fl 1718 4922 a(R) p Fp 1793 4922 a(\() p Fl(E) p Fp 1931 4922 a(+) p Fl 2029 4922 a(i) p Fp(0;) p Fl 2155 4922 a(K) p Fi 2238 4937 a(am) p Fp 2342 4922 a(\)) p Fl(s) p Fi 2426 4937 a(j) p Fp 2490 4922 a(=) p 2598 4922 a(~) p Fl 2594 4922 a(r) p Fi 2638 4937 a(L) p Fp 0 5142 a(for) p 151 5142 a(an) m(y) p Fl 337 5142 a(L) p Fk 434 5142 a(\035) p Fp 564 5142 a(1.) p 689 5142 a(W) p 781 5142 a(e) p 859 5142 a(appro) m(ximate) p Fl 1424 5142 a(R) p Fp 1499 5142 a(\() p Fl(E) p Fp 1639 5142 a(+) p Fl 1738 5142 a(i) p Fp(0;) p Fl 1864 5142 a(H) p Fi 1945 5157 a(a) p Fp 1986 5142 a(\)) p Fl(X) p Fh 2113 5106 a(1) p Fi 2105 5167 a(am) p Fp 2243 5142 a(in) p 2359 5142 a(the) p 2529 5142 a(form) p 2761 5142 a(\(3.24\).) p 3086 5142 a(Then) p 3343 5142 a(\(4.4\)) 0 5262 y(again) p 260 5262 a(implies) p Fl 853 5383 a(s) p Fi 899 5398 a(j) p Fl 936 5383 a(R) p Fp 1011 5383 a(\() p Fl(E) p Fp 1149 5383 a(+) p Fl 1247 5383 a(i) p Fp(0;) p Fl 1373 5383 a(H) p Fi 1454 5398 a(a) p Fp 1495 5383 a(\)) p Fl(X) p Fh 1622 5342 a(1) p Fi 1614 5407 a(am) p Fl 1718 5383 a(R) p Fp 1793 5383 a(\() p Fl(E) p Fp 1931 5383 a(+) p Fl 2029 5383 a(i) p Fp(0;) p Fl 2155 5383 a(K) p Fi 2238 5398 a(am) p Fp 2342 5383 a(\)) p Fl(s) p Fi 2426 5398 a(j) p Fp 2490 5383 a(=) p 2598 5383 a(~) p Fl 2594 5383 a(r) p Fi 2638 5398 a(L) p Fp 1723 5753 a(21) p 90 rotate dyy eop %%Page: 22 22 22 21 bop Fp 0 407 a(b) m(y) p 147 407 a(use) p 327 407 a(of) p 450 407 a(calculus) p 830 407 a(of) p 953 407 a(pseudo) s(di\013eren) m(tial) p 1748 407 a(op) s(erators.) p 2252 407 a(Recall) p 2557 407 a(that) p 2780 407 a(the) p 2960 407 a(co) s(e\016cien) m(ts) p 3465 407 a(of) p Fl 0 527 a(X) p Fi 81 542 a(am) p Fp 218 527 a(=) p Fl 328 527 a(g) p Fi 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2188 a(\)) p Fk 1458 2188 a(\000) p Fl 1557 2188 a(R) p Fp 1632 2188 a(\() p Fl(E) p Fp 1771 2188 a(+) p Fl 1869 2188 a(i) p Fp(0;) p Fl 1995 2188 a(H) p Fi 2076 2203 a(b) p Fp 2110 2188 a(\)\)) p Fl 2202 2188 a(s) p Fi 2248 2203 a(j) p Fk 2284 2188 a(k) p Fp 2362 2188 a(=) p Fl 2466 2188 a(O) p Fp 2544 2188 a(\() p Fl(d) p Fh 2633 2146 a(\000) p Fm(1+) p Fi(c\033) p Fp 2854 2188 a(\)) 0 2408 y(and) p 190 2408 a(\(4.13\)) p 471 2408 a(is) p 570 2408 a(v) m(eri\014ed) p 911 2408 a(b) m(y) p 1046 2408 a(making) p 1391 2408 a(rep) s(eated) p 1789 2408 a(use) p 1958 2408 a(of) p 2069 2408 a(the) p 2237 2408 a(ab) s(o) m(v) m(e) p 2513 2408 a(argumen) m(t.) 146 2578 y(W) p 238 2578 a(e) p 314 2578 a(end) p 498 2578 a(the) p 666 2578 a(section) p 992 2578 a(b) m(y) p 1128 2578 a(pro) m(ving) p 1480 2578 a(a) p 1561 2578 a(lemma) p 1875 2578 a(similar) p 2195 2578 a(to) p 2315 2578 a(Lemma) p 2663 2578 a(4.2.) p 2858 2578 a(In) p 2980 2578 a(later) p 3207 2578 a(applica-) 0 2698 y(tion,) p 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a(j) p Fl(y) p Fk 2079 4637 a(j) p Fp 2127 4637 a(+) p Fl 2225 4637 a(d) p Fp(\)) p Fm 2314 4588 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fp 0 4811 a(for) p Fk 147 4811 a(\006) p Fl(t) p 288 4811 a(>) p Fp 391 4811 a(0,) p 498 4811 a(when) p Fl 751 4811 a(x) p Fk 834 4811 a(2) p Fl 928 4811 a(B) p Fi 1002 4826 a(l) p Fp 1059 4811 a(and) p 1247 4811 a(\() p Fl(y) t(;) p 1381 4811 a(\030) p Fp 1429 4811 a(\)) p Fk 1493 4811 a(2) p Fp 1587 4811 a(supp) p Fl 1804 4811 a(Z) p Fh 1878 4775 a(\006) p Fi 1871 4836 a(am) p Fp 1975 4811 a(.) p 2045 4811 a(This) p 2266 4811 a(implies) p 2595 4811 a(the) p 2762 4811 a(desired) p 3091 4811 a(results.) p Fe 3438 4811 a(2) p Fp 146 4981 a(Lemmas) p 546 4981 a(4.1,) p 744 4981 a(4.2) p 914 4981 a(and) p 1117 4981 a(4.3) p 1288 4981 a(are) p 1464 4981 a(often) p 1724 4981 a(used) p 1960 4981 a(in) p 2087 4981 a(pro) m(ving) p 2452 4981 a(Theorem) p 2877 4981 a(4.1) p 3048 4981 a(in) p 3175 4981 a(the) p 3356 4981 a(next) 0 5102 y(section.) p 376 5102 a(W) p 468 5102 a(e) p 548 5102 a(should) p 861 5102 a(note) p 1082 5102 a(that) p 1298 5102 a(Theorem) p 1714 5102 a(4.1) p 1875 5102 a(is) p 1977 5102 a(not) p 2155 5102 a(used) p 2382 5102 a(in) p 2499 5102 a(the) p 2672 5102 a(ab) s(o) m(v) m(e) p 2952 5102 a(pro) s(of) p 3211 5102 a(of) p 3326 5102 a(these) 0 5222 y(lemmas.) p Fq 146 5461 a(5.) p 271 5461 a(Resolv) m(en) m(t) p 784 5461 a(estimates) p Fp 1723 5753 a(22) p 90 rotate dyy eop %%Page: 23 23 23 22 bop Fp 146 407 a(The) p 353 407 a(presen) m(t) p 699 407 a(section) p 1032 407 a(is) p 1136 407 a(dev) m(oted) p 1506 407 a(to) p 1632 407 a(pro) m(ving) p 1991 407 a(Theorem) p 2409 407 a(4.1.) p 2624 407 a(W) p 2716 407 a(e) p 2799 407 a(denote) p 3120 407 a(b) m(y) p Fk 3262 407 a(j) p Fl(a) p Fk(j) p Fp 3408 407 a(the) 0 527 y(n) m(um) m(b) s(er) p 357 527 a(of) p 470 527 a(elemen) m(ts) p 871 527 a(in) p Fl 986 527 a(a) p Fp(.) p 1114 527 a(W) p 1206 527 a(e) p 1283 527 a(pro) m(v) m(e) p 1548 527 a(the) p 1718 527 a(theorem) p 2099 527 a(b) m(y) p 2237 527 a(induction) p 2672 527 a(on) p Fk 2809 527 a(j) p Fl(a) p Fk(j) p Fl(;) p Fp 2994 527 a(0) p Fk 3074 527 a(\024) p 3182 527 a(j) p Fl(a) p Fk(j) p 3319 527 a(\024) p Fl 3428 527 a(N) p Fp 3516 527 a(.) 0 648 y(The) p 210 648 a(pro) s(of) p 474 648 a(is) p 582 648 a(rather) p 884 648 a(length) m(y) p 1240 648 a(and) p 1440 648 a(it) p 1547 648 a(is) p 1654 648 a(divided) p 2008 648 a(in) m(to) p 2215 648 a(sev) m(eral) p 2545 648 a(steps.) p 2856 648 a(Throughout) p 3408 648 a(the) 0 768 y(pro) s(of,) p 291 768 a(w) m(e) p 442 768 a(use) p 618 768 a(the) p 793 768 a(notation) p Fk 1190 768 a(k) p Fl(Q) p Fk(k) p 1407 768 a(') p Fl 1525 768 a(O) p Fp 1603 768 a(\() p Fl(d) p Fi 1692 732 a(\027) p Fp 1734 768 a(\)) p 1811 768 a(when) p 2073 768 a(a) p 2162 768 a(b) s(ounded) p 2567 768 a(op) s(erator) p Fl 2968 768 a(Q) p Fp 3085 768 a(:) p Fl 3152 768 a(L) p Fm 3218 732 a(2) p Fk 3298 768 a(!) p Fl 3438 768 a(L) p Fm 3504 732 a(2) p Fp 0 888 a(ob) s(eys) p 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5185 a(j) p Fm 586 5185 a(1) p Fl 626 5170 a( ) p Fi 689 5185 a(m) p Fl 756 5170 a(R) p Fp 831 5170 a(\() p Fl(E) p Fp 969 5170 a(+) p Fl 1067 5170 a(i) p Fp(0;) p Fl 1193 5170 a(K) p Fi 1276 5185 a(am) p Fp 1380 5170 a(\)) p Fl(b) p Fi 1459 5185 a(k) p Fm 1498 5185 a(1) p Fp 1559 5170 a(+) p Fl 1657 5170 a(b) p Fi 1698 5185 a(j) p Fm 1731 5185 a(1) p Fl 1771 5170 a(R) p Fp 1846 5170 a(\() p Fl(E) p Fp 1984 5170 a(+) p Fl 2082 5170 a(i) p Fp(0;) p Fl 2208 5170 a(H) p Fi 2289 5185 a(a) p Fp 2330 5170 a(\)) p Fl(V) p Fi 2425 5185 a(am) p Fl 2529 5170 a(R) p Fp 2604 5170 a(\() p Fl(E) p Fp 2742 5170 a(+) p Fl 2840 5170 a(i) p Fp(0;) p Fl 2966 5170 a(K) p Fi 3049 5185 a(am) p Fp 3153 5170 a(\)) p Fl(b) p Fi 3232 5185 a(k) p Fm 3271 5185 a(1) p Fp 0 5384 a(b) m(y) p 142 5384 a(Lemma) p 496 5384 a(3.1,) p 688 5384 a(where) p Fl 977 5384 a(K) p Fi 1060 5399 a(am) p Fp 1202 5384 a(=) p Fl 1316 5384 a(K) p Fi 1399 5399 a(am) p Fp 1503 5384 a(\() p Fl(\022) p Fp 1589 5384 a(\)) p 1666 5384 a(=) p Fl 1780 5384 a(e) p Fi 1825 5347 a(iq) p Fg 1881 5355 a(m) p Fl 1944 5384 a(H) p Fm 2025 5399 a(0) p Fl 2064 5384 a(e) p Fh 2109 5347 a(\000) p Fi(iq) p Fg 2220 5355 a(m) p Fp 2321 5384 a(is) p 2426 5384 a(de\014ned) p 2768 5384 a(b) m(y) p 2910 5384 a(\(3.6\)) p 3149 5384 a(with) p Fl 3378 5384 a(a) p Fp 3467 5384 a(=) p Fk 0 5504 a(f) p Fl(m) p Fk(g) p Fp(.) p 273 5504 a(The) p 479 5504 a(direction) p Fl 892 5504 a(\022) p Fk 977 5504 a(2) p Fl 1081 5504 a(S) p Fm 1147 5468 a(1) p Fp 1225 5504 a(is) p 1329 5504 a(sp) s(eci\014ed) p 1728 5504 a(later.) p 2011 5504 a(The) p 2218 5504 a(\014rst) p 2425 5504 a(op) s(erator) p 2823 5504 a(on) p 2965 5504 a(the) p 3139 5504 a(righ) m(t) p 3380 5504 a(side) 1723 5753 y(23) p 90 rotate dyy eop %%Page: 24 24 24 23 bop Fp 0 407 a(ob) s(eys) p 265 407 a(the) p 427 407 a(b) s(ound) p 722 407 a(\(5.2\),) p 977 407 a(and) p 1161 407 a(hence) p 1425 407 a(it) p 1517 407 a(satis\014es) p 1870 407 a(\(4.5\).) p 2139 407 a(W) p 2231 407 a(e) p 2301 407 a(estimate) p 2685 407 a(the) p 2847 407 a(second) p 3156 407 a(op) s(erator.) 0 527 y(First) p 242 527 a(w) m(e) p 389 527 a(deal) p 599 527 a(with) p 826 527 a(the) p 998 527 a(case) p 1208 527 a(that) p Fl 1424 527 a(j) p Fp 1504 527 a(=) p Fl 1615 527 a(m) p Fp 1737 527 a(and) p Fl 1931 527 a(k) p Fk 2019 527 a(6) p Fp(=) p Fl 2130 527 a(m) p Fp(.) p 2298 527 a(W) p 2390 527 a(e) p 2470 527 a(tak) m(e) p Fl 2685 527 a(\022) p Fp 2768 527 a(=) p Fj 2897 494 a(b) p Fl 2879 527 a(d) p Fi 2930 542 a(k) r(m) p Fp 3035 527 a(.) p 3117 527 a(Then) p 3376 527 a(it) p 3478 527 a(is) 0 648 y(ob) m(vious) p 346 648 a(that) p Fl 551 648 a(m) p Fp 663 648 a(and) p Fl 846 648 a(\022) p Fp 922 648 a(=) p Fj 1044 614 a(b) p Fl 1026 648 a(d) p Fi 1077 663 a(k) r(m) p Fp 1208 648 a(satisfy) p 1506 648 a(\(3.12\).) p 1824 648 a(W) p 1916 648 a(e) p 1985 648 a(decomp) s(ose) p Fl 2470 648 a(V) p Fi 2527 663 a(am) p Fp 2658 648 a(=) p Fl 2762 648 a(V) p Fi 2819 663 a(am) p Fp 2923 648 a(\() p 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4019 a(w) m(e) p 394 4019 a(consider) p 779 4019 a(the) p 953 4019 a(case) p 1165 4019 a(that) p Fl 1382 4019 a(j) p Fk 1466 4019 a(6) p Fp(=) p Fl 1579 4019 a(m) p Fp 1703 4019 a(and) p Fl 1898 4019 a(k) p Fk 1990 4019 a(6) p Fp(=) p Fl 2103 4019 a(m) p Fp(.) p 2276 4019 a(The) p 2482 4019 a(argumen) m(t) p 2924 4019 a(is) p 3028 4019 a(divided) p 3378 4019 a(in) m(to) 0 4139 y(t) m(w) m(o) p 184 4139 a(cases) p 429 4139 a(\(a\)) p 585 4139 a(and) p 775 4139 a(\(b\)) p 937 4139 a(according) p 1376 4139 a(to) p 1495 4139 a(the) p 1662 4139 a(lo) s(cation) p 2033 4139 a(of) p 2144 4139 a(three) p 2393 4139 a(cen) m(ters) p Fl 2721 4139 a(d) p Fi 2772 4154 a(j) p Fl 2808 4139 a(;) p 2884 4139 a(d) p Fi 2935 4154 a(k) p Fp 3010 4139 a(and) p Fl 3199 4139 a(d) p Fi 3250 4154 a(m) p Fp 3348 4139 a(:) p 3419 4139 a(\(a\)) 0 4260 y(three) p 253 4260 a(cen) m(ters) p 585 4260 a(are) p 751 4260 a(on) p 890 4260 a(an) p 1029 4260 a(ev) m(en) p 1255 4260 a(segmen) m(t) p 1636 4260 a(with) p Fl 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a(+) p Fl 1720 5504 a(i) p Fp(0;) p Fl 1846 5504 a(H) p Fi 1927 5519 a(a) p Fp 1968 5504 a(\)) p Fl(b) p Fi 2047 5519 a(k) p Fm 2086 5519 a(1) p Fk 2126 5504 a(k) p 2203 5504 a(') p Fl 2308 5504 a(O) p Fp 2386 5504 a(\() p Fk(j) p Fl(d) p Fk(j) p Fm 2531 5463 a(2) p Fi(\033) p Fp 2612 5504 a(\)) p Fl(:) p Fp 3343 5504 a(\(5.5\)) 1723 5753 y(24) p 90 rotate dyy eop %%Page: 25 25 25 24 bop Fp 0 407 a(W) p 92 407 a(e) p 169 407 a(note) p 386 407 a(that) p 598 407 a(this) p 789 407 a(is) p 887 407 a(true) p 1094 407 a(ev) m(en) p 1317 407 a(for) p Fl 1466 407 a(j) p Fp 1541 407 a(=) p Fl 1645 407 a(k) p Fp 1699 407 a(.) p 1772 407 a(If) p 1870 407 a(three) p 2119 407 a(cen) m(ters) p 2448 407 a(are) p 2612 407 a(on) p 2748 407 a(the) p 2916 407 a(segmen) m(t) p 3294 407 a(\(3.27\)) 0 527 y(with) p Fl 219 527 a(d) p Fi 270 542 a(m) p Fp 366 527 a(as) p 483 527 a(an) p 615 527 a(in) m(terior) p 957 527 a(p) s(oin) m(t) p 1208 527 a(for) p 1354 527 a(some) p 1596 527 a(direction) p Fl 1999 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a(R) p Fp 2435 936 a(\() p Fl(E) p Fp 2575 936 a(+) p Fl 2676 936 a(i) p Fp(0;) p Fl 2802 936 a(H) p Fi 2883 951 a(a) p Fp 2924 936 a(\)) p Fl(s) p Fi 3008 951 a(k) p Fm 3047 951 a(1) p Fp 3122 936 a(for) p Fl 3274 936 a(j) p Fk 3353 936 a(6) p Fp(=) p Fl 3462 936 a(k) p Fp 3516 936 a(.) 0 1065 y(If) p Fl 98 1065 a(j) p Fp 171 1065 a(=) p Fl 275 1065 a(m) p Fp 393 1065 a(and) p Fl 582 1065 a(k) p Fk 664 1065 a(6) p Fp(=) p Fl 768 1065 a(m) p Fp(,) p 912 1065 a(then) p 1135 1065 a(w) m(e) p 1278 1065 a(tak) m(e) p Fl 1490 1065 a(\022) p Fp 1565 1065 a(=) p Fj 1688 1032 a(b) p Fl 1669 1065 a(d) p Fi 1720 1080 a(k) r(m) p Fp 1857 1065 a(and) p 2047 1065 a(w) m(e) p 2191 1065 a(ha) m(v) m(e) p Fl 183 1278 a(B) p Fi 257 1293 a(mk) p Fp 390 1278 a(=) p Fl 493 1278 a(b) p Fi 534 1293 a(m) p Fm(1) p Fl 637 1278 a( ) p Fi 700 1293 a(m) p Fl 767 1278 a(R) p Fp 842 1278 a(\() p Fl(E) p Fp 980 1278 a(+) p Fl 1078 1278 a(i) p Fp(0;) p Fl 1204 1278 a(K) p Fi 1287 1293 a(am) p Fp 1391 1278 a(\)) p Fl(s) p Fi 1475 1293 a(k) p Fm 1514 1293 a(1) p Fp 1575 1278 a(+) p Fl 1673 1278 a(b) p Fi 1714 1293 a(m) p Fm(1) p Fl 1816 1278 a(R) p Fp 1891 1278 a(\() p Fl(E) p Fp 2029 1278 a(+) p Fl 2127 1278 a(i) p Fp(0;) p Fl 2253 1278 a(H) p Fi 2334 1293 a(a) p Fp 2376 1278 a(\)) p Fl(V) p Fi 2471 1293 a(am) p Fl 2574 1278 a(R) p Fp 2649 1278 a(\() p Fl(E) p Fp 2788 1278 a(+) p Fl 2886 1278 a(i) p Fp(0;) p Fl 3012 1278 a(K) p Fi 3095 1293 a(am) p Fp 3198 1278 a(\)) p Fl(s) p Fi 3282 1293 a(k) p Fm 3321 1293 a(1) p Fp 0 1490 a(with) p Fl 225 1490 a(V) p Fi 282 1505 a(am) p Fp 418 1490 a(=) p Fl 527 1490 a(V) p Fi 584 1505 a(am) p Fp 688 1490 a(\() p Fl(\022) p Fp 774 1490 a(\).) p 891 1490 a(W) p 983 1490 a(e) p 1061 1490 a(decomp) s(ose) p Fl 1555 1490 a(V) p Fi 1612 1505 a(am) p Fp 1752 1490 a(as) p 1874 1490 a(in) p 1991 1490 a(\(3.25\)) p 2275 1490 a(and) p 2468 1490 a(use) p 2639 1490 a(Lemma) p 2990 1490 a(4.2) p 3150 1490 a(and) p 3343 1490 a(\(5.3\)) 0 1610 y(to) p 125 1610 a(obtain) p 433 1610 a(that) p Fk 650 1610 a(k) p Fl(B) p Fi 774 1625 a(mk) p Fk 879 1610 a(k) p 965 1610 a(') p Fl 1080 1610 a(O) p Fp 1158 1610 a(\() p Fl(d) p Fh 1247 1574 a(\000) p Fm(1) p Fi(=) p Fm(4+) p Fi(\033) p Fp 1508 1610 a(\).) p 1632 1610 a(If) p Fl 1735 1610 a(j) p Fk 1818 1610 a(6) p Fp(=) p Fl 1930 1610 a(m) p Fp 2053 1610 a(and) p Fl 2248 1610 a(k) p Fp 2339 1610 a(=) p Fl 2452 1610 a(m) p Fp(,) p 2603 1610 a(then) p 2831 1610 a(w) m(e) p 2980 1610 a(tak) m(e) p Fl 3196 1610 a(\022) p Fp 3281 1610 a(=) p Fj 3412 1577 a(b) p Fl 3394 1610 a(d) p Fi 3445 1625 a(j) t(m) p Fp 0 1730 a(and) p 190 1730 a(w) m(e) p 333 1730 a(apply) p 602 1730 a(a) p 683 1730 a(similar) p 1003 1730 a(argumen) m(t) p 1439 1730 a(to) p Fl 176 1943 a(B) p Fh 255 1901 a(\003) p Fi 250 1967 a(j) t(m) p Fp 377 1943 a(=) p Fl 481 1943 a(s) p Fi 527 1958 a(m) p Fm(1) p Fl 628 1943 a( ) p Fi 691 1958 a(m) p Fl 758 1943 a(R) p Fp 833 1943 a(\() p Fl(E) p Fk 972 1943 a(\000) p Fl 1071 1943 a(i) p Fp(0;) p Fl 1197 1943 a(K) p Fi 1280 1958 a(am) p Fp 1384 1943 a(\)) p Fl(b) p Fi 1463 1958 a(j) p Fm 1496 1958 a(1) p Fp 1557 1943 a(+) p Fl 1655 1943 a(s) p Fi 1701 1958 a(m) p Fm(1) p Fl 1803 1943 a(R) p Fp 1878 1943 a(\() p Fl(E) p Fk 2016 1943 a(\000) p Fl 2116 1943 a(i) p Fp(0;) p Fl 2242 1943 a(H) p Fi 2323 1958 a(a) p Fp 2364 1943 a(\)) p Fl(V) p Fi 2459 1958 a(am) p Fl 2563 1943 a(R) p Fp 2638 1943 a(\() p Fl(E) p Fk 2776 1943 a(\000) p Fl 2876 1943 a(i) p Fp(0;) p Fl 3002 1943 a(K) p Fi 3085 1958 a(am) p Fp 3189 1943 a(\)) p Fl(b) p Fi 3268 1958 a(j) p Fm 3301 1958 a(1) p Fl 3340 1943 a(:) p Fp 0 2166 a(W) p 92 2166 a(e) p 172 2166 a(ha) m(v) m(e) p Fk 402 2166 a(k) p Fl(B) p Fi 526 2181 a(j) t(m) p Fk 625 2166 a(k) p 710 2166 a(') p Fl 822 2166 a(O) p Fp 900 2166 a(\() p Fl(d) p Fh 989 2130 a(\000) p Fm(1) p Fi(=) p Fm(4+) p Fi(\033) p Fp 1251 2166 a(\)) p 1326 2166 a(b) m(y) p 1466 2166 a(decomp) s(osing) p Fl 2048 2166 a(V) p Fi 2105 2181 a(am) p Fp 2246 2166 a(as) p 2370 2166 a(in) p 2488 2166 a(\(3.14\).) p 2821 2166 a(The) p 3026 2166 a(same) p 3275 2166 a(b) s(ound) 0 2286 y(is) p 98 2286 a(also) p 294 2286 a(obtained) p 696 2286 a(in) p 810 2286 a(the) p 978 2286 a(case) p 1185 2286 a(that) p Fl 1396 2286 a(j) p Fk 1470 2286 a(6) p Fp(=) p Fl 1574 2286 a(m) p Fp 1692 2286 a(and) p Fl 1882 2286 a(k) p Fk 1965 2286 a(6) p Fp(=) p Fl 2069 2286 a(m) p Fp(.) p 2225 2286 a(W) p 2317 2286 a(e) p 2393 2286 a(divide) p 2684 2286 a(the) p 2852 2286 a(argumen) m(t) p 3288 2286 a(to) p 3408 2286 a(the) 0 2407 y(t) m(w) m(o) p 192 2407 a(cases) p 444 2407 a(\(a\)) p 608 2407 a(and) p 805 2407 a(\(b\)) p 975 2407 a(ab) s(o) m(v) m(e) p 1259 2407 a(and) p 1456 2407 a(w) m(e) p 1606 2407 a(tak) m(e) p Fl 1825 2407 a(\022) p Fp 1913 2407 a(as) p 2040 2407 a(b) s(efore.) p 2392 2407 a(In) p 2521 2407 a(case) p 2735 2407 a(\(b\),) p 2934 2407 a(w) m(e) p 3085 2407 a(decomp) s(ose) p Fl 0 2527 a(V) p Fi 57 2542 a(am) p Fp 161 2527 a(\() p Fl(\022) p Fp 247 2527 a(\)) p 319 2527 a(as) p 440 2527 a(in) p 555 2527 a(\(3.14\)) p 838 2527 a(and) p 1029 2527 a(use) p 1199 2527 a(Lemma) p 1549 2527 a(4.2,) p 1735 2527 a(while) p 1991 2527 a(in) p 2106 2527 a(case) p 2314 2527 a(\(a\),) p 2500 2527 a(w) m(e) p 2645 2527 a(decomp) s(ose) p Fl 3137 2527 a(V) p Fi 3194 2542 a(am) p Fp 3298 2527 a(\() p Fl(\022) p Fp 3384 2527 a(\)) p 3456 2527 a(as) 0 2648 y(in) p 114 2648 a(\(3.28\)) p 396 2648 a(and) p 585 2648 a(use) p 754 2648 a(Lemma) p 1102 2648 a(4.3.) p 1297 2648 a(In) p 1419 2648 a(either) p 1695 2648 a(case,) p 1929 2648 a(w) m(e) p 2073 2648 a(ha) m(v) m(e) p 2298 2648 a(b) m(y) p 2433 2648 a(\(5.4\)) p 2666 2648 a(that) p Fk 1333 2860 a(k) p Fl(B) p Fi 1457 2875 a(j) t(k) p Fk 1532 2860 a(k) p Fp 1610 2860 a(=) p Fl 1713 2860 a(O) p Fp 1791 2860 a(\() p Fl(d) p Fh 1880 2819 a(\000) p Fm(1) p Fi(=) p Fm(4+) p Fi(c\033) p Fp 2172 2860 a(\)) p 3343 2860 a(\(5.6\)) 0 3072 y(with) p Fl 237 3072 a(c) p 332 3072 a(>) p Fp 461 3072 a(2.) p 625 3072 a(Th) m(us) p 887 3072 a(\(4.6\)) p 1135 3072 a(is) p 1248 3072 a(obtained.) p 1732 3072 a(Similarly) p 2161 3072 a(w) m(e) p 2320 3072 a(can) p 2514 3072 a(sho) m(w) p 2770 3072 a(that) p 2997 3072 a(\(4.6\)) p 3245 3072 a(implies) 0 3192 y(\(4.7\).) p 283 3192 a(Set) p Fl 455 3192 a(C) p Fi 525 3207 a(j) t(k) p Fp 635 3192 a(=) p Fl 746 3192 a(s) p Fi 792 3207 a(j) p Fm 825 3207 a(1) p Fl 863 3192 a(R) p Fp 938 3192 a(\() p Fl(E) p Fp 1079 3192 a(+) p Fl 1180 3192 a(i) p Fp(0;) p Fl 1306 3192 a(H) p Fi 1387 3207 a(a) p Fp 1428 3192 a(\)) p Fl(s) p Fi 1512 3207 a(k) p Fm 1551 3207 a(1) p Fp 1627 3192 a(for) p Fl 1780 3192 a(j) p Fk 1861 3192 a(6) p Fp(=) p Fl 1971 3192 a(k) p Fp 2025 3192 a(.) p 2108 3192 a(If) p 2210 3192 a(either) p Fl 2490 3192 a(j) p Fp 2573 3192 a(or) p Fl 2696 3192 a(k) p Fp 2787 3192 a(is) p Fl 2889 3192 a(m) p Fp(,) p 3039 3192 a(then) p 3266 3192 a(w) m(e) p 3413 3192 a(get) p Fk 0 3313 a(k) p Fl(C) p Fi 120 3328 a(j) t(k) p Fk 195 3313 a(k) p 272 3313 a(') p Fl 377 3313 a(O) p Fp 455 3313 a(\() p Fl(d) p Fh 544 3276 a(\000) p Fm(1) p Fi(=) p Fm(2+) p Fi(\033) p Fp 806 3313 a(\)) p 874 3313 a(b) m(y) p 1008 3313 a(decomp) s(osing) p Fl 1584 3313 a(V) p Fi 1641 3328 a(am) p Fp 1776 3313 a(as) p 1894 3313 a(in) p 2007 3313 a(\(3.14\)) p 2287 3313 a(and) p 2475 3313 a(b) m(y) p 2609 3313 a(making) p 2951 3313 a(use) p 3118 3313 a(of) p 3228 3313 a(Lemma) 0 3433 y(4.2) p 160 3433 a(and) p 353 3433 a(\(5.3\).) p 634 3433 a(If) p Fl 735 3433 a(j) p Fk 814 3433 a(6) p Fp(=) p Fl 923 3433 a(m) p Fp 1044 3433 a(and) p Fl 1237 3433 a(k) p Fk 1325 3433 a(6) p Fp(=) p Fl 1434 3433 a(m) p Fp(,) p 1583 3433 a(then) p 1808 3433 a(w) m(e) p 1955 3433 a(decomp) s(ose) p Fl 2450 3433 a(V) p Fi 2507 3448 a(am) p Fp 2646 3433 a(as) p 2769 3433 a(in) p 2886 3433 a(\(3.28\)) p 3172 3433 a(or) p 3294 3433 a(\(3.14\)) 0 3553 y(according) p 445 3553 a(to) p 570 3553 a(case) p 783 3553 a(\(a\)) p 946 3553 a(or) p 1072 3553 a(\(b\).) p 1290 3553 a(It) p 1402 3553 a(follo) m(ws) p 1729 3553 a(from) p 1965 3553 a(\(5.6\)) p 2204 3553 a(that) p Fk 2422 3553 a(k) p Fl(C) p Fi 2542 3568 a(j) t(k) p Fk 2616 3553 a(k) p Fp 2704 3553 a(=) p Fl 2818 3553 a(O) p Fp 2896 3553 a(\() p Fl(d) p Fh 2985 3517 a(\000) p Fm(1) p Fi(=) p Fm(2+) p Fi(c\033) p Fp 3277 3553 a(\)) p 3354 3553 a(with) p Fl 0 3674 a(c) p 70 3674 a(>) p Fp 173 3674 a(4.) p 292 3674 a(Th) m(us) p 540 3674 a(w) m(e) p 683 3674 a(ha) m(v) m(e) p 908 3674 a(pro) m(v) m(ed) p 1225 3674 a(\(4) p Fl(:) p Fp(3\)) p Fk 1453 3674 a(\030) p Fp 1558 3674 a(\(4) p Fl(:) p Fp(7\)) p 1792 3674 a(in) p 1905 3674 a(the) p 2073 3674 a(case) p Fk 2280 3674 a(j) p Fl(a) p Fk(j) p Fp 2414 3674 a(=) p 2518 3674 a(1.) 146 3842 y(\(3\)) p 308 3842 a(W) p 400 3842 a(e) p 480 3842 a(pro) s(ceed) p 845 3842 a(to) p 968 3842 a(the) p 1141 3842 a(case) p Fk 1351 3842 a(j) p Fl(a) p Fk(j) p Fp 1493 3842 a(=) p Fl 1604 3842 a(n) p Fk 1697 3842 a(\025) p Fp 1809 3842 a(2,) p 1923 3842 a(assuming) p 2351 3842 a(the) p 2524 3842 a(case) p 2734 3842 a(0) p Fk 2818 3842 a(\024) p 2931 3842 a(j) p Fl(a) p Fk(j) p 3072 3842 a(\024) p Fl 3185 3842 a(n) p Fk 3268 3842 a(\000) p Fp 3370 3842 a(1) p 3456 3842 a(as) 0 3962 y(inductiv) m(e) p 419 3962 a(assumption.) p 972 3962 a(W) p 1064 3962 a(e) p 1136 3962 a(assume) p 1469 3962 a(that) p 1677 3962 a(\(4) p Fl(:) p Fp(3\)) p Fk 1905 3962 a(\030) p Fp 2010 3962 a(\(4) p Fl(:) p Fp(7\)) p 2239 3962 a(are) p 2398 3962 a(true) p 2600 3962 a(for) p 2746 3962 a(some) p Fl 2986 3962 a(c) p Fp 3056 3962 a(=) p Fl 3160 3962 a(c) p Fi 3202 3977 a(n) p Fh(\000) p Fm(1) p Fp 3339 3962 a(.) p 3408 3962 a(W) p 3500 3962 a(e) 0 4082 y(b) s(egin) p 263 4082 a(b) m(y) p 398 4082 a(pro) m(ving) p 751 4082 a(\(4.3\)) p 984 4082 a(and) p 1173 4082 a(\(4.4\).) p 1444 4082 a(This) p 1667 4082 a(step) p 1873 4082 a(o) s(ccupies) p 2262 4082 a(the) p 2430 4082 a(core) p 2635 4082 a(of) p 2747 4082 a(the) p 2915 4082 a(pro) s(of.) p 3207 4082 a(W) p 3299 4082 a(e) p 3375 4082 a(set) p Fl 626 4294 a(Q) p Fi 703 4309 a(\027) p Fp 775 4294 a(=) p Fl 878 4294 a(r) p Fi 922 4309 a(\027) p Fl 965 4294 a(R) p Fp 1040 4294 a(\() p Fl(E) p Fp 1178 4294 a(+) p Fl 1276 4294 a(i) p Fp(0;) p Fl 1402 4294 a(H) p Fi 1483 4309 a(a) p Fp 1525 4294 a(\)) p Fl(r) p Fi 1607 4309 a(\027) p Fl 1650 4294 a(;) p 1889 4294 a(P) p Fi 1952 4309 a(j) p Fp 2016 4294 a(=) p Fl 2119 4294 a(r) p Fi 2163 4309 a(\027) p Fl 2206 4294 a(R) p Fp 2281 4294 a(\() p Fl(E) p Fp 2419 4294 a(+) p Fl 2517 4294 a(i) p Fp(0;) p Fl 2643 4294 a(H) p Fi 2724 4309 a(a) p Fp 2766 4294 a(\)) p Fl(b) p Fi 2845 4309 a(j) p Fm 2878 4309 a(1) p Fp 0 4507 a(for) p Fl 156 4507 a(\027) p Fk 251 4507 a(\035) p Fp 390 4507 a(1,) p 508 4507 a(where) p Fl 797 4507 a(r) p Fh 841 4522 a(\006) p Fi(\027) p Fp 979 4507 a(is) p 1084 4507 a(the) p 1259 4507 a(m) m(ultiplication) p 1892 4507 a(op) s(erator) p 2292 4507 a(de\014ned) p 2636 4507 a(b) m(y) p 2778 4507 a(\(4.2\).) p 3071 4507 a(Let) p Fl 3253 4507 a(j;) p Fp 3377 4507 a(1) p Fk 3466 4507 a(\024) p Fl 0 4627 a(j) p Fk 88 4627 a(\024) p Fl 207 4627 a(N) p Fp 295 4627 a(,) p 365 4627 a(b) s(e) p 506 4627 a(\014xed) p 750 4627 a(arbitrarily) p 1227 4627 a(through) p 1604 4627 a(the) p 1781 4627 a(step.) p 2050 4627 a(W) p 2142 4627 a(e) p 2226 4627 a(tak) m(e) p Fl 2446 4627 a(m) p Fk 2573 4627 a(2) p Fl 2681 4627 a(a) p Fp 2773 4627 a(suc) m(h) p 3001 4627 a(that) p Fk 3221 4627 a(j) p Fl(d) p Fi 3300 4642 a(j) t(m) p Fk 3398 4627 a(j) p Fp 3467 4627 a(=) 0 4747 y(max) p Fk 198 4747 a(fj) p Fl(d) p Fi 327 4762 a(j) t(k) p Fk 401 4747 a(j) p Fp 457 4747 a(:) p Fl 511 4747 a(k) p Fk 593 4747 a(2) p Fl 687 4747 a(a) p Fk(g) p Fp 821 4747 a(and) p 1011 4747 a(w) m(e) p 1154 4747 a(write) p Fl 1403 4747 a(Q) p Fi 1480 4762 a(\027) p Fp 1556 4747 a(as) p 1676 4747 a(the) p 1844 4747 a(sum) p 2051 4747 a(of) p 2162 4747 a(t) m(w) m(o) p 2346 4747 a(op) s(erators) p Fl 376 4959 a(Q) p Fm 453 4974 a(1) p Fi(\027) p Fp 559 4959 a(=) p Fl 663 4959 a(r) p Fi 707 4974 a(\027) p Fl 750 4959 a(R) p Fp 825 4959 a(\() p Fl(E) p Fp 963 4959 a(+) p Fl 1061 4959 a(i) p Fp(0;) p Fl 1187 4959 a(H) p Fi 1268 4974 a(a) p Fp 1309 4959 a(\)) p Fl( ) p Fi 1410 4974 a(m) p Fl 1477 4959 a(r) p Fi 1521 4974 a(\027) p Fl 1564 4959 a(;) p 1706 4959 a(Q) p Fm 1783 4974 a(2) p Fi(\027) p Fp 1889 4959 a(=) p Fl 1992 4959 a(r) p Fi 2036 4974 a(\027) p Fl 2080 4959 a(R) p Fp 2155 4959 a(\() p Fl(E) p Fp 2293 4959 a(+) p Fl 2391 4959 a(i) p Fp(0;) p Fl 2517 4959 a(H) p Fi 2598 4974 a(a) p Fp 2639 4959 a(\)\(1) p Fk 2786 4959 a(\000) p Fl 2885 4959 a( ) p Fi 2948 4974 a(m) p Fp 3015 4959 a(\)) p Fl(r) p Fi 3097 4974 a(\027) p Fl 3141 4959 a(;) p Fp 0 5172 a(where) p Fl 275 5172 a( ) p Fi 338 5187 a(m) p Fp 431 5172 a(is) p 523 5172 a(de\014ned) p 853 5172 a(b) m(y) p 982 5172 a(\(3.8\).) p 1251 5172 a(De\014ne) p 1546 5172 a(the) p 1708 5172 a(auxiliary) p 2108 5172 a(op) s(erator) p Fl 2494 5172 a(K) p Fi 2577 5187 a(am) p Fp 2709 5172 a(=) p Fl 2813 5172 a(K) p Fi 2896 5187 a(am) p Fp 3000 5172 a(\() p Fl(\022) p Fi 3083 5187 a(m) p Fp 3150 5172 a(\)) p 3214 5172 a(b) m(y) p 3343 5172 a(\(3.6\)) 0 5292 y(with) p Fl 222 5292 a(\022) p Fi 267 5307 a(m) p Fp 362 5292 a(=) 483 5266 y(^) p Fl 465 5292 a(d) p Fi 516 5307 a(j) t(m) p Fp 615 5292 a(.) p 686 5292 a(Then) p 940 5292 a(Lemma) p 1288 5292 a(3.1) p 1446 5292 a(yields) p Fl 274 5504 a(Q) p Fm 351 5519 a(1) p Fi(\027) p Fp 458 5504 a(=) p Fl 561 5504 a(r) p Fi 605 5519 a(\027) p Fl 648 5504 a( ) p Fi 711 5519 a(m) p Fl 778 5504 a(R) p Fp 853 5504 a(\() p Fl(E) p Fp 991 5504 a(+) p Fl 1089 5504 a(i) p Fp(0;) p Fl 1215 5504 a(K) p Fi 1298 5519 a(am) p Fp 1402 5504 a(\)) p Fl(r) p Fi 1484 5519 a(\027) p Fp 1549 5504 a(+) p Fl 1648 5504 a(r) p Fi 1692 5519 a(\027) p Fl 1735 5504 a(R) p Fp 1810 5504 a(\() p Fl(E) p Fp 1948 5504 a(+) p Fl 2046 5504 a(i) p Fp(0;) p Fl 2172 5504 a(H) p Fi 2253 5519 a(a) p Fp 2294 5504 a(\)) p Fl(V) p Fi 2389 5519 a(am) p Fl 2493 5504 a(R) p Fp 2568 5504 a(\() p Fl(E) p Fp 2706 5504 a(+) p Fl 2804 5504 a(i) p Fp(0;) p Fl 2930 5504 a(K) p Fi 3013 5519 a(am) p Fp 3117 5504 a(\)) p Fl(r) p Fi 3199 5519 a(\027) p Fl 3242 5504 a(:) p Fp 1723 5753 a(25) p 90 rotate dyy eop %%Page: 26 26 26 25 bop Fp 0 407 a(By) p 171 407 a(inductiv) m(e) p 612 407 a(assumption,) p 1177 407 a(the) p 1363 407 a(\014rst) p 1582 407 a(op) s(erator) p 1993 407 a(on) p 2146 407 a(the) p 2332 407 a(righ) m(t) p 2586 407 a(side) p 2800 407 a(ob) s(eys) p 3089 407 a(the) p 3275 407 a(b) s(ound) p Fl 0 527 a(O) p Fp 78 527 a(\() p Fl(d) p Fh 167 491 a(\000) p Fi(\027) p Fp 264 527 a(\).) p 415 527 a(T) p 477 527 a(o) p 573 527 a(estimate) p 978 527 a(the) p 1161 527 a(second) p 1490 527 a(op) s(erator,) p 1928 527 a(w) m(e) p 2086 527 a(decomp) s(ose) p Fl 2591 527 a(V) p Fi 2648 542 a(am) p Fp 2804 527 a(=) p Fl 2932 527 a(V) p Fi 2989 542 a(am) p Fp 3093 527 a(\() p Fl(\022) p Fi 3176 542 a(m) p Fp 3243 527 a(\)) p 3328 527 a(as) p 3462 527 a(in) 0 648 y(\(3.14\).) p 320 648 a(W) p 412 648 a(e) p 488 648 a(ha) m(v) m(e) p Fk 546 863 a(k) p Fl(r) p Fi 640 878 a(\027) p Fl 683 863 a(R) p Fp 758 863 a(\() p Fl(E) p Fp 896 863 a(+) p Fl 994 863 a(i) p Fp(0;) p Fl 1120 863 a(H) p Fi 1201 878 a(a) p Fp 1243 863 a(\)) p Fl(X) p Fi 1362 878 a(am) p Fl 1465 863 a(R) p Fp 1540 863 a(\() p Fl(E) p Fp 1679 863 a(+) p Fl 1777 863 a(i) p Fp(0;) p Fl 1903 863 a(K) p Fi 1986 878 a(am) p Fp 2089 863 a(\)) p Fl(r) p Fi 2171 878 a(\027) p Fk 2215 863 a(k) p Fp 2292 863 a(=) p Fl 2396 863 a(O) p Fp 2474 863 a(\() p Fl(d) p Fh 2563 822 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2730 863 a(\)) p Fk(k) p Fl(P) p Fi 2881 878 a(m) p Fk 2947 863 a(k) p Fp 0 1079 a(again) p 264 1079 a(b) m(y) p 404 1079 a(inductiv) m(e) p 831 1079 a(assumption.) p 1398 1079 a(Recall) p 1697 1079 a(that) p Fl 1912 1079 a(R) p Fp 1987 1079 a(\() p Fl(E) p Fp 2128 1079 a(+) p Fl 2229 1079 a(i) p Fp(0;) p Fl 2355 1079 a(H) p Fi 2436 1094 a(a) p Fp 2478 1079 a(\)) p Fl(X) p Fh 2605 1043 a(1) p Fi 2597 1104 a(am) p Fp 2737 1079 a(is) p 2840 1079 a(appro) m(ximated) p 3462 1079 a(in) 0 1199 y(the) p 168 1199 a(form) p 398 1199 a(\(3.24\).) p 718 1199 a(Hence) p 1008 1199 a(a) p 1089 1199 a(calculus) p 1458 1199 a(of) p 1569 1199 a(pseudo) s(di\013eren) m(tial) p 2353 1199 a(op) s(erators) p 2784 1199 a(yields) p Fk 370 1415 a(k) p Fl(r) p Fi 464 1430 a(\027) p Fl 507 1415 a(R) p Fp 582 1415 a(\() p Fl(E) p Fp 721 1415 a(+) p Fl 819 1415 a(i) p Fp(0;) p Fl 945 1415 a(H) p Fi 1026 1430 a(a) p Fp 1067 1415 a(\)) p Fl(X) p Fh 1194 1374 a(1) p Fi 1186 1440 a(am) p Fl 1290 1415 a(R) p Fp 1365 1415 a(\() p Fl(E) p Fp 1503 1415 a(+) p Fl 1601 1415 a(i) p Fp(0;) p Fl 1727 1415 a(K) p Fi 1810 1430 a(am) p Fp 1914 1415 a(\)) p Fl(r) p Fi 1996 1430 a(\027) p Fk 2039 1415 a(k) p Fp 2116 1415 a(=) p Fl 2220 1415 a(O) p Fp 2298 1415 a(\() p Fl(d) p Fh 2387 1374 a(\000) p Fi(\027) p Fp 2484 1415 a(\)) p 2544 1415 a(+) p Fl 2642 1415 a(O) p Fp 2720 1415 a(\() p Fl(d) p Fh 2809 1374 a(\000) p Fi(L) p Fp 2915 1415 a(\)) p Fk(k) p Fl(Q) p Fi 3080 1430 a(\027) p Fk 3123 1415 a(k) p Fp 0 1631 a(for) p 149 1631 a(an) m(y) p Fl 333 1631 a(L) p Fk 427 1631 a(\035) p Fp 555 1631 a(1.) p 674 1631 a(W) p 766 1631 a(e) p 842 1631 a(pro) m(v) m(e) p 1105 1631 a(the) p 1273 1631 a(follo) m(wing) p 1685 1631 a(t) m(w) m(o) p 1869 1631 a(estimates) p Fk 594 1846 a(k) p Fl(r) p Fi 688 1861 a(\027) p Fl 731 1846 a(R) p Fp 806 1846 a(\() p Fl(E) p Fp 944 1846 a(+) p Fl 1042 1846 a(i) p Fp(0;) p Fl 1168 1846 a(H) p Fi 1249 1861 a(a) p Fp 1290 1846 a(\)) p Fl(X) p Fm 1417 1805 a(+) p Fi 1409 1871 a(am) p Fl 1513 1846 a(r) p Fh 1557 1862 a(\000) p Fi(\027) t(=) p Fm(3) p Fk 1726 1846 a(k) p Fp 1859 1846 a(=) p Fl 2017 1846 a(O) p Fp 2095 1846 a(\() p Fl(d) p Fh 2184 1805 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2352 1846 a(\)) p 2412 1846 a(+) p Fl 2510 1846 a(O) p Fp 2588 1846 a(\() p Fl(d) p Fh 2677 1805 a(\000) p Fi(L) p Fp 2783 1846 a(\)) p Fk(k) p Fl(Q) p Fi 2948 1861 a(\027) p Fk 2991 1846 a(k) p Fl(;) p Fp 3343 1846 a(\(5.7\)) p Fk 459 1992 a(k) p Fl(r) p Fh 553 2007 a(\000) p Fi(\027) t(=) p Fm(3) p Fl 721 1992 a(X) p Fh 810 1951 a(\000) p Fi 802 2016 a(am) p Fl 906 1992 a(R) p Fp 981 1992 a(\() p Fl(E) p Fp 1119 1992 a(+) p Fl 1217 1992 a(i) p Fp(0;) p Fl 1343 1992 a(K) p Fi 1426 2007 a(am) p Fp 1530 1992 a(\)) p Fl(r) p Fi 1612 2007 a(\027) t(=) p Fm(2) p Fk 1726 1992 a(k) p Fp 1859 1992 a(=) p Fl 2017 1992 a(O) p Fp 2095 1992 a(\(1\)) p 3343 1992 a(\(5.8\)) 0 2207 y(after) p 230 2207 a(completing) p 729 2207 a(the) p 897 2207 a(pro) s(of.) p 1189 2207 a(Let) p 1364 2207 a(\005) p Fi 1437 2222 a(j) p Fp 1473 2207 a(\() p Fl(\022) p Fp 1559 2207 a(\)) p 1630 2207 a(b) s(e) p 1763 2207 a(de\014ned) p 2098 2207 a(b) m(y) p 2234 2207 a(\(3.5\).) p 2505 2207 a(W) p 2597 2207 a(e) p 2673 2207 a(denote) p 2987 2207 a(b) m(y) p Fl 3122 2207 a(\031) p Fi 3177 2222 a(m) p Fp 3244 2207 a(\() p Fl(x) p Fp(\)) p 3408 2207 a(the) 0 2328 y(c) m(haracteristic) p 599 2328 a(function) p 981 2328 a(of) p 1093 2328 a(\005) p Fi 1166 2343 a(m) p Fp 1232 2328 a(\() p Fl(\022) p Fi 1315 2343 a(m) p Fp 1382 2328 a(\)) p 1453 2328 a(and) p 1642 2328 a(w) m(e) p 1786 2328 a(set) p Fl 1938 2328 a(R) p Fi 2012 2343 a(m) p Fp 2107 2328 a(=) p Fl 2210 2328 a(r) p Fi 2254 2343 a(\027) p Fl 2297 2328 a(R) p Fp 2372 2328 a(\() p Fl(E) p Fp 2511 2328 a(+) p Fl 2609 2328 a(i) p Fp(0;) p Fl 2735 2328 a(H) p Fi 2816 2343 a(a) p Fp 2857 2328 a(\)) p Fl(\031) p Fi 2950 2343 a(m) p Fl 3017 2328 a(r) p Fi 3061 2343 a(\027) t(=) p Fm(3) p Fp 3174 2328 a(.) p 3245 2328 a(Since) p Fk 230 2554 a(k) p Fl(r) p Fi 324 2570 a(\027) t(=) p Fm(3) p Fl 438 2554 a(R) p Fp 513 2554 a(\() p Fl(E) p Fp 651 2554 a(+) p Fl 749 2554 a(i) p Fp(0;) p Fl 875 2554 a(K) p Fi 958 2569 a(am) p Fp 1062 2554 a(\)) p Fl(r) p Fi 1144 2569 a(\027) p Fk 1187 2554 a(k) p Fp 1264 2554 a(=) p Fl 1368 2554 a(O) p Fp 1446 2554 a(\() p Fl(d) p Fh 1535 2513 a(\000) p Fm(2) p Fi(\027) t(=) p Fm(3) p Fp 1738 2554 a(\)) p Fk(k) p Fl(r) p Fi 1870 2570 a(\027) t(=) p Fm(3) p Fl 1983 2554 a(R) p Fp 2058 2554 a(\() p Fl(E) p Fp 2196 2554 a(+) p Fl 2294 2554 a(i) p Fp(0;) p Fl 2420 2554 a(K) p Fi 2503 2569 a(am) p Fp 2607 2554 a(\)) p Fl(r) p Fi 2689 2570 a(\027) t(=) p Fm(3) p Fk 2803 2554 a(k) p Fp 2880 2554 a(=) p Fl 2984 2554 a(O) p Fp 3062 2554 a(\() p Fl(d) p Fh 3151 2513 a(\000) p Fi(\027) p Fp 3248 2554 a(\)) p Fl(;) p Fp 0 2770 a(w) m(e) p 144 2770 a(ha) m(v) m(e) p Fk 318 2986 a(k) p Fl(r) p Fi 412 3001 a(\027) p Fl 454 2986 a(R) p Fp 529 2986 a(\() p Fl(E) p Fp 668 2986 a(+) p Fl 766 2986 a(i) p Fp(0;) p Fl 892 2986 a(H) p Fi 973 3001 a(a) p Fp 1014 2986 a(\)) p Fl(X) p Fm 1141 2945 a(+) p Fi 1133 3011 a(am) p Fl 1237 2986 a(R) p Fp 1312 2986 a(\() p Fl(E) p Fp 1450 2986 a(+) p Fl 1548 2986 a(i) p Fp(0;) p Fl 1674 2986 a(K) p Fi 1757 3001 a(am) p Fp 1861 2986 a(\)) p Fl(r) p Fi 1943 3001 a(\027) p Fk 1986 2986 a(k) p Fp 2063 2986 a(=) p Fl 2167 2986 a(O) p Fp 2245 2986 a(\() p Fl(d) p Fh 2334 2945 a(\000) p Fm(3) p Fi(\027) t(=) p Fm(2) p Fp 2537 2986 a(\)) p 2597 2986 a(+) p Fl 2695 2986 a(O) p Fp 2773 2986 a(\() p Fl(d) p Fh 2862 2945 a(\000) p Fi(L) p Fp 2968 2986 a(\)) p Fk(k) p Fl(Q) p Fi 3133 3001 a(\027) p Fk 3176 2986 a(k) p Fp 0 3202 a(b) m(y) p 135 3202 a(\(5.7\),) p 396 3202 a(and) p 585 3202 a(since) p Fl 824 3202 a(\031) p Fi 879 3217 a(m) p Fl 946 3202 a(X) p Fh 1035 3165 a(\000) p Fi 1027 3226 a(am) p Fp 1159 3202 a(=) p Fl 1262 3202 a(X) p Fh 1351 3165 a(\000) p Fi 1343 3226 a(am) p Fp 1447 3202 a(,) p 1507 3202 a(it) p 1605 3202 a(follo) m(ws) p 1925 3202 a(from) p 2155 3202 a(\(5.8\)) p 2388 3202 a(that) p Fk 527 3417 a(k) p Fl(r) p Fi 621 3432 a(\027) p Fl 664 3417 a(R) p Fp 739 3417 a(\() p Fl(E) p Fp 877 3417 a(+) p Fl 975 3417 a(i) p Fp(0;) p Fl 1101 3417 a(H) p Fi 1182 3432 a(a) p Fp 1223 3417 a(\)) p Fl(X) p Fh 1350 3376 a(\000) p Fi 1342 3442 a(am) p Fl 1446 3417 a(R) p Fp 1521 3417 a(\() p Fl(E) p Fp 1659 3417 a(+) p Fl 1757 3417 a(i) p Fp(0;) p Fl 1883 3417 a(K) p Fi 1966 3432 a(am) p Fp 2070 3417 a(\)) p Fl(r) p Fi 2152 3432 a(\027) p Fk 2195 3417 a(k) p Fp 2273 3417 a(=) p Fl 2376 3417 a(O) p Fp 2454 3417 a(\() p Fl(d) p Fh 2543 3376 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2711 3417 a(\)) p Fk(k) p Fl(R) p Fi 2873 3432 a(m) p Fk 2939 3417 a(k) p Fl(:) p Fp 0 3633 a(W) p 92 3633 a(e) p 168 3633 a(com) m(bine) p 550 3633 a(the) p 718 3633 a(ab) s(o) m(v) m(e) p 994 3633 a(estimates) p 1424 3633 a(to) p 1543 3633 a(obtain) p Fk 501 3849 a(k) p Fl(Q) p Fm 628 3864 a(1) p Fi(\027) p Fk 706 3849 a(k) p Fp 784 3849 a(=) p Fl 888 3849 a(O) p Fp 966 3849 a(\() p Fl(d) p Fh 1055 3808 a(\000) p Fi(\027) p Fp 1151 3849 a(\)) p 1212 3849 a(+) p Fl 1310 3849 a(O) p Fp 1388 3849 a(\() p Fl(d) p Fh 1477 3808 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 1644 3849 a(\)) p 1699 3849 a(\() p Fk(k) p Fl(P) p Fi 1850 3864 a(m) p Fk 1916 3849 a(k) p Fp 1988 3849 a(+) p Fk 2086 3849 a(k) p Fl(R) p Fi 2210 3864 a(m) p Fk 2276 3849 a(k) p Fp(\)) p 2386 3849 a(+) p Fl 2484 3849 a(O) p Fp 2562 3849 a(\() p Fl(d) p Fh 2651 3808 a(\000) p Fi(L) p Fp 2757 3849 a(\)) p Fk(k) p Fl(Q) p Fi 2922 3864 a(\027) p Fk 2965 3849 a(k) p Fl(:) p Fp 3343 3849 a(\(5.9\)) 0 4064 y(W) p 92 4064 a(e) p 173 4064 a(ev) p 262 4064 a(aluate) p 559 4064 a(the) p 732 4064 a(other) p 991 4064 a(op) s(erator) p Fl 1389 4064 a(Q) p Fm 1466 4079 a(2) p Fi(\027) p Fp 1545 4064 a(.) p 1629 4064 a(Let) p Fl 1808 4064 a(m) p Fk 1929 4064 a(2) p Fl 2031 4064 a(a) p Fp 2120 4064 a(b) s(e) p 2257 4064 a(as) p 2382 4064 a(ab) s(o) m(v) m(e.) p 2710 4064 a(W) p 2802 4064 a(e) p 2883 4064 a(tak) m(e) p Fl 3099 4064 a(l) p Fk 3165 4064 a(2) p Fl 3267 4064 a(a) p Fp 3356 4064 a(suc) m(h) 0 4185 y(that) p Fk 213 4185 a(j) p Fl(d) p Fi 292 4200 a(ml) p Fk 379 4185 a(j) p Fp 437 4185 a(=) p 542 4185 a(max) p Fk 741 4185 a(fj) p Fl(d) p Fi 870 4200 a(mk) p Fk 974 4185 a(j) p Fp 1031 4185 a(:) p Fl 1088 4185 a(k) p Fk 1172 4185 a(2) p Fl 1268 4185 a(a) p Fk(g) p Fp(.) p 1443 4185 a(Since) p Fk 1699 4185 a(j) p Fl(a) p Fk(j) p 1835 4185 a(\025) p Fp 1943 4185 a(2,) p Fl 2053 4185 a(l) p Fk 2114 4185 a(6) p Fp(=) p Fl 2219 4185 a(m) p Fp(.) p 2379 4185 a(W) p 2471 4185 a(e) p 2548 4185 a(de\014ne) p Fl 2831 4185 a(K) p Fi 2914 4200 a(al) p Fp 3007 4185 a(=) p Fl 3113 4185 a(K) p Fi 3196 4200 a(al) p Fp 3259 4185 a(\() p Fl(\022) p Fi 3342 4200 a(l) p Fp 3369 4185 a(\)) p 3440 4185 a(b) m(y) 0 4305 y(\(3.6\)) p 233 4305 a(with) p Fl 455 4305 a(\022) p Fi 500 4320 a(l) p Fp 554 4305 a(=) p Fj 676 4272 a(b) p Fl 658 4305 a(d) p Fi 709 4320 a(ml) p Fp 797 4305 a(.) p 867 4305 a(Since) p 1122 4305 a(1) p Fk 1193 4305 a(\000) p Fl 1293 4305 a( ) p Fi 1356 4320 a(m) p Fp 1455 4305 a(v) p 1501 4305 a(anishes) p 1838 4305 a(around) p Fl 2169 4305 a(d) p Fi 2220 4320 a(l) p Fp 2246 4305 a(,) p 2305 4305 a(w) m(e) p 2449 4305 a(ha) m(v) m(e) p Fl 208 4521 a(Q) p Fm 285 4536 a(2) p Fi(\027) p Fp 391 4521 a(=) p Fl 495 4521 a(r) p Fi 539 4536 a(\027) p Fp 582 4521 a(\(1) p Fk 691 4521 a(\000) p Fl 790 4521 a( ) p Fi 853 4536 a(m) p Fp 920 4521 a(\)) p Fl(R) p Fp 1033 4521 a(\() p Fl(E) p Fp 1171 4521 a(+) p Fl 1269 4521 a(i) p Fp(0;) p Fl 1395 4521 a(K) p Fi 1478 4536 a(al) p Fp 1542 4521 a(\)) p Fl(r) p Fi 1624 4536 a(\027) p Fp 1689 4521 a(+) p Fl 1787 4521 a(r) p Fi 1831 4536 a(\027) p Fl 1874 4521 a(R) p Fp 1949 4521 a(\() p Fl(E) p Fp 2087 4521 a(+) p Fl 2185 4521 a(i) p Fp(0;) p Fl 2311 4521 a(H) p Fi 2392 4536 a(a) p Fp 2434 4521 a(\)) p Fl(W) p Fi 2564 4536 a(al) p Fl 2627 4521 a(R) p Fp 2702 4521 a(\() p Fl(E) p Fp 2840 4521 a(+) p Fl 2938 4521 a(i) p Fp(0;) p Fl 3064 4521 a(K) p Fi 3147 4536 a(al) p Fp 3210 4521 a(\)) p Fl(r) p Fi 3292 4536 a(\027) p Fp 0 4737 a(b) m(y) p 135 4737 a(Lemma) p 484 4737 a(3.1,) p 668 4737 a(where) p Fl 860 4952 a(W) p Fi 952 4967 a(al) p Fp 1043 4952 a(=) p 1147 4952 a([1) p Fk 1245 4952 a(\000) p Fl 1344 4952 a( ) p Fi 1407 4967 a(m) p Fl 1474 4952 a(;) p 1518 4952 a(K) p Fi 1601 4967 a(al) p Fp 1664 4952 a(]) p Fk 1714 4952 a(\000) p Fp 1813 4952 a(\() p Fl(H) p Fi 1932 4967 a(a) p Fk 1996 4952 a(\000) p Fl 2096 4952 a(K) p Fi 2179 4967 a(al) p Fp 2242 4952 a(\)\(1) p Fk 2389 4952 a(\000) p Fl 2488 4952 a( ) p Fi 2551 4967 a(m) p Fp 2618 4952 a(\)) p Fl(:) p Fp 0 5168 a(As) p 151 5168 a(is) p 256 5168 a(easily) p 532 5168 a(seen,) p 780 5168 a(\() p Fl(H) p Fi 899 5183 a(a) p Fk 968 5168 a(\000) p Fl 1072 5168 a(K) p Fi 1155 5183 a(al) p Fp 1219 5168 a(\)\(1) p Fk 1370 5168 a(\000) p Fl 1475 5168 a( ) p Fi 1538 5183 a(m) p Fp 1605 5168 a(\)) p 1682 5168 a(=) p 1798 5168 a(0) p 1887 5168 a(and) p 2083 5168 a(hence) p 2361 5168 a(the) p 2537 5168 a(co) s(e\016cien) m(ts) p 3037 5168 a(of) p Fl 3156 5168 a(W) p Fi 3248 5183 a(al) p Fp 3351 5168 a(ha) m(v) m(e) 0 5288 y(supp) s(ort) p 361 5288 a(in) p Fk 475 5288 a(f) p Fl(d) p Fi 576 5252 a(\033) p Fl 622 5288 a(=) p Fp(2) p Fl 747 5288 a(<) p Fk 851 5288 a(j) p Fl(x) p Fk 956 5288 a(\000) p Fl 1056 5288 a(d) p Fi 1107 5303 a(m) p Fk 1173 5288 a(j) p Fl 1228 5288 a(<) p 1332 5288 a(d) p Fi 1383 5252 a(\033) p Fk 1429 5288 a(g) p Fp 1512 5288 a(only) p 1685 5288 a(.) p 1756 5288 a(Th) m(us) p 2003 5288 a(w) m(e) p 2146 5288 a(ha) m(v) m(e) p Fk 1053 5504 a(k) p Fl(Q) p Fm 1180 5519 a(2) p Fi(\027) p Fk 1259 5504 a(k) p Fp 1336 5504 a(=) p Fl 1440 5504 a(O) p Fp 1518 5504 a(\() p Fl(d) p Fh 1607 5463 a(\000) p Fi(\027) p Fp 1704 5504 a(\)) p 1764 5504 a(+) p Fl 1862 5504 a(O) p Fp 1940 5504 a(\() p Fl(d) p Fh 2029 5463 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2196 5504 a(\)) p Fk(k) p Fl(P) p Fi 2347 5519 a(m) p Fk 2413 5504 a(k) p Fl(:) p Fp 1723 5753 a(26) p 90 rotate dyy eop %%Page: 27 27 27 26 bop Fp 0 407 a(This,) p 250 407 a(together) p 635 407 a(with) p 857 407 a(\(5.9\),) p 1117 407 a(implies) p 1448 407 a(that) p Fk 836 621 a(k) p Fl(Q) p Fi 963 636 a(\027) p Fk 1006 621 a(k) p Fp 1084 621 a(=) p Fl 1187 621 a(O) p Fp 1265 621 a(\() p Fl(d) p Fh 1354 580 a(\000) p Fi(\027) p Fp 1451 621 a(\)) p 1511 621 a(+) p Fl 1609 621 a(O) p Fp 1687 621 a(\() p Fl(d) p Fh 1776 580 a(\000) p 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s(ound) p Fl 2440 1383 a(O) p Fp 2518 1383 a(\() p Fl(d) p Fh 2607 1347 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2774 1383 a(\)) p 2851 1383 a(b) m(y) p 2994 1383 a(inductiv) m(e) p 3424 1383 a(as-) 0 1504 y(sumption.) p 478 1504 a(W) p 570 1504 a(e) p 650 1504 a(estimate) p 1045 1504 a(the) p 1217 1504 a(second) p 1535 1504 a(op) s(erator.) p 1978 1504 a(Note) p 2217 1504 a(that) p Fl 2433 1504 a(l) p Fk 2498 1504 a(2) p Fl 2599 1504 a(a) p Fp 2686 1504 a(and) p Fl 2880 1504 a(\022) p Fi 2925 1519 a(l) p Fp 2986 1504 a(=) p Fj 3114 1470 a(b) p Fl 3096 1504 a(d) p Fi 3147 1519 a(ml) p Fp 3271 1504 a(satisfy) 0 1624 y(\(3.12\).) p 357 1624 a(W) p 449 1624 a(e) p 537 1624 a(decomp) s(ose) p Fl 1040 1624 a(V) p Fi 1097 1639 a(al) p Fp 1205 1624 a(as) p 1337 1624 a(in) p 1464 1624 a(\(3.14\).) p 1820 1624 a(The) p 2033 1624 a(co) s(e\016cien) m(ts) p 2539 1624 a(of) p Fl 2662 1624 a(X) p Fi 2743 1639 a(al) p Fp 2852 1624 a(ha) m(v) m(e) p 3089 1624 a(supp) s(ort) p 3462 1624 a(in) 17 1719 y(~) 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1558 2507 a(R) p Fp 1633 2507 a(\() p Fl(E) p Fp 1771 2507 a(+) p Fl 1869 2507 a(i) p Fp(0;) p Fl 1995 2507 a(K) p Fi 2078 2522 a(al) p Fp 2142 2507 a(\)) p Fl(b) p Fi 2221 2522 a(m) p Fm(1) p Fk 2323 2507 a(k) p Fp 2400 2507 a(=) p Fl 2504 2507 a(o) p Fp(\(1\)) p Fk(k) p Fl(P) p Fi 2789 2522 a(l) p Fk 2814 2507 a(k) p Fp 0 2721 a(for) p 149 2721 a(0) p Fl 225 2721 a(<) p 329 2721 a(\033) p Fk 416 2721 a(\034) p Fp 543 2721 a(1) p 624 2721 a(small) p 880 2721 a(enough.) p 1254 2721 a(W) p 1346 2721 a(e) p 1421 2721 a(claim) p 1682 2721 a(that) p Fk 608 2935 a(k) p Fl(r) p Fi 702 2950 a(\027) p Fl 745 2935 a(R) p Fp 820 2935 a(\() p Fl(E) p Fp 959 2935 a(+) p Fl 1057 2935 a(i) p Fp(0;) p Fl 1183 2935 a(H) p Fi 1264 2950 a(a) p Fp 1305 2935 a(\)) p Fl(X) p Fm 1432 2894 a(+) p Fi 1424 2960 a(al) p Fl 1491 2935 a(r) p Fh 1535 2951 a(\000) p Fi(\027) t(=) p Fm(3) p Fk 1703 2935 a(k) p Fp 1781 2935 a(=) p Fl 1884 2935 a(O) p Fp 1962 2935 a(\() p Fl(d) p Fh 2051 2894 a(\000) p Fi(\027) t(=) p 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a(X) p Fh 1343 3964 a(\000) p Fi 1335 4031 a(al) p Fl 1402 4006 a(R) p Fp 1477 4006 a(\() p Fl(E) p Fp 1615 4006 a(+) p Fl 1713 4006 a(i) p Fp(0;) p Fl 1839 4006 a(K) p Fi 1922 4021 a(al) p Fp 1985 4006 a(\)) p Fl(b) p Fi 2064 4021 a(m) p Fm(1) p Fk 2167 4006 a(k) p Fp 2244 4006 a(=) p Fl 2348 4006 a(O) p Fp 2426 4006 a(\(1\)) p 2582 4006 a(for) p 2731 4006 a(an) m(y) p Fl 2915 4006 a(L) p Fk 3009 4006 a(\035) p Fp 3136 4006 a(1,) p 3245 4006 a(so) p 3364 4006 a(that) p Fk 579 4220 a(k) p Fl(r) p Fi 673 4235 a(\027) p Fl 716 4220 a(R) p Fp 791 4220 a(\() p Fl(E) p Fp 929 4220 a(+) p Fl 1027 4220 a(i) p Fp(0;) p Fl 1153 4220 a(H) p Fi 1234 4235 a(a) p Fp 1275 4220 a(\)) p Fl(X) p Fh 1402 4178 a(\000) p Fi 1394 4245 a(al) p Fl 1461 4220 a(R) p Fp 1536 4220 a(\() p Fl(E) p Fp 1674 4220 a(+) p Fl 1772 4220 a(i) p Fp(0;) p Fl 1898 4220 a(K) p Fi 1981 4235 a(al) p Fp 2044 4220 a(\)) p Fl(b) p Fi 2123 4235 a(m) p Fm(1) p Fk 2226 4220 a(k) p Fp 2303 4220 a(=) p Fl 2407 4220 a(O) p Fp 2485 4220 a(\() p Fl(d) p Fh 2574 4179 a(\000) p Fi(L) p Fp 2680 4220 a(\)) p Fk(k) p Fl(Q) p Fi 2845 4235 a(\027) p Fk 2888 4220 a(k) p Fl(:) p Fp 0 4434 a(A) p 106 4434 a(similar) p 426 4434 a(b) s(ound) p 727 4434 a(is) p 825 4434 a(true) p 1031 4434 a(for) p Fl 1180 4434 a(X) p Fh 1269 4398 a(1) p Fi 1261 4458 a(al) p Fp 1343 4434 a(.) p 1414 4434 a(Th) m(us) p 1661 4434 a(w) m(e) p 1804 4434 a(ha) m(v) m(e) p 2029 4434 a(sho) m(wn) p 2325 4434 a(that) p Fl 2537 4434 a(P) p Fi 2600 4449 a(m) p Fp 2699 4434 a(ob) s(eys) p Fk 826 4648 a(k) p Fl(P) p Fi 939 4663 a(m) p Fk 1005 4648 a(k) p Fp 1083 4648 a(=) p Fl 1186 4648 a(O) p Fp 1264 4648 a(\() p Fl(d) p Fh 1353 4607 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 1521 4648 a(\)) p 1581 4648 a(+) p Fl 1679 4648 a(o) p Fp(\(1\)) p Fk(k) p Fl(P) p Fi 1964 4663 a(l) p Fk 1989 4648 a(k) p Fp 2061 4648 a(+) p Fl 2159 4648 a(O) p Fp 2237 4648 a(\() p Fl(d) p Fh 2326 4607 a(\000) p Fi(L) p Fp 2432 4648 a(\)) p Fk(k) p Fl(Q) p Fi 2597 4663 a(\027) p Fk 2640 4648 a(k) p Fl(:) p Fp 3294 4648 a(\(5.13\)) 0 4862 y(A) p 106 4862 a(similar) p 426 4862 a(argumen) m(t) p 862 4862 a(applies) p 1188 4862 a(to) p Fl 1307 4862 a(R) p Fi 1381 4877 a(m) p Fp 1448 4862 a(.) p 1518 4862 a(W) p 1610 4862 a(e) p 1686 4862 a(represen) m(t) p Fl 2107 4862 a(R) p Fi 2181 4877 a(m) p Fp 2280 4862 a(as) p Fl 170 5076 a(R) p Fi 244 5091 a(m) p Fp 339 5076 a(=) p Fl 442 5076 a(r) p Fi 486 5091 a(\027) p Fl 529 5076 a( ) p Fi 592 5091 a(l) p Fl 619 5076 a(R) p Fp 694 5076 a(\() p Fl(E) p Fp 832 5076 a(+) p Fl 930 5076 a(i) p Fp(0;) p Fl 1056 5076 a(K) p Fi 1139 5091 a(al) p Fp 1202 5076 a(\)) p Fl(\031) p Fi 1295 5091 a(m) p Fl 1362 5076 a(r) p Fi 1406 5091 a(\027) t(=) p Fm(3) p Fp 1542 5076 a(+) p Fl 1640 5076 a(r) p Fi 1684 5091 a(\027) p Fl 1727 5076 a(R) p Fp 1802 5076 a(\() p Fl(E) p Fp 1940 5076 a(+) p Fl 2038 5076 a(i) p Fp(0;) p Fl 2164 5076 a(H) p Fi 2245 5091 a(a) p Fp 2287 5076 a(\)) p Fl(V) p Fi 2382 5091 a(al) p Fl 2445 5076 a(R) p Fp 2520 5076 a(\() p Fl(E) p Fp 2658 5076 a(+) p Fl 2756 5076 a(i) p Fp(0;) p Fl 2882 5076 a(K) p Fi 2965 5091 a(al) p Fp 3028 5076 a(\)) p Fl(\031) p Fi 3121 5091 a(m) p Fl 3188 5076 a(r) p Fi 3232 5091 a(\027) t(=) p Fm(3) p Fl 3346 5076 a(:) p Fp 0 5290 a(The) p 201 5290 a(\014rst) p 402 5290 a(op) s(erator) p 794 5290 a(ob) s(eys) p Fk 165 5504 a(k) p Fl(r) p Fi 259 5519 a(\027) p Fl 302 5504 a( ) p Fi 365 5519 a(l) p Fl 392 5504 a(R) p Fp 467 5504 a(\() p Fl(E) p Fp 605 5504 a(+) p Fl 703 5504 a(i) p Fp(0;) p Fl 829 5504 a(K) p Fi 912 5519 a(al) p Fp 975 5504 a(\)) p Fl(\031) p Fi 1068 5519 a(m) p Fl 1135 5504 a(r) p Fi 1179 5520 a(\027) t(=) p Fm(3) p Fk 1293 5504 a(k) p Fp 1370 5504 a(=) p Fl 1474 5504 a(O) p Fp 1552 5504 a(\() p Fl(d) p Fh 1641 5463 a(\000) p Fm(2) p Fi(\027) t(=) p Fm(3) p Fp 1843 5504 a(\)) p Fk(k) p Fl(r) p Fi 1975 5520 a(\027) t(=) p Fm(3) p Fl 2089 5504 a(R) p Fp 2164 5504 a(\() p Fl(E) p Fp 2302 5504 a(+) p Fl 2400 5504 a(i) p Fp(0;) p Fl 2526 5504 a(K) p Fi 2609 5519 a(al) p Fp 2672 5504 a(\)) p Fl(r) p Fi 2754 5520 a(\027) t(=) p Fm(3) p Fk 2868 5504 a(k) p Fp 2946 5504 a(=) p Fl 3049 5504 a(O) p Fp 3127 5504 a(\() p Fl(d) p Fh 3216 5463 a(\000) p Fi(\027) p Fp 3313 5504 a(\)) p Fl(:) p Fp 1723 5753 a(27) p 90 rotate dyy eop %%Page: 28 28 28 27 bop Fp 0 407 a(W) p 92 407 a(e) p 172 407 a(estimate) p 567 407 a(the) p 739 407 a(second) p 1058 407 a(op) s(erator) p 1455 407 a(b) m(y) p 1595 407 a(decomp) s(osing) p Fl 2177 407 a(V) p Fi 2234 422 a(al) p Fp 2332 407 a(=) p Fl 2443 407 a(V) p Fi 2500 422 a(al) p Fp 2563 407 a(\() p Fl(\022) p Fi 2646 422 a(l) p Fp 2672 407 a(\)) p 2747 407 a(as) p 2871 407 a(in) p 2989 407 a(\(3.14\).) p 3321 407 a(Since) p Fk 0 527 a(k) p Fp 54 527 a(~) p Fl 50 527 a(s) p Fi 96 542 a(l) p Fm 118 542 a(1) p Fl 157 527 a(R) p Fp 232 527 a(\() p Fl(E) p Fp 370 527 a(+) p Fl 468 527 a(i) p Fp(0;) p Fl 594 527 a(K) p Fi 677 542 a(al) p Fp 740 527 a(\)) p Fl(\031) p Fi 833 542 a(m) p Fl 900 527 a(r) p Fi 944 543 a(\027) t(=) p Fm(3) p Fk 1058 527 a(k) p Fp 1136 527 a(=) p Fl 1239 527 a(O) p Fp 1317 527 a(\() p Fl(d) p Fh 1406 491 a(\000) p Fi(\027) t(=) p Fm(6) p Fp 1574 527 a(\),) p 1671 527 a(w) m(e) p 1815 527 a(ha) m(v) m(e) p Fk 611 728 a(k) p Fl(r) p Fi 705 743 a(\027) p Fl 748 728 a(R) p Fp 823 728 a(\() p Fl(E) p Fp 961 728 a(+) p Fl 1059 728 a(i) p Fp(0;) p Fl 1185 728 a(H) p Fi 1266 743 a(a) p Fp 1308 728 a(\)) p Fl(X) p Fi 1427 743 a(al) p Fl 1490 728 a(R) p Fp 1565 728 a(\() p Fl(E) p Fp 1703 728 a(+) p Fl 1801 728 a(i) p Fp(0;) p Fl 1927 728 a(K) p Fi 2010 743 a(al) p Fp 2073 728 a(\)) p Fl(\031) p Fi 2166 743 a(m) p Fl 2233 728 a(r) p Fi 2277 744 a(\027) t(=) p Fm(3) p Fk 2391 728 a(k) p Fp 2468 728 a(=) p Fl 2572 728 a(o) p Fp(\(1\)) p Fk(k) p Fl(P) p Fi 2857 743 a(l) p Fk 2882 728 a(k) p Fp 0 929 a(and) p 190 929 a(it) p 287 929 a(follo) m(ws) p 608 929 a(from) p 838 929 a(\(5.12\)) p 1120 929 a(that) p Fk 264 1130 a(k) p Fl(r) p Fi 358 1145 a(\027) p Fl 401 1130 a(R) p Fp 476 1130 a(\() p Fl(E) p Fp 614 1130 a(+) p Fl 712 1130 a(i) p Fp(0;) p Fl 838 1130 a(H) p Fi 919 1145 a(a) p Fp 961 1130 a(\)) p Fl(X) p Fm 1088 1089 a(+) p Fi 1080 1155 a(al) p Fl 1146 1130 a(R) p Fp 1221 1130 a(\() p Fl(E) p Fp 1360 1130 a(+) p Fl 1458 1130 a(i) p Fp(0;) p Fl 1584 1130 a(K) p Fi 1667 1145 a(al) p Fp 1730 1130 a(\)) p Fl(\031) p Fi 1823 1145 a(m) p Fl 1890 1130 a(r) p Fi 1934 1146 a(\027) t(=) p Fm(3) p Fk 2047 1130 a(k) p Fp 2125 1130 a(=) p Fl 2228 1130 a(O) p Fp 2306 1130 a(\() p Fl(d) p Fh 2395 1089 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2563 1130 a(\)) p 2623 1130 a(+) p Fl 2721 1130 a(O) p Fp 2799 1130 a(\() p Fl(d) p Fh 2888 1089 a(\000) p Fi(L) p Fp 2994 1130 a(\)) p Fk(k) p Fl(Q) p Fi 3159 1145 a(\027) p Fk 3202 1130 a(k) p Fl(:) p Fp 0 1331 a(The) p 204 1331 a(free) p 395 1331 a(particle) p 751 1331 a(starting) p 1118 1331 a(from) p 1352 1331 a(supp) p Fl 1570 1331 a(X) p Fh 1659 1290 a(\000) p Fi 1651 1356 a(al) p Fp 1754 1331 a(nev) m(er) p 2017 1331 a(passes) p 2315 1331 a(o) m(v) m(er) p 2528 1331 a(\005) p Fi 2601 1346 a(m) p Fp 2667 1331 a(\() p Fl(\022) p Fi 2750 1346 a(m) p Fp 2817 1331 a(\)) p 2891 1331 a(for) p Fl 3044 1331 a(t) p 3113 1331 a(<) p Fp 3223 1331 a(0.) p 3353 1331 a(This) 0 1452 y(enables) p 339 1452 a(us) p 461 1452 a(to) p 577 1452 a(use) p 742 1452 a(the) p 907 1452 a(same) p 1148 1452 a(argumen) m(t) p 1581 1452 a(as) p 1698 1452 a(in) p 1808 1452 a(the) p 1973 1452 a(pro) s(of) p 2225 1452 a(of) p 2333 1452 a(Lemma) p 2678 1452 a(4.2) p 2832 1452 a(and) p 3018 1452 a(w) m(e) p 3158 1452 a(can) p 3334 1452 a(sho) m(w) 0 1572 y(that) p Fk 955 1692 a(k) p Fl(r) p Fh 1049 1707 a(\000) p Fi(L) p Fl 1156 1692 a(X) p Fh 1245 1651 a(\000) p Fi 1237 1717 a(al) p Fl 1304 1692 a(R) p Fp 1379 1692 a(\() p Fl(E) p Fp 1517 1692 a(+) p Fl 1615 1692 a(i) p Fp(0;) p Fl 1741 1692 a(K) p Fi 1824 1707 a(al) p Fp 1887 1692 a(\)) p Fl(\031) p Fi 1980 1707 a(m) p Fl 2047 1692 a(r) p Fi 2091 1708 a(\027) t(=) p Fm(3) p Fk 2205 1692 a(k) p Fp 2282 1692 a(=) p Fl 2386 1692 a(O) p Fp 2464 1692 a(\(1\)) 0 1859 y(for) p 149 1859 a(an) m(y) p Fl 333 1859 a(L) p Fk 427 1859 a(\035) p Fp 555 1859 a(1.) p 674 1859 a(The) p 874 1859 a(op) s(erator) p Fl 1267 1859 a(X) p Fh 1356 1822 a(1) p Fi 1348 1883 a(al) p Fp 1463 1859 a(also) p 1659 1859 a(satis\014es) p 2018 1859 a(the) p 2186 1859 a(same) p 2431 1859 a(b) s(ound.) p 2769 1859 a(Th) m(us) p 3017 1859 a(w) m(e) p 3160 1859 a(get) p Fk 820 2060 a(k) p Fl(R) p Fi 944 2075 a(m) p Fk 1011 2060 a(k) p Fp 1089 2060 a(=) p Fl 1192 2060 a(O) p Fp 1270 2060 a(\() p Fl(d) p Fh 1359 2018 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 1527 2060 a(\)) p 1587 2060 a(+) p Fl 1685 2060 a(o) p Fp(\(1\)) p Fk(k) p Fl(P) p Fi 1970 2075 a(l) p Fk 1995 2060 a(k) p Fp 2067 2060 a(+) p Fl 2165 2060 a(O) p Fp 2243 2060 a(\() p Fl(d) p Fh 2332 2018 a(\000) p Fi(L) p Fp 2438 2060 a(\)) p Fk(k) p Fl(Q) p Fi 2603 2075 a(\027) p Fk 2646 2060 a(k) p Fl(:) p Fp 3294 2060 a(\(5.14\)) 0 2261 y(W) p 92 2261 a(e) p 159 2261 a(ha) m(v) m(e) p 375 2261 a(to) p 485 2261 a(estimate) p Fl 867 2261 a(P) p Fi 930 2276 a(l) p Fp 979 2261 a(on) p 1105 2261 a(the) p 1264 2261 a(righ) m(t) p 1491 2261 a(side) p 1678 2261 a(of) p 1780 2261 a(\(5.13\)) p 2052 2261 a(and) p 2233 2261 a(\(5.14\).) p 2550 2261 a(T) p 2612 2261 a(o) p 2684 2261 a(do) p 2811 2261 a(this,) p 3021 2261 a(w) m(e) p 3155 2261 a(represen) m(t) p Fl 0 2381 a(P) p Fi 63 2396 a(l) p Fp 121 2381 a(as) p Fl 306 2582 a(P) p Fi 369 2597 a(l) p Fp 422 2582 a(=) p Fl 526 2582 a(r) p Fi 570 2597 a(\027) p Fl 613 2582 a( ) p Fi 676 2597 a(m) p Fl 743 2582 a(R) p Fp 818 2582 a(\() p Fl(E) p Fp 956 2582 a(+) p Fl 1054 2582 a(i) p Fp(0;) p Fl 1180 2582 a(K) p Fi 1263 2597 a(am) p Fp 1367 2582 a(\)) p Fl(b) p Fi 1446 2597 a(l) p Fm 1468 2597 a(1) p Fp 1530 2582 a(+) p Fl 1628 2582 a(r) p Fi 1672 2597 a(\027) p Fl 1715 2582 a(R) p Fp 1790 2582 a(\() p Fl(E) p Fp 1928 2582 a(+) p Fl 2026 2582 a(i) p Fp(0;) p Fl 2152 2582 a(H) p Fi 2233 2597 a(a) p Fp 2274 2582 a(\)) p Fl(V) p Fi 2369 2597 a(am) p Fl 2473 2582 a(R) p Fp 2548 2582 a(\() p Fl(E) p Fp 2686 2582 a(+) p Fl 2784 2582 a(i) p Fp(0;) p Fl 2910 2582 a(K) p Fi 2993 2597 a(am) p Fp 3097 2582 a(\)) p Fl(b) p Fi 3176 2597 a(l) p Fm 3198 2597 a(1) p Fp 0 2783 a(with) p Fl 222 2783 a(V) p Fi 279 2798 a(am) p Fp 411 2783 a(=) p Fl 514 2783 a(V) p Fi 571 2798 a(am) p Fp 675 2783 a(\() p Fl(\022) p Fi 758 2798 a(m) p Fp 825 2783 a(\)) p Fl(;) p 939 2783 a(\022) p Fi 984 2798 a(m) p Fp 1079 2783 a(=) 1200 2757 y(^) p Fl 1183 2783 a(d) p Fi 1234 2798 a(j) t(m) p Fp 1332 2783 a(.) p 1403 2783 a(Then) p 1657 2783 a(w) m(e) p 1801 2783 a(ha) m(v) m(e) p Fk 840 2984 a(k) p Fl(P) p Fi 953 2999 a(l) p Fk 978 2984 a(k) p Fp 1056 2984 a(=) p Fl 1159 2984 a(O) p Fp 1237 2984 a(\() p Fl(d) p Fh 1326 2943 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 1494 2984 a(\)) p 1554 2984 a(+) p Fl 1652 2984 a(o) p Fp(\(1\)) p Fk(k) p Fl(P) p Fi 1937 2999 a(m) p Fk 2003 2984 a(k) p Fp 2075 2984 a(+) p Fl 2173 2984 a(O) p Fp 2251 2984 a(\() p Fl(d) p Fh 2340 2943 a(\000) p Fi(L) p Fp 2446 2984 a(\)) p Fk(k) p Fl(Q) p Fi 2611 2999 a(\027) p Fk 2654 2984 a(k) p Fp 3294 2984 a(\(5.15\)) 0 3185 y(b) m(y) p 142 3185 a(the) p 317 3185 a(same) p 568 3185 a(argumen) m(t) p 1010 3185 a(as) p 1137 3185 a(used) p 1366 3185 a(to) p 1492 3185 a(pro) m(v) m(e) p 1761 3185 a(\(5.13\).) p 2100 3185 a(This,) p 2358 3185 a(together) p 2750 3185 a(with) p 2979 3185 a(\(5.10\),) p 3294 3185 a(\(5.13\)) 0 3305 y(and) p 190 3305 a(\(5.14\),) p 498 3305 a(forms) p 767 3305 a(a) p 848 3305 a(closed) p 1136 3305 a(system) p 1459 3305 a(of) p 1570 3305 a(inequalities) p 2083 3305 a(on) p Fl 2218 3305 a(Q) p Fi 2295 3320 a(\027) p Fl 2339 3305 a(;) p 2415 3305 a(P) p Fi 2478 3320 a(m) p Fl 2544 3305 a(;) p 2620 3305 a(R) p Fi 2694 3320 a(m) p Fp 2794 3305 a(and) p Fl 2983 3305 a(P) p Fi 3046 3320 a(l) p Fp 3072 3305 a(.) p 3142 3305 a(Hence) p 3432 3305 a(w) m(e) 0 3426 y(can) p 175 3426 a(obtain) p Fk 474 3426 a(k) p Fl(Q) p Fi 601 3441 a(\027) p Fk 644 3426 a(k) p Fp 722 3426 a(=) p Fl 825 3426 a(O) p Fp 903 3426 a(\() p Fl(d) p Fh 992 3390 a(\000) p Fi(\027) p Fp 1089 3426 a(\).) p 1196 3426 a(This) p 1415 3426 a(pro) m(v) m(es) p 1712 3426 a(\(4.3\).) p 1981 3426 a(W) p 2073 3426 a(e) p 2145 3426 a(can) p 2320 3426 a(also) p 2511 3426 a(obtain) p Fk 2811 3426 a(k) p Fl(P) p Fi 2924 3441 a(m) p Fk 2990 3426 a(k) p Fp 3067 3426 a(=) p Fl 3171 3426 a(O) p Fp 3249 3426 a(\() p Fl(d) p Fh 3338 3390 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 3505 3426 a(\)) 0 3546 y(sim) m(ultaneously) p 619 3546 a(.) p 692 3546 a(T) p 754 3546 a(o) p 836 3546 a(pro) m(v) m(e) p 1099 3546 a(\(4.4\),) p 1359 3546 a(w) m(e) p 1502 3546 a(represen) m(t) p Fl 1923 3546 a(P) p Fi 1986 3561 a(j) p Fp 2055 3546 a(as) p Fl 290 3747 a(P) p Fi 353 3762 a(j) p Fp 417 3747 a(=) p Fl 520 3747 a(r) p Fi 564 3762 a(\027) p Fl 608 3747 a( ) p Fi 671 3762 a(m) p Fl 738 3747 a(R) p Fp 813 3747 a(\() p Fl(E) p Fp 951 3747 a(+) p Fl 1049 3747 a(i) p Fp(0;) p Fl 1175 3747 a(K) p Fi 1258 3762 a(am) p Fp 1362 3747 a(\)) p Fl(b) p Fi 1441 3762 a(j) p Fm 1474 3762 a(1) p Fp 1535 3747 a(+) p Fl 1633 3747 a(r) p Fi 1677 3762 a(\027) p Fl 1720 3747 a(R) p Fp 1795 3747 a(\() p Fl(E) p Fp 1933 3747 a(+) p Fl 2031 3747 a(i) p Fp(0;) p Fl 2157 3747 a(H) p Fi 2238 3762 a(a) p Fp 2279 3747 a(\)) p Fl(V) p Fi 2374 3762 a(am) p Fl 2478 3747 a(R) p Fp 2553 3747 a(\() p Fl(E) p Fp 2692 3747 a(+) p Fl 2790 3747 a(i) p Fp(0;) p Fl 2916 3747 a(K) p Fi 2999 3762 a(am) p Fp 3102 3747 a(\)) p Fl(b) p Fi 3181 3762 a(j) p Fm 3214 3762 a(1) p Fp 0 3948 a(for) p Fl 149 3948 a(j) p Fk 223 3948 a(6) p Fp(=) p Fl 326 3948 a(m) p Fp(.) p 482 3948 a(Then) p 737 3948 a(w) m(e) p 880 3948 a(can) p 1059 3948 a(sho) m(w) p Fk 834 4149 a(k) p Fl(P) p Fi 947 4164 a(j) p Fk 984 4149 a(k) p Fp 1061 4149 a(=) p Fl 1165 4149 a(O) p Fp 1243 4149 a(\() p Fl(d) p Fh 1332 4108 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 1499 4149 a(\)) p 1559 4149 a(+) p Fl 1657 4149 a(o) p Fp(\(1\)) p Fk(k) p Fl(P) p Fi 1942 4164 a(m) p Fk 2008 4149 a(k) p Fp 2080 4149 a(+) p Fl 2178 4149 a(O) p Fp 2256 4149 a(\() p Fl(d) p Fh 2345 4108 a(\000) p Fi(L) p Fp 2451 4149 a(\)) p Fk(k) p Fl(Q) p Fi 2616 4164 a(\027) p Fk 2659 4149 a(k) p Fp 0 4350 a(again) p 260 4350 a(in) p 374 4350 a(the) p 542 4350 a(same) p 787 4350 a(w) m(a) m(y) p 985 4350 a(as) p 1104 4350 a(used) p 1327 4350 a(to) p 1446 4350 a(pro) m(v) m(e) p 1709 4350 a(\(5.13\).) p 2029 4350 a(Hence) p Fk 2319 4350 a(k) p Fl(P) p Fi 2432 4365 a(j) p Fk 2469 4350 a(k) p Fp 2546 4350 a(=) p Fl 2650 4350 a(O) p Fp 2728 4350 a(\() p Fl(d) p Fh 2817 4314 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2984 4350 a(\)) p 3055 4350 a(and) p 3245 4350 a(\(4.4\)) p 3478 4350 a(is) 0 4471 y(pro) m(v) m(ed.) 146 4635 y(\(4\)) p 307 4635 a(Let) p Fl 486 4635 a(m) p Fp 608 4635 a(and) p Fl 802 4635 a(l) r(;) p 913 4635 a(m) p Fk 1033 4635 a(6) p Fp(=) p Fl 1143 4635 a(l) p Fp 1174 4635 a(,) p 1239 4635 a(b) s(e) p 1375 4635 a(as) p 1499 4635 a(ab) s(o) m(v) m(e.) p 1825 4635 a(Both) p Fl 2072 4635 a(m) p Fp 2193 4635 a(and) p Fl 2387 4635 a(l) p Fp 2455 4635 a(are) p 2621 4635 a(in) p Fl 2739 4635 a(a) p Fp(.) p 2872 4635 a(The) p 3077 4635 a(aim) p 3271 4635 a(of) p 3386 4635 a(this) 0 4756 y(step) p 206 4756 a(is) p 305 4756 a(to) p 424 4756 a(pro) m(v) m(e) p 687 4756 a(that) p Fk 907 4957 a(k) p Fl(F) p Fm 1020 4972 a(1) p Fk 1059 4957 a(k) p Fp 1137 4957 a(=) p Fk 1240 4957 a(k) p Fl(b) p Fi 1331 4972 a(m) p Fm(1) p Fl 1433 4957 a(R) p Fp 1508 4957 a(\() p Fl(E) p Fp 1647 4957 a(+) p Fl 1745 4957 a(i) p Fp(0;) p Fl 1871 4957 a(H) p Fi 1952 4972 a(a) p Fp 1993 4957 a(\)) 2027 4930 y(~) p Fl 2031 4957 a(b) p Fi 2072 4972 a(m) p Fm(1) p Fk 2174 4957 a(k) p Fp 2252 4957 a(=) p Fl 2355 4957 a(O) p Fp 2433 4957 a(\() p Fl(d) p Fi 2522 4916 a(c\033) p Fp 2598 4957 a(\)) p 3294 4957 a(\(5.16\)) 0 5158 y(for) p Fl 149 5158 a(c) p Fp 219 5158 a(=) p Fl 322 5158 a(c) p Fi 364 5173 a(n) p Fh(\000) p Fm(1) p Fp 501 5158 a(.) p 572 5158 a(T) p 634 5158 a(o) p 715 5158 a(pro) m(v) m(e) p 978 5158 a(this,) p 1196 5158 a(w) m(e) p 1339 5158 a(set) p Fl 1491 5158 a(F) p Fm 1554 5173 a(2) p Fp 1622 5158 a(=) p Fl 1725 5158 a(b) p Fi 1766 5173 a(m) p Fm(1) p Fl 1869 5158 a(R) p Fp 1944 5158 a(\() p Fl(E) p Fp 2082 5158 a(+) p Fl 2180 5158 a(i) p Fp(0;) p Fl 2306 5158 a(H) p Fi 2387 5173 a(a) p Fp 2428 5158 a(\)) t(~) p Fl 2466 5158 a(s) p Fi 2512 5173 a(l) p Fm 2534 5173 a(1) p Fp 2573 5158 a(.) p 2644 5158 a(Then) p Fl 183 5359 a(F) p Fm 246 5374 a(1) p Fp 368 5359 a(=) p Fl 527 5359 a(b) p Fi 568 5374 a(m) p Fm(1) p Fl 671 5359 a( ) p Fi 734 5374 a(l) p Fl 760 5359 a(R) p Fp 835 5359 a(\() p Fl(E) p Fp 973 5359 a(+) p Fl 1071 5359 a(i) p Fp(0;) p Fl 1197 5359 a(K) p Fi 1280 5374 a(al) p Fp 1343 5359 a(\)) 1377 5332 y(~) p Fl 1381 5359 a(b) p Fi 1422 5374 a(m) p Fm(1) p Fp 1547 5359 a(+) p Fl 1645 5359 a(b) p Fi 1686 5374 a(m) p Fm(1) p Fl 1788 5359 a(R) p Fp 1863 5359 a(\() p Fl(E) p Fp 2001 5359 a(+) p Fl 2099 5359 a(i) p Fp(0;) p Fl 2225 5359 a(H) p Fi 2306 5374 a(a) p Fp 2348 5359 a(\)) p Fl(V) p Fi 2443 5374 a(al) p Fl 2506 5359 a(R) p Fp 2581 5359 a(\() p Fl(E) p Fp 2719 5359 a(+) p Fl 2817 5359 a(i) p Fp(0;) p Fl 2943 5359 a(K) p Fi 3026 5374 a(al) p Fp 3089 5359 a(\)) 3123 5332 y(~) p Fl 3127 5359 a(b) p Fi 3168 5374 a(m) p Fm(1) p Fl 3271 5359 a(;) 183 5504 y(F) p Fm 246 5519 a(2) p Fp 368 5504 a(=) p Fl 527 5504 a(b) p Fi 568 5519 a(m) p Fm(1) p Fl 671 5504 a( ) p Fi 734 5519 a(m) p Fl 800 5504 a(R) p Fp 875 5504 a(\() p Fl(E) p Fp 1014 5504 a(+) p Fl 1112 5504 a(i) p Fp(0;) p Fl 1238 5504 a(K) p Fi 1321 5519 a(am) p Fp 1425 5504 a(\)) t(~) p Fl 1463 5504 a(s) p Fi 1509 5519 a(l) p Fm 1531 5519 a(1) p Fp 1592 5504 a(+) p Fl 1690 5504 a(b) p Fi 1731 5519 a(m) p Fm(1) p Fl 1833 5504 a(R) p Fp 1908 5504 a(\() p Fl(E) p Fp 2046 5504 a(+) p Fl 2144 5504 a(i) p Fp(0;) p Fl 2270 5504 a(H) p Fi 2351 5519 a(a) p Fp 2393 5504 a(\)) p Fl(V) p Fi 2488 5519 a(am) p Fl 2591 5504 a(R) p Fp 2666 5504 a(\() p Fl(E) p Fp 2805 5504 a(+) p Fl 2903 5504 a(i) p Fp(0;) p Fl 3029 5504 a(K) p Fi 3112 5519 a(am) p Fp 3215 5504 a(\)) t(~) p Fl 3253 5504 a(s) p Fi 3299 5519 a(l) p Fm 3321 5519 a(1) p Fp 1723 5753 a(28) p 90 rotate dyy eop %%Page: 29 29 29 28 bop Fp 0 407 a(b) m(y) p 132 407 a(Lemma) p 478 407 a(3.1.) p 672 407 a(W) p 764 407 a(e) p 837 407 a(decomp) s(ose) p Fl 1325 407 a(V) p Fi 1382 422 a(al) p Fp 1474 407 a(as) p 1591 407 a(in) p 1702 407 a(\(3.14\)) p 1981 407 a(and) p Fl 2167 407 a(V) p Fi 2224 422 a(am) p Fp 2358 407 a(as) p 2474 407 a(in) p 2585 407 a(\(3.25\).) p 2904 407 a(In) p 3023 407 a(the) p 3188 407 a(previous) 0 527 y(step,) p 232 527 a(w) m(e) p 374 527 a(ha) m(v) m(e) p 597 527 a(already) p 939 527 a(pro) m(v) m(ed) p 1255 527 a(\(4.4\)) p 1486 527 a(for) p Fl 1633 527 a(H) p Fi 1714 542 a(a) p Fp 1756 527 a(,) p 1814 527 a(and) p 2002 527 a(hence) p Fl 2271 527 a(H) p Fi 2352 542 a(a) p Fp 2424 527 a(satis\014es) p 2782 527 a(the) p 2948 527 a(assumption) p 3462 527 a(in) 0 648 y(Lemma) p 348 648 a(4.2.) p 543 648 a(If) p 641 648 a(w) m(e) p 784 648 a(use) p 953 648 a(inductiv) m(e) p 1376 648 a(assumptions) p 1930 648 a(for) p Fl 2079 648 a(K) p Fi 2162 663 a(am) p Fp 2299 648 a(and) p Fl 2488 648 a(K) p Fi 2571 663 a(al) p Fp 2635 648 a(,) p 2694 648 a(then) p 2917 648 a(w) m(e) p 3060 648 a(ha) m(v) m(e) p Fk 159 868 a(k) p Fl(F) p Fm 272 883 a(1) p Fk 312 868 a(k) p Fp 389 868 a(=) p Fl 493 868 a(O) p Fp 571 868 a(\() p Fl(d) p Fi 660 826 a(c\033) p Fp 736 868 a(\)) p 796 868 a(+) p Fl 894 868 a(O) p Fp 972 868 a(\() p Fl(d) p Fh 1061 826 a(\000) p Fm(1) p Fi(=) p Fm(4+) p Fi(c\033) p Fp 1353 868 a(\)) p Fk(k) p Fl(F) p Fm 1504 883 a(2) p Fk 1543 868 a(k) p Fl(;) p Fk 1734 868 a(k) p Fl(F) p Fm 1847 883 a(2) p Fk 1887 868 a(k) p Fp 1964 868 a(=) p Fl 2068 868 a(O) p Fp 2146 868 a(\() p Fl(d) p Fh 2235 826 a(\000) p Fm(1) p Fi(=) p Fm(4+) p Fi(c\033) p Fp 2527 868 a(\)) p 2587 868 a(+) p Fl 2685 868 a(O) p Fp 2763 868 a(\() p Fl(d) p Fh 2852 826 a(\000) p Fm(1) p Fi(=) p Fm(4+) p Fi(c\033) p Fp 3144 868 a(\)) p Fk(k) p Fl(F) p Fm 3295 883 a(1) p Fk 3334 868 a(k) p Fp 0 1088 a(for) p Fl 149 1088 a(c) p Fp 219 1088 a(=) p Fl 322 1088 a(c) p Fi 364 1103 a(n) p Fh(\000) p Fm(1) p Fp 501 1088 a(.) p 572 1088 a(This) p 795 1088 a(implies) p 1126 1088 a(\(5.16\).) 146 1258 y(\(5\)) p 310 1258 a(W) p 402 1258 a(e) p 484 1258 a(pro) s(ceed) p 851 1258 a(to) p 977 1258 a(pro) m(ving) p 1335 1258 a(\(4.5\),) p 1602 1258 a(\(4.6\)) p 1841 1258 a(and) p 2037 1258 a(\(4.7\).) p 2327 1258 a(Once) p 2583 1258 a(\(5.16\)) p 2871 1258 a(has) p 3051 1258 a(b) s(een) p 3288 1258 a(estab-) 0 1378 y(lished,) p 302 1378 a(\(4.5\)) p 532 1378 a(is) p 627 1378 a(pro) m(v) m(ed) p 942 1378 a(in) p 1053 1378 a(almost) p 1365 1378 a(the) p 1530 1378 a(same) p 1772 1378 a(w) m(a) m(y) p 1967 1378 a(as) p 2084 1378 a(in) p 2195 1378 a(the) p 2360 1378 a(case) p Fk 2564 1378 a(j) p Fl(a) p Fk(j) p Fp 2698 1378 a(=) p 2802 1378 a(1.) p 2920 1378 a(W) p 3012 1378 a(e) p 3085 1378 a(giv) m(e) p 3283 1378 a(only) p 3495 1378 a(a) 0 1499 y(sk) m(etc) m(h.) p 333 1499 a(W) p 425 1499 a(e) p 500 1499 a(set) p Fl 651 1499 a(A) p Fi 724 1514 a(j) t(k) p Fp 827 1499 a(=) p Fl 930 1499 a(b) p Fi 971 1514 a(j) p Fm 1004 1514 a(1) p Fl 1043 1499 a(R) p Fp 1118 1499 a(\() p Fl(E) p Fp 1254 1499 a(+) p Fl 1349 1499 a(i) p Fp(0;) p Fl 1475 1499 a(H) p Fi 1556 1514 a(a) p Fp 1597 1499 a(\)) p Fl(b) p Fi 1676 1514 a(k) p Fm 1715 1514 a(1) p Fp 1755 1499 a(.) p 1824 1499 a(W) p 1916 1499 a(e) p 1991 1499 a(\014rst) p 2191 1499 a(deal) p 2395 1499 a(with) p 2616 1499 a(the) p 2783 1499 a(case) p 2988 1499 a(that) p Fl 3198 1499 a(j) p Fp 3275 1499 a(or) p Fl 3393 1499 a(k) p Fp 3478 1499 a(is) 0 1619 y(in) p Fl 112 1619 a(a) p Fp(.) p 234 1619 a(Assume) p 594 1619 a(for) p 742 1619 a(brevit) m(y) p 1074 1619 a(that) p Fl 1284 1619 a(k) p Fk 1365 1619 a(2) p Fl 1459 1619 a(a) p Fp(.) p 1581 1619 a(Then) p 1834 1619 a(w) m(e) p 1976 1619 a(tak) m(e) p Fl 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p Fk 1898 3881 a(2) p Fl 1992 3881 a(a) p Fp 2069 3881 a(and) p Fl 2252 3881 a(\022) p Fp 2326 3881 a(as) p 2440 3881 a(in) p 2547 3881 a(the) p 2708 3881 a(case) p Fk 2908 3881 a(j) p Fl(a) p Fk(j) p Fp 3042 3881 a(=) p 3146 3881 a(1,) p 3249 3881 a(and) p 3432 3881 a(w) m(e) 0 4002 y(decomp) s(ose) p Fl 489 4002 a(V) p Fi 546 4017 a(am) p Fp 650 4002 a(\() p Fl(\022) p Fp 736 4002 a(\)) p 805 4002 a(as) p 924 4002 a(in) p 1036 4002 a(\(3.28\)) p 1316 4002 a(or) p 1434 4002 a(\(3.25\)) p 1714 4002 a(according) p 2151 4002 a(to) p 2269 4002 a(case) p 2474 4002 a(\(a\)) p 2629 4002 a(or) p 2747 4002 a(\(b\).) p 2947 4002 a(In) p 3067 4002 a(either) p 3342 4002 a(case,) 0 4122 y(w) m(e) p 142 4122 a(can) p 319 4122 a(sho) m(w) p Fk 559 4122 a(k) p Fl(A) p Fi 682 4137 a(j) t(k) p Fk 757 4122 a(k) p Fp 834 4122 a(=) p Fl 938 4122 a(O) p Fp 1016 4122 a(\() p Fl(d) p Fm 1105 4086 a(4) p Fi(c\033) p Fp 1216 4122 a(\)) p 1285 4122 a(b) m(y) p 1419 4122 a(\(5.18\).) p 1738 4122 a(Th) m(us) p 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4363 a(ha) m(v) m(e) p 3345 4363 a(b) s(een) 0 4483 y(pro) m(v) m(ed) p 317 4483 a(in) p 431 4483 a(the) p 599 4483 a(case) p Fk 805 4483 a(j) p Fl(a) p Fk(j) p Fp 940 4483 a(=) p Fl 1043 4483 a(n) p Fp 1134 4483 a(and) p 1324 4483 a(the) p 1492 4483 a(pro) s(of) p 1746 4483 a(is) p 1844 4483 a(no) m(w) p 2048 4483 a(complete.) p Fe 2497 4483 a(2) p Fp 146 4654 a(W) p 238 4654 a(e) p 310 4654 a(pro) m(v) m(e) p 569 4654 a(\(5.7\),) p 826 4654 a(\(5.8\)) p 1055 4654 a(and) p 1241 4654 a(\(5.12\)) p 1518 4654 a(whic) m(h) p 1794 4654 a(remain) p 2115 4654 a(unpro) m(v) m(ed.) p 2577 4654 a(The) p 2774 4654 a(pro) s(of) p 3025 4654 a(uses) p 3228 4654 a(Lemma) 0 4774 y(4.1.) p 229 4774 a(The) p 441 4774 a(op) s(erator) p Fl 846 4774 a(R) p Fp 921 4774 a(\() p Fl(E) p Fp 1067 4774 a(+) p Fl 1172 4774 a(i) p Fp(0;) p Fl 1298 4774 a(H) p Fi 1379 4789 a(a) p Fp 1421 4774 a(\)) p Fl(X) p Fm 1548 4738 a(+) p Fi 1540 4799 a(am) p Fp 1687 4774 a(is) p 1797 4774 a(appro) m(ximated) p 2426 4774 a(b) m(y) p 2573 4774 a(\(3.19\).) p 2927 4774 a(This,) p 3191 4774 a(together) 0 4894 y(with) p 227 4894 a(Lemma) p 579 4894 a(4.1,) p 769 4894 a(implies) p 1105 4894 a(\(5.7\),) p 1371 4894 a(and) p 1565 4894 a(\(5.12\)) p 1851 4894 a(is) p 1954 4894 a(sho) m(wn) p 2254 4894 a(in) p 2372 4894 a(exactly) p 2713 4894 a(the) p 2885 4894 a(same) p 3134 4894 a(w) m(a) m(y) p 3290 4894 a(.) p 3375 4894 a(The) 0 5015 y(appro) m(ximation) p 650 5015 a(for) p Fl 799 5015 a(X) p Fh 888 4979 a(\000) p Fi 880 5039 a(am) p Fl 984 5015 a(R) p Fp 1059 5015 a(\() p Fl(E) p Fp 1198 5015 a(+) p Fl 1296 5015 a(i) p Fp(0;) p Fl 1422 5015 a(K) p Fi 1505 5030 a(am) p Fp 1608 5015 a(\)) p 1679 5015 a(tak) m(es) p 1929 5015 a(the) p 2097 5015 a(form) p 2327 5015 a(\(3.22\),) p 2636 5015 a(and) p Fk 981 5235 a(k) p Fl(r) p Fi 1075 5250 a(\027) t(=) p Fm(2) p Fl 1189 5235 a(R) p Fp 1264 5235 a(\() p Fl(E) p Fp 1402 5235 a(+) p Fl 1500 5235 a(i) p Fp(0;) p Fl 1626 5235 a(K) p Fi 1709 5250 a(am) p Fp 1813 5235 a(\)) p Fl(r) p Fi 1895 5250 a(\027) t(=) p Fm(2) p Fk 2009 5235 a(k) p Fp 2086 5235 a(=) p Fl 2190 5235 a(O) p Fp 2268 5235 a(\() p Fl(d) p Fh 2357 5194 a(\000) p Fi(\027) t(=) p Fm(2) p Fp 2524 5235 a(\)) 0 5455 y(b) m(y) p 135 5455 a(inductiv) m(e) p 558 5455 a(assumption.) p 1112 5455 a(Hence) p 1402 5455 a(\(5.8\)) p 1635 5455 a(again) p 1895 5455 a(follo) m(ws) p 2215 5455 a(from) p 2446 5455 a(Lemma) p 2794 5455 a(4.1.) 1723 5753 y(29) p 90 rotate dyy eop %%Page: 30 30 30 29 bop Fq 146 407 a(6.) p 271 407 a(Scattering) p 808 407 a(b) m(y) p 964 407 a(a) p 1056 407 a(c) m(hain) p 1350 407 a(of) p 1478 407 a(\014elds) p 1766 407 a(:) p 1847 407 a(Pro) s(of) p 2156 407 a(of) p 2284 407 a(Theorem) p 2759 407 a(1.2) p Fp 146 601 a(The) p 355 601 a(remaining) p 819 601 a(t) m(w) m(o) p 1012 601 a(sections) p 1385 601 a(are) p 1556 601 a(dev) m(oted) p 1928 601 a(to) p 2056 601 a(pro) m(ving) p 2417 601 a(the) p 2593 601 a(second) p 2917 601 a(main) p 3169 601 a(theorem.) 0 722 y(W) p 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p Fi 1062 4423 a(b) p Fp 1129 4408 a(is) p 1227 4408 a(obtained) p 1628 4408 a(b) m(y) p 1764 4408 a(rep) s(eating) p 2195 4408 a(the) p 2363 4408 a(argumen) m(t) p 2799 4408 a(again.) p Fe 3097 4408 a(2) p Fq 0 4687 a(Lemma) p 397 4687 a(6.3) p Fo 589 4687 a(L) p 645 4687 a(et) p Fl 756 4687 a(f) p Fm 804 4702 a(1) p Fo 877 4687 a(b) p 917 4687 a(e) p 996 4687 a(again) p 1259 4687 a(as) p 1382 4687 a(in) p 1500 4687 a(L) p 1556 4687 a(emma) p Fp 1844 4687 a(6) p Fl(:) p Fp(1) p Fo 2003 4687 a(and) p 2191 4687 a(let) p Fl 2326 4687 a(K) p Fi 2409 4702 a(b) p Fo 2477 4687 a(b) p 2517 4687 a(e) p 2596 4687 a(de\014ne) p 2841 4687 a(d) p 2923 4687 a(by) p Fp 3049 4687 a(\(6) p Fl(:) p Fp(2\)) p Fo(.) p 3324 4687 a(Then) p Fk 516 4907 a(k) p Fl(f) p Fm 614 4922 a(1) p Fp 668 4880 a(~) p Fl 653 4907 a(\014) p Fm 708 4922 a(1) p Fp 765 4907 a(\() p Fl(R) p Fp 878 4907 a(\() p Fl(E) p Fp 1016 4907 a(+) p Fl 1114 4907 a(i) p Fp(0;) p Fl 1240 4907 a(H) p Fi 1321 4922 a(d) p Fp 1361 4907 a(\)) p 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rotate dyy eop %%Page: 33 33 33 32 bop Fo 0 407 a(Pr) p 102 407 a(o) p 147 407 a(of.) p Fp 354 407 a(This) p 579 407 a(lemma) p 896 407 a(is) p 996 407 a(also) p 1194 407 a(pro) m(v) m(ed) p 1513 407 a(in) p 1629 407 a(almost) p 1946 407 a(the) p 2116 407 a(same) p 2363 407 a(w) m(a) m(y) p 2563 407 a(as) p 2685 407 a(Lemma) p 3035 407 a(6.1.) p 3237 407 a(W) p 3329 407 a(e) p 3407 407 a(use) 0 527 y(Lemma) p 348 527 a(3.1) p 505 527 a(for) p Fl 654 527 a(H) p Fi 735 542 a(d) p Fp 808 527 a(and) p Fl 998 527 a(K) p Fi 1081 542 a(b) p Fp 1115 527 a(.) p 1186 527 a(Then) p Fl 303 738 a(R) p Fp 378 738 a(\() p Fl(E) p Fk 516 738 a(\006) p Fl 615 738 a(i) p Fp(0;) p Fl 741 738 a(H) p Fi 822 753 a(d) p Fp 862 738 a(\)) p Fl( ) p Fm 963 753 a(1) p Fk 1025 738 a(\000) p Fl 1125 738 a( ) p Fm 1188 753 a(1) p Fl 1228 738 a(R) p Fp 1303 738 a(\() p Fl(E) p Fk 1441 738 a(\006) p Fl 1541 738 a(i) p Fp(0;) p Fl 1667 738 a(K) p Fi 1750 753 a(b) p Fp 1784 738 a(\)) p 1849 738 a(=) p Fl 1953 738 a(R) p Fp 2028 738 a(\() p Fl(E) p Fk 2166 738 a(\006) p Fl 2266 738 a(i) p Fp(0;) p Fl 2392 738 a(H) p Fi 2473 753 a(d) p Fp 2513 738 a(\)) p Fl(V) p Fm 2608 753 a(1) p Fl 2647 738 a(R) p Fp 2722 738 a(\() p Fl(E) p Fk 2860 738 a(\006) p Fl 2960 738 a(i) p Fp(0;) p Fl 3086 738 a(K) p Fi 3169 753 a(b) p Fp 3203 738 a(\)) 0 949 y(and) p 190 949 a(hence) p Fl 281 1160 a( ) p Fm 344 1175 a(1) p Fl 384 1160 a(R) p Fp 459 1160 a(\() p Fl(E) p Fp 597 1160 a(+) p Fl 695 1160 a(i) p Fp(0;) p Fl 821 1160 a(H) p Fi 902 1175 a(d) p Fp 942 1160 a(\)) p Fk 1003 1160 a(\000) p Fl 1102 1160 a(R) p Fp 1177 1160 a(\() p Fl(E) p Fp 1315 1160 a(+) p Fl 1413 1160 a(i) p Fp(0;) p Fl 1539 1160 a(K) p Fi 1622 1175 a(b) p Fp 1656 1160 a(\)) p Fl( ) p Fm 1757 1175 a(1) p Fp 1825 1160 a(=) p Fl 1928 1160 a(R) p Fp 2003 1160 a(\() p Fl(E) p Fp 2142 1160 a(+) p Fl 2240 1160 a(i) p Fp(0;) p Fl 2366 1160 a(K) p Fi 2449 1175 a(b) p Fp 2483 1160 a(\)) p Fl(V) p Fh 2599 1119 a(\003) p Fm 2578 1185 a(1) p Fl 2639 1160 a(R) p Fp 2714 1160 a(\() p Fl(E) p Fp 2852 1160 a(+) p Fl 2950 1160 a(i) p Fp(0;) p Fl 3076 1160 a(H) p Fi 3157 1175 a(d) p Fp 3197 1160 a(\)) p Fl(;) p Fp 0 1371 a(where) p Fl 288 1371 a(V) p Fm 345 1386 a(1) p Fp 422 1371 a(=) p Fl 536 1371 a(V) p Fi 593 1386 a(a) p Fm(1) p Fp 670 1371 a(\() p Fk(\000) p Fl(!) p Fm 846 1386 a(1) p Fp 885 1371 a(\)) p 962 1371 a(is) p 1066 1371 a(de\014ned) p 1408 1371 a(b) m(y) p 1549 1371 a(\(3.9\)) p 1788 1371 a(with) p Fl 2016 1371 a(a) p Fp 2105 1371 a(=) p Fk 2219 1371 a(f) p Fp(1) p Fl(;) p Fp 2362 1371 a(2) p Fl(;) p Fp 2455 1371 a(3) p Fk(g) p Fp(.) p 2641 1371 a(W) p 2733 1371 a(e) p 2815 1371 a(\014rst) p 3022 1371 a(consider) p 3408 1371 a(the) 0 1491 y(op) s(erator) p Fl 395 1491 a(f) p Fm 443 1506 a(1) p Fp 496 1465 a(~) p Fl 482 1491 a(\014) p Fm 537 1506 a(1) p Fl 577 1491 a(R) p Fp 652 1491 a(\() p Fl(E) p Fp 791 1491 a(+) p Fl 891 1491 a(i) p Fp(0;) p Fl 1017 1491 a(H) p Fi 1098 1506 a(d) p Fp 1138 1491 a(\)) p Fl(g) p Fp 1260 1491 a(with) p Fl 1485 1491 a(g) p Fp 1569 1491 a(in) p 1685 1491 a(Lemma) p 2035 1491 a(6.2.) p 2236 1491 a(W) p 2328 1491 a(e) p 2406 1491 a(decomp) s(ose) p Fl 2899 1491 a(V) p Fm 2956 1506 a(1) p Fp 3029 1491 a(as) p 3151 1491 a(in) p 3267 1491 a(\(3.14\).) 0 1612 y(W) p 92 1612 a(e) p 168 1612 a(see) p 326 1612 a(b) m(y) p 461 1612 a(Theorem) p 873 1612 a(4.1) p 1030 1612 a(and) p 1220 1612 a(Lemma) p 1568 1612 a(6.2) p 1725 1612 a(that) p Fk 638 1823 a(k) p Fl(f) p Fm 736 1838 a(1) p Fp 790 1796 a(~) p Fl 776 1823 a(\014) p Fm 831 1838 a(1) p Fl 870 1823 a(R) p Fp 945 1823 a(\() p Fl(E) p Fp 1083 1823 a(+) p Fl 1181 1823 a(i) p Fp(0;) p Fl 1307 1823 a(K) p Fi 1390 1838 a(b) p Fp 1425 1823 a(\)) p Fl(V) p Fh 1541 1781 a(\003) p Fm 1520 1847 a(1) p Fl 1580 1823 a(R) p Fp 1655 1823 a(\() p Fl(E) p Fp 1794 1823 a(+) p Fl 1892 1823 a(i) p Fp(0;) p Fl 2018 1823 a(H) p Fi 2099 1838 a(d) p Fp 2139 1823 a(\)) p Fl(g) p Fk 2228 1823 a(k) p Fp 2304 1823 a(=) p Fl 2408 1823 a(O) p Fp 2486 1823 a(\() p Fl(d) p Fh 2575 1781 a(\000) p Fm(3) p Fi(=) p Fm(4+) p Fi(c\033) p Fp 2867 1823 a(\)) 0 2034 y(and) p 199 2034 a(hence) p Fk 479 2034 a(k) p Fl(f) p Fm 577 2049 a(1) p Fp 630 2007 a(~) p Fl 616 2034 a(\014) p Fm 671 2049 a(1) p Fl 711 2034 a(R) p Fp 786 2034 a(\() p Fl(E) p Fp 930 2034 a(+) p Fl 1034 2034 a(i) p Fp(0;) p Fl 1160 2034 a(H) p Fi 1241 2049 a(d) p Fp 1281 2034 a(\)) p Fl(g) p Fk 1370 2034 a(k) p Fp 1462 2034 a(=) p Fl 1581 2034 a(O) p Fp 1659 2034 a(\() p Fl(d) p Fh 1748 1997 a(\000) p Fm(3) p Fi(=) p Fm(4+) p Fi(c\033) p Fp 2040 2034 a(\).) p 2175 2034 a(This,) p 2436 2034 a(together) p 2830 2034 a(with) p 3061 2034 a(Lemma) p 3419 2034 a(6.2) 0 2154 y(again,) p 287 2154 a(implies) p 618 2154 a(that) p Fk 583 2365 a(k) p Fl(f) p Fm 681 2380 a(1) p Fp 735 2339 a(~) p Fl 721 2365 a(\014) p Fm 776 2380 a(1) p Fl 815 2365 a(R) p Fp 890 2365 a(\() p Fl(E) p Fp 1028 2365 a(+) p Fl 1126 2365 a(i) p Fp(0;) p Fl 1252 2365 a(H) p Fi 1333 2380 a(d) p Fp 1373 2365 a(\)) p Fl(V) p Fm 1468 2380 a(1) p Fl 1508 2365 a(R) p Fp 1583 2365 a(\() p Fl(E) p Fp 1721 2365 a(+) p Fl 1819 2365 a(i) p Fp(0;) p Fl 1945 2365 a(K) p Fi 2028 2380 a(b) p Fp 2062 2365 a(\)) p Fl(\014) p Fm 2155 2380 a(1) p Fl 2194 2365 a(f) p Fm 2242 2380 a(1) p Fk 2282 2365 a(k) p Fp 2359 2365 a(=) p Fl 2463 2365 a(O) p Fp 2541 2365 a(\() p Fl(d) p Fh 2630 2324 a(\000) p Fm(3) p Fi(=) p Fm(2+) p Fi(c\033) p Fp 2922 2365 a(\)) 0 2576 y(for) p 146 2576 a(another) p Fl 501 2576 a(c) p 570 2576 a(>) p Fp 674 2576 a(0.) p 792 2576 a(Th) m(us) p 1036 2576 a(the) p 1201 2576 a(\014rst) p 1399 2576 a(b) s(ound) p 1696 2576 a(follo) m(ws) p 2014 2576 a(and) p 2200 2576 a(the) p 2365 2576 a(second) p 2677 2576 a(one) p 2853 2576 a(is) p 2948 2576 a(obtained) p 3345 2576 a(from) 0 2696 y(Lemma) p 348 2696 a(6.2) p 505 2696 a(at) p 625 2696 a(once.) p Fe 885 2696 a(2) p Fp 146 2864 a(W) p 238 2864 a(e) p 314 2864 a(no) m(w) p 518 2864 a(analyze) p Fl 867 2864 a(f) p Fm 915 2879 a(11) p Fp 1022 2864 a(b) m(y) p 1158 2864 a(use) p 1326 2864 a(of) p 1438 2864 a(Lemma) p 1786 2864 a(6.3.) p 1981 2864 a(It) p 2086 2864 a(follo) m(ws) p 2407 2864 a(that) p Fl 359 3075 a(f) p Fm 407 3090 a(11) p Fk 510 3075 a(\030) p Fp 615 3075 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 844 3075 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1039 3075 a(\)\() p Fl(R) p Fp 1190 3075 a(\() p Fl(E) p Fp 1327 3075 a(+) p Fl 1425 3075 a(i) p Fp(0;) p Fl 1551 3075 a(K) p Fi 1634 3090 a(b) p Fp 1669 3075 a(\)) p Fl(e) p Fi 1752 3034 a(i\022) p Fg 1809 3046 a(d) p Fl 1849 3075 a(\037) p Fm 1910 3090 a(11) p Fp 1985 3075 a([) p Fl(H) p Fm 2093 3090 a(0) p Fl 2132 3075 a(;) p 2176 3075 a(e) p Fm 2221 3090 a(1) p Fp 2261 3075 a(]) p Fl(') p Fm 2352 3090 a(0) p Fl 2391 3075 a(;) p 2435 3075 a(e) p Fi 2480 3034 a(i\022) p Fg 2537 3046 a(d) p Fl 2577 3075 a(\037) p Fm 2638 3090 a(11) p Fp 2713 3075 a([) p Fl(H) p Fm 2821 3090 a(0) p Fl 2860 3075 a(;) p 2904 3075 a(e) p Fm 2949 3090 a(1) p Fp 2989 3075 a(]) p 3016 3022 64 4 v Fl(') p Fm 3080 3098 a(0) p Fp 3119 3075 a(\)) p Fl(:) p Fp 0 3286 a(Let) p Fl 171 3286 a(Z) p Fp 273 3286 a(b) s(e) p 401 3286 a(the) p 565 3286 a(set) p 713 3286 a(consisting) p 1160 3286 a(of) p 1267 3286 a(t) m(w) m(o) p 1447 3286 a(comp) s(onen) m(ts) p 1980 3286 a(+) p 2084 3286 a(and) p Fk 2270 3286 a(\000) p Fp(.) p 2416 3286 a(W) p 2508 3286 a(e) p 2580 3286 a(write) p Fl 2825 3286 a(\037) p Fm 2886 3301 a(11) p Fp 2989 3286 a(=) p Fl 3092 3286 a(\037) p Fm 3153 3301 a(11+) p Fp 3283 3286 a(\() p Fl(x) p Fm 3376 3301 a(2) p Fp 3416 3286 a(\)) p 3468 3286 a(+) p Fl 0 3406 a(\037) p Fm 61 3421 a(11) p Fh(\000) p Fp 191 3406 a(\() p Fl(x) p Fm 284 3421 a(2) p Fp 324 3406 a(\),) p 424 3406 a(where) p Fl 708 3406 a(\037) p Fm 769 3421 a(11) p Fh(\006) p Fp 934 3406 a(has) p 1110 3406 a(supp) s(ort) p 1473 3406 a(in) p Fk 1589 3406 a(f) p Fp(3) p Fl(d) p Fi 1739 3370 a(\033) p Fl 1817 3406 a(<) p Fk 1925 3406 a(\006) p Fl(x) p Fm 2057 3421 a(2) p Fl 2129 3406 a(<) p Fp 2236 3406 a(6) p Fl(d) p Fm 2336 3370 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fk 2543 3406 a(g) p Fp(.) p 2671 3406 a(Then) p Fl 2928 3406 a(f) p Fm 2976 3421 a(11) p Fp 3085 3406 a(admits) p 3408 3406 a(the) 0 3526 y(decomp) s(osition) p Fl 176 3737 a(f) p Fm 224 3752 a(11) p Fk 327 3737 a(\030) p Fp 432 3737 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 661 3737 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 856 3737 a(\)) p Fj 953 3654 a(X) p Fi 910 3839 a(";") p Fd 996 3820 a(0) p Fh 1017 3839 a(2) p Fi(Z) p Fp 1117 3737 a(\() p Fl(e) p Fh 1200 3696 a(\000) p Fi(i\022) p Fg 1312 3708 a(d) p Fl 1352 3737 a(R) p Fp 1427 3737 a(\() p Fl(E) p Fp 1565 3737 a(+) p Fl 1663 3737 a(i) p Fp(0;) p Fl 1789 3737 a(K) p Fi 1872 3752 a(b) p Fp 1906 3737 a(\)) p Fl(e) p Fi 1989 3696 a(i\022) p Fg 2046 3708 a(d) p Fl 2087 3737 a(\037) p Fm 2148 3752 a(11) p Fi(") p Fp 2255 3737 a([) p Fl(H) p Fm 2363 3752 a(0) p Fl 2403 3737 a(;) p 2447 3737 a(e) p Fm 2492 3752 a(1) p Fp 2531 3737 a(]) p Fl(') p Fm 2622 3752 a(0) p Fl 2661 3737 a(;) p 2705 3737 a(\037) p Fm 2766 3752 a(11) p Fi(") p Fd 2869 3733 a(0) p Fp 2896 3737 a([) p Fl(H) p Fm 3004 3752 a(0) p Fl 3043 3737 a(;) p 3087 3737 a(e) p Fm 3132 3752 a(1) p Fp 3172 3737 a(]) p 3199 3684 V Fl(') p Fm 3263 3761 a(0) p Fp 3302 3737 a(\)) p Fl(:) p Fp 0 4028 a(The) p 201 4028 a(op) s(erator) p 593 4028 a(on) p 729 4028 a(the) p 897 4028 a(righ) m(t) p 1133 4028 a(side) p 1328 4028 a(is) p 1426 4028 a(represen) m(ted) p 1944 4028 a(as) p Fl 599 4239 a(e) p Fh 644 4198 a(\000) p Fi(i\022) p Fg 756 4210 a(d) p Fl 797 4239 a(R) p Fp 872 4239 a(\() p Fl(E) p Fp 1010 4239 a(+) p Fl 1108 4239 a(i) p Fp(0;) p Fl 1234 4239 a(K) p Fi 1317 4254 a(b) p Fp 1351 4239 a(\)) p Fl(e) p Fi 1434 4198 a(i\022) p Fg 1491 4210 a(d) p Fp 1559 4239 a(=) p Fl 1662 4239 a(e) p Fh 1707 4198 a(\000) p Fi(i) p Fm(\() p Fi(\022) p Fg 1846 4210 a(d) p Fh 1883 4198 a(\000) p Fi(q) p Ff 1970 4207 a(1) p Fm 2004 4198 a(\)) p Fl 2036 4239 a(R) p Fp 2111 4239 a(\() p Fl(E) p Fp 2249 4239 a(+) p Fl 2347 4239 a(i) p Fp(0;) p Fl 2473 4239 a(H) p Fi 2554 4254 a(b) p Fp 2588 4239 a(\)) p Fl(e) p Fi 2671 4198 a(i) p Fm(\() p Fi(\022) p Fg 2755 4210 a(d) p Fh 2792 4198 a(\000) p Fi(q) p Ff 2879 4207 a(1) p Fm 2913 4198 a(\)) p Fp 0 4450 a(with) p Fl 222 4450 a(q) p Fm 265 4465 a(1) p Fp 337 4450 a(as) p 457 4450 a(in) p 571 4450 a(\(6.2\).) p 842 4450 a(W) p 934 4450 a(e) p 1010 4450 a(calculate) p 1416 4450 a(the) p 1584 4450 a(phase) p 1856 4450 a(factor) p 2135 4450 a(as) p Fl 524 4661 a(\022) p Fi 569 4676 a(d) p Fp 610 4661 a(\() p Fl(x) p Fp(\)) p Fk 764 4661 a(\000) p Fl 863 4661 a(q) p Fm 906 4676 a(1) p Fp 946 4661 a(\() p Fl(x) p Fp(\)) p 1105 4661 a(=) p Fl 1208 4661 a(\022) p Fi 1253 4676 a(b) p Fp 1288 4661 a(\() p Fl(x) p Fp(\)) p 1442 4661 a(+) p Fl 1540 4661 a(\013) p Fm 1602 4676 a(1) p Fp 1658 4661 a(\() p Fl(\015) p Fp 1752 4661 a(\() p Fl(x) p Fk 1867 4661 a(\000) p Fl 1967 4661 a(d) p Fm 2018 4676 a(1) p Fp 2057 4661 a(;) p Fl 2101 4661 a(!) p Fm 2162 4676 a(1) p Fp 2201 4661 a(\)) p Fk 2261 4661 a(\000) p Fl 2361 4661 a(\015) p Fp 2417 4661 a(\() p Fl(x) p Fk 2532 4661 a(\000) p Fl 2632 4661 a(d) p Fm 2683 4676 a(1) p Fp 2722 4661 a(;) p Fk 2766 4661 a(\000) p Fl(!) p Fm 2904 4676 a(1) p Fp 2943 4661 a(\)\)) 0 4872 y(on) p 143 4872 a(supp) p Fk 361 4872 a(r) p Fl(e) p Fm 489 4887 a(1) p Fp 528 4872 a(,) p 597 4872 a(where) p Fl 887 4872 a(\022) p Fi 932 4887 a(b) p Fp 967 4872 a(\() p Fl(x) p Fp(\)) p 1139 4872 a(=) p Fj 1255 4806 a(P) p Fm 1343 4832 a(3) p Fi 1343 4897 a(j) p Fm 1376 4897 a(=2) p Fl 1486 4872 a(\013) p Fi 1548 4887 a(j) p Fl 1584 4872 a(\015) p Fp 1640 4872 a(\() p Fl(x) p Fk 1761 4872 a(\000) p Fl 1866 4872 a(d) p Fi 1917 4887 a(j) p Fp 1953 4872 a(;) p Fl 1997 4872 a(!) p Fm 2058 4887 a(1) p Fp 2097 4872 a(\).) p 2228 4872 a(If,) p 2362 4872 a(in) p 2484 4872 a(addition,) p Fl 2905 4872 a(x) p Fk 3001 4872 a(2) p Fp 3108 4872 a(supp) p Fl 3325 4872 a(\037) p Fm 3386 4887 a(11) p Fh(\006) p Fp 3516 4872 a(,) 0 4993 y(then) p Fl 834 5113 a(\013) p Fm 896 5128 a(1) p Fp 952 5113 a(\() p Fl(\015) p Fp 1046 5113 a(\() p Fl(x) p Fk 1161 5113 a(\000) p Fl 1261 5113 a(d) p Fm 1312 5128 a(1) p Fp 1351 5113 a(;) p Fl 1395 5113 a(!) p Fm 1456 5128 a(1) p Fp 1495 5113 a(\)) p Fk 1555 5113 a(\000) p Fl 1655 5113 a(\015) p Fp 1711 5113 a(\() p Fl(x) p Fk 1826 5113 a(\000) p Fl 1926 5113 a(d) p Fm 1977 5128 a(1) p Fp 2016 5113 a(;) p Fk 2060 5113 a(\000) p Fl(!) p Fm 2198 5128 a(1) p Fp 2237 5113 a(\)\)) p 2341 5113 a(=) p Fk 2444 5113 a(\007) p Fl(\013) p Fm 2583 5128 a(1) p Fl 2623 5113 a(\031) t(:) p Fp 0 5283 a(On) p 163 5283 a(the) p 331 5283 a(other) p 585 5283 a(hand,) p 856 5283 a([) p Fl(H) p Fm 964 5298 a(0) p Fl 1004 5283 a(;) p 1048 5283 a(e) p Fm 1093 5298 a(1) p Fp 1132 5283 a(]) p Fl(') p Fm 1223 5298 a(0) p Fp 1295 5283 a(b) s(eha) m(v) m(es) p 1659 5283 a(lik) m(e) 804 5504 y([) p Fl(H) p Fm 912 5519 a(0) p Fl 951 5504 a(;) p 995 5504 a(e) p Fm 1040 5519 a(1) p Fp 1079 5504 a(]) p Fl(') p Fm 1170 5519 a(0) p Fp 1237 5504 a(=) p Fk 1341 5504 a(\000) p Fp(2) p Fl(i) p Fk 1500 5415 a(p) p 1583 5415 79 4 v Fl 1583 5504 a(E) p Fp 1678 5504 a(\() p Fl(@) p Fm 1767 5519 a(1) p Fl 1807 5504 a(e) p Fm 1852 5519 a(1) p Fp 1892 5504 a(\)) p Fl 1946 5504 a(') p Fm 2010 5519 a(0) p Fp 2072 5504 a(+) p Fl 2170 5504 a(O) p Fp 2248 5504 a(\() p Fk(j) p Fl(x) p Fk 2390 5504 a(\000) p Fl 2490 5504 a(d) p Fm 2541 5519 a(1) p Fk 2580 5504 a(j) p Fh 2608 5463 a(\000) p Fm(2) p Fp 2702 5504 a(\)) 1723 5753 y(33) p 90 rotate dyy eop %%Page: 34 34 34 33 bop Fp 0 407 a(and) p 190 407 a(similarly) p 589 407 a(for) p 738 407 a([) p Fl(H) p Fm 846 422 a(0) p Fl 885 407 a(;) p 929 407 a(e) p Fm 974 422 a(1) p Fp 1013 407 a(]) p 1040 354 64 4 v Fl(') p Fm 1104 430 a(0) p Fp 1144 407 a(.) p 1214 407 a(If) p 1312 407 a(w) m(e) p 1455 407 a(set) p Fl 605 624 a(u) p Fm 661 639 a(1) p Fi(") p Fp 733 624 a(\() p Fl(x) p Fp(\)) p 892 624 a(=) p Fl 995 624 a(e) p Fh 1040 582 a(\000) p Fi(i"\013) p Ff 1197 591 a(1) p Fi 1232 582 a(\031) p Fp 1296 624 a(\() p Fl 1333 624 a(@) p Fm 1384 639 a(1) p Fl 1424 624 a(e) p Fm 1469 639 a(1) p Fp 1509 624 a(\)) p 1564 624 a(\() p Fl(x) p Fp(\)) p Fl(;) p 1934 624 a(\021) p Fm 1982 639 a(1) p Fi(") p Fp 2054 624 a(\() p Fl(x) p Fm 2147 639 a(2) p Fp 2187 624 a(\)) p 2252 624 a(=) p 2356 624 a(2) p Fl(i) p Fk 2438 535 a(p) p 2521 535 79 4 v Fl 2521 624 a(E) p 2599 624 a(\037) p Fm 2660 639 a(11) p Fi(") p Fp 2767 624 a(\() p Fl(x) p Fm 2860 639 a(2) p Fp 2900 624 a(\)) 0 831 y(for) p Fl 149 831 a(") p Fk 222 831 a(2) p Fl 316 831 a(Z) p Fp 390 831 a(,) p 450 831 a(then) p 672 831 a(it) p 770 831 a(follo) m(ws) p 1090 831 a(from) p 1320 831 a(Lemma) p 1669 831 a(6.2) p 1826 831 a(that) p Fl 420 1038 a(f) p Fm 468 1053 a(11) p Fk 571 1038 a(\030) p Fp 676 1038 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 905 1038 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1100 1038 a(\)) p Fj 1197 955 a(X) p Fi 1154 1140 a(";") p Fd 1240 1121 a(0) p Fh 1261 1140 a(2) p Fi(Z) p Fp 1361 1038 a(\() p Fl(R) p Fp 1474 1038 a(\() p Fl(E) p Fp 1612 1038 a(+) p Fl 1710 1038 a(i) p Fp(0;) p Fl 1836 1038 a(H) p Fi 1917 1053 a(b) p Fp 1951 1038 a(\)) p Fl(e) p Fi 2034 997 a(i\022) p Fg 2091 1009 a(b) p Fl 2126 1038 a(\021) p Fm 2174 1053 a(1) p Fi(") p Fl 2246 1038 a(u) p Fm 2302 1053 a(1) p Fi(") p Fl 2374 1038 a(') p Fm 2438 1053 a(0) p Fl 2477 1038 a(;) p 2521 1038 a(e) p Fi 2566 997 a(i\022) p Fg 2623 1009 a(b) p 2659 985 52 4 v Fl 2659 1038 a(\021) p Fm 2711 1061 a(1) p Fi(") p Fd 2779 1043 a(0) p Fl 2805 1038 a(u) p Fm 2861 1053 a(1) p Fi(") p Fd 2929 1034 a(0) p 2955 985 64 4 v Fl 2955 1038 a(') p Fm 3019 1061 a(0) p Fp 3058 1038 a(\)) p Fl(:) p Fp 3343 1038 a(\(6.3\)) 146 1325 y(W) p 238 1325 a(e) p 320 1325 a(consider) p Fl 705 1325 a(f) p Fi 753 1340 a(l) q(m) p Fp 879 1325 a(with) p Fl 1107 1325 a(l) p Fp 1175 1325 a(=) p 1288 1325 a(2) p 1375 1325 a(or) p Fl 1499 1325 a(m) p Fp 1621 1325 a(=) p 1734 1325 a(2.) p 1869 1325 a(W) p 1961 1325 a(e) p 2043 1325 a(shall) p 2276 1325 a(sho) m(w) p 2523 1325 a(that) p 2740 1325 a(these) p 2995 1325 a(terms) p 3272 1325 a(are) p 3440 1325 a(all) 0 1446 y(negligible.) p 471 1446 a(T) p 533 1446 a(o) p 615 1446 a(see) p 773 1446 a(this,) p 990 1446 a(w) m(e) p 1134 1446 a(write) p Fl 1383 1446 a(\037) p Fm 1444 1461 a(21) p Fp 1547 1446 a(=) p Fl 1650 1446 a(\037) p Fm 1711 1461 a(21+) p Fp 1841 1446 a(\() p Fl(x) p Fm 1934 1461 a(2) p Fp 1974 1446 a(\)) p 2034 1446 a(+) p Fl 2132 1446 a(\037) p Fm 2193 1461 a(21) p Fh(\000) p Fp 2322 1446 a(\() p Fl(x) p Fm 2415 1461 a(2) p Fp 2455 1446 a(\),) p 2553 1446 a(and) p 2742 1446 a(w) m(e) p 2886 1446 a(de\014ne) p Fl 413 1653 a(T) p Fh 470 1668 a(\006) p Fp 530 1653 a(\() p Fl(x;) p 667 1653 a(D) p Fi 748 1668 a(x) p Fp 791 1653 a(\)) p 857 1653 a(=) p Fl 961 1653 a(\037) p Fm 1022 1668 a(21) p Fh(\006) p Fp 1151 1653 a([) p Fl(H) p Fm 1259 1668 a(0) p Fl 1299 1653 a(;) p 1343 1653 a(e) p Fm 1388 1668 a(1) p Fp 1427 1653 a(]) p Fl(\014) p Fm 1509 1668 a(1) p Fl 1549 1653 a(\015) p Fm 1600 1668 a(0) p Fl 1639 1653 a(;) p Fp 1897 1628 a(~) p Fl 1878 1653 a(T) p Fh 1935 1668 a(\006) p Fp 1994 1653 a(\() p Fl(x;) p 2131 1653 a(D) p Fi 2212 1668 a(x) p Fp 2256 1653 a(\)) p 2321 1653 a(=) p Fl 2425 1653 a(\037) p Fm 2486 1668 a(21) p Fh(\006) p Fp 2616 1653 a([) p Fl(H) p Fm 2724 1668 a(0) p Fl 2763 1653 a(;) p 2807 1653 a(e) p Fm 2852 1668 a(1) p Fp 2891 1653 a(]) 2932 1627 y(~) p Fl 2918 1653 a(\014) p Fm 2973 1668 a(1) p Fl 3013 1653 a(\015) p Fm 3064 1668 a(0) p Fl 3103 1653 a(;) p Fp 0 1860 a(where) p Fl 281 1860 a(\037) p Fm 342 1875 a(21) p Fh(\006) p Fp 504 1860 a(has) p 678 1860 a(supp) s(ort) p 1039 1860 a(in) p Fk 1152 1860 a(f\006) p Fl(x) p Fm 1334 1875 a(2) p Fl 1402 1860 a(>) p Fp 1506 1860 a(3) p Fl(d) p Fm 1606 1824 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fk 1813 1860 a(g) p Fp 1895 1860 a(and) p Fl 2084 1860 a(\015) p Fm 2135 1875 a(0) p Fp 2206 1860 a(is) p 2304 1860 a(de\014ned) p 2640 1860 a(b) m(y) p Fl 2775 1860 a(\015) p Fm 2826 1875 a(0) p Fp 2893 1860 a(=) p Fl 2996 1860 a(\015) p Fm 3047 1875 a(0) p Fp 3086 1860 a(\() p Fl(D) p Fi 3205 1875 a(x) p Ff 3245 1884 a(2) p Fp 3283 1860 a(\)) p 3354 1860 a(with) p Fl 0 1980 a(\015) p Fm 51 1995 a(0) p Fp 90 1980 a(\() p Fl(\030) p Fm 171 1995 a(2) p Fp 210 1980 a(\)) p 276 1980 a(=) p Fl 379 1980 a(\037) p Fp(\() p Fl(d) p Fm 529 1944 a(1) p Fi(=) p Fm(2) p Fk 639 1980 a(j) p Fl(\030) p Fm 710 1995 a(2) p Fk 749 1980 a(j) p Fp(\).) p 885 1980 a(The) p 1085 1980 a(sym) m(b) s(ol) p Fl 1419 1980 a(T) p Fh 1476 1995 a(\006) p Fp 1535 1980 a(\() p Fl(x;) p 1672 1980 a(\030) p Fp 1720 1980 a(\)) p 1790 1980 a(ob) s(eys) p Fk 730 2223 a(j) p Fl(@) p Fi 814 2182 a(\014) 809 2248 y(x) p Fl 861 2223 a(@) p Fi 917 2182 a(\013) 912 2248 y(\030) p Fl 968 2223 a(T) p Fh 1025 2238 a(\006) p Fp 1084 2223 a(\() p Fl(x;) p 1221 2223 a(\030) p Fp 1269 2223 a(\)) p Fk(j) p 1362 2223 a(\024) p Fl 1467 2223 a(C) p Fi 1537 2238 a(\013\014) p Fj 1646 2127 a(\020) p Fk 1695 2223 a(j) p Fl(x) p Fk 1801 2223 a(\000) p Fl 1900 2223 a(d) p Fm 1951 2238 a(1) p Fk 1990 2223 a(j) p Fp 2040 2223 a(+) p Fl 2138 2223 a(d) p Fm 2189 2182 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fj 2396 2127 a(\021) p Fh 2446 2150 a(\000j) p Fi(\014) p Fh 2564 2150 a(j) p Fl 2604 2223 a(d) p Fh 2655 2182 a(j) p Fi(\013) p Fh(j) p Fi(=) p Fm(2) p Fp 0 2460 a(and) p 200 2460 a(similarly) p 610 2460 a(for) 789 2434 y(~) p Fl 769 2460 a(T) p Fh 826 2475 a(\006) p Fp 886 2460 a(\() p Fl(x;) p 1023 2460 a(\030) p Fp 1071 2460 a(\).) p 1210 2460 a(The) p 1421 2460 a(classical) p 1807 2460 a(particle) p 2170 2460 a(starting) p 2544 2460 a(from) p 2785 2460 a(supp) p Fl 3003 2460 a(T) p Fh 3060 2475 a(\006) p Fp 3162 2460 a(at) p Fl 3292 2460 a(t) p Fp 3373 2460 a(=) p 3495 2460 a(0) 0 2580 y(passes) p 295 2580 a(far) p 444 2580 a(a) m(w) m(a) m(y) p 688 2580 a(from) p 919 2580 a(cen) m(ters) p Fl 1248 2580 a(d) p Fm 1299 2595 a(2) p Fp 1371 2580 a(and) p Fl 1561 2580 a(d) p Fm 1612 2595 a(3) p Fp 1684 2580 a(for) p Fl 1833 2580 a(t) p 1897 2580 a(>) p Fp 2001 2580 a(0) p 2083 2580 a(and) p 2273 2580 a(it) p 2371 2580 a(mo) m(v) m(es) p 2662 2580 a(lik) m(e) p 2841 2580 a(the) p 3009 2580 a(free) p 3196 2580 a(particle.) 0 2700 y(This) p 219 2700 a(enables) p 558 2700 a(us) p 679 2700 a(to) p 795 2700 a(construct) p 1220 2700 a(an) p 1352 2700 a(appro) m(ximation) p 1999 2700 a(to) p Fl 2114 2700 a(R) p Fp 2189 2700 a(\() p Fl(E) p Fp 2320 2700 a(+) p Fl 2411 2700 a(i) p Fp(0;) p Fl 2537 2700 a(H) p Fi 2618 2715 a(d) p Fp 2658 2700 a(\)) p Fl(T) p Fh 2753 2715 a(\006) p Fp 2841 2700 a(in) p 2951 2700 a(a) p 3029 2700 a(form) p 3256 2700 a(similar) 0 2821 y(to) p 119 2821 a(\(3.29\).) p 440 2821 a(W) p 532 2821 a(e) p 608 2821 a(can) p 787 2821 a(construct) p 1216 2821 a(a) p 1297 2821 a(similar) p 1618 2821 a(appro) m(ximation) p 2268 2821 a(for) 2437 2796 y(~) p Fl 2418 2821 a(T) p Fh 2489 2785 a(\003) 2475 2845 y(\006) p Fl 2534 2821 a(R) p Fp 2609 2821 a(\() p Fl(E) p Fp 2747 2821 a(+) p Fl 2845 2821 a(i) p Fp(0;) p Fl 2971 2821 a(H) p Fi 3052 2836 a(d) p Fp 3092 2821 a(\)) p 3163 2821 a(also,) p 3386 2821 a(and) 0 2941 y(w) m(e) p 144 2941 a(can) p 322 2941 a(sho) m(w) 615 3123 y(~) p Fl 596 3148 a(T) p Fh 667 3107 a(\003) 653 3173 y(\006) p Fl 713 3148 a(R) p Fp 788 3148 a(\() p Fl(E) p Fp 926 3148 a(+) p Fl 1024 3148 a(i) p Fp(0;) p Fl 1150 3148 a(H) p Fi 1231 3163 a(d) p Fp 1271 3148 a(\)) p Fl(T) p Fm 1366 3163 a(+) p Fp 1453 3148 a(=) p 1561 3148 a(~) p Fl 1556 3148 a(r) p Fi 1600 3163 a(L) p Fl 1652 3148 a(;) p Fp 1910 3123 a(~) p Fl 1891 3148 a(T) p Fh 1962 3107 a(\003) 1948 3173 y(\006) p Fl 2007 3148 a(R) p Fp 2082 3148 a(\() p Fl(E) p Fp 2220 3148 a(+) p Fl 2318 3148 a(i) p Fp(0;) p Fl 2444 3148 a(H) p Fi 2525 3163 a(d) p Fp 2566 3148 a(\)) p Fl(T) p Fh 2661 3163 a(\000) p Fp 2747 3148 a(=) p 2855 3148 a(~) p Fl 2851 3148 a(r) p Fi 2895 3163 a(L) p Fp 0 3355 a(in) p 116 3355 a(the) p 287 3355 a(same) p 534 3355 a(w) m(a) m(y) p 734 3355 a(as) p 856 3355 a(used) p 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3763 a(b) s(eha) m(v) m(es) p 1719 3763 a(lik) m(e) p Fl 382 3970 a(f) p Fi 430 3985 a(d) p Fk 553 3970 a(\030) p Fl 714 3970 a(f) p Fm 762 3985 a(1) p Fp 801 3970 a(\() p Fl(!) p Fm 900 3985 a(1) p Fk 967 3970 a(!) p 1095 3970 a(\000) p Fl(!) p Fm 1233 3985 a(1) p Fp 1272 3970 a(;) p Fl 1316 3970 a(E) p Fp 1394 3970 a(\)) 554 4115 y(+) p 714 4115 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 943 4115 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1138 4115 a(\)) p Fj 1235 4032 a(X) p Fi 1192 4217 a(";") p Fd 1278 4198 a(0) p Fh 1299 4217 a(2) p Fi(Z) p Fp 1399 4115 a(\() p Fl(R) p Fp 1512 4115 a(\() p Fl(E) p Fp 1650 4115 a(+) p Fl 1748 4115 a(i) p Fp(0;) p Fl 1874 4115 a(H) p Fi 1955 4130 a(b) p Fp 1989 4115 a(\)) p Fl(e) p Fi 2072 4074 a(i\022) p Fg 2129 4086 a(b) p Fl 2165 4115 a(\021) p Fm 2213 4130 a(1) p Fi(") p Fl 2285 4115 a(u) p Fm 2341 4130 a(1) p Fi(") p Fl 2412 4115 a(') p Fm 2476 4130 a(0) p Fl 2516 4115 a(;) p 2560 4115 a(e) p Fi 2605 4074 a(i\022) p Fg 2662 4086 a(b) p 2697 4062 52 4 v Fl 2697 4115 a(\021) p Fm 2749 4139 a(1) p Fi(") p Fd 2817 4120 a(0) p Fl 2843 4115 a(u) p Fm 2899 4130 a(1) p Fi(") p Fd 2967 4111 a(0) p 2993 4062 64 4 v Fl 2993 4115 a(') p Fm 3057 4139 a(0) p Fp 3096 4115 a(\)) p Fl(:) p Fp 3343 4115 a(\(6.4\)) p Fq 146 4521 a(7.) p 271 4521 a(Analysis) p 719 4521 a(on) p 875 4521 a(free) p 1095 4521 a(resolv) m(en) m(t) p 1570 4521 a(:) p 1651 4521 a(Completion) p 2257 4521 a(of) p 2384 4521 a(pro) s(of) p Fp 146 4733 a(In) p 261 4733 a(this) p 444 4733 a(section) p 762 4733 a(w) m(e) p 899 4733 a(complete) p 1303 4733 a(the) p 1464 4733 a(pro) s(of) p 1712 4733 a(b) m(y) p 1840 4733 a(calculating) p 2326 4733 a(the) p 2486 4733 a(co) s(e\016cien) m(ts) p 2973 4733 a(of) p 3077 4733 a(amplitudes) p Fl 0 4854 a(f) p Fi 48 4869 a(j) p Fp 85 4854 a(\() p Fl(!) p Fm 184 4869 a(1) p Fk 250 4854 a(!) p 378 4854 a(\000) p Fl(!) p Fm 516 4869 a(1) p Fp 555 4854 a(;) p Fl 599 4854 a(E) p Fp 677 4854 a(\)) p Fl(;) p Fp 783 4854 a(2) p Fk 860 4854 a(\024) p Fl 965 4854 a(j) p Fk 1038 4854 a(\024) p Fp 1144 4854 a(3.) p 1260 4854 a(Let) p Fl 1427 4854 a(e) p Fm 1472 4869 a(2) p Fp 1512 4854 a(\() p Fl(x) p Fp(\)) p 1671 4854 a(=) p Fl 1774 4854 a(e) p Fm 1819 4869 a(0) p Fp 1859 4854 a(\() p Fl(x) p Fk 1958 4854 a(\000) p Fl 2041 4854 a(d) p Fm 2092 4869 a(2) p Fp 2131 4854 a(\)) p 2194 4854 a(b) s(e) p 2318 4854 a(as) p 2430 4854 a(in) p 2536 4854 a(section) p 2854 4854 a(6.) p 2970 4854 a(By) p 3115 4854 a(de\014nition,) p Fl 0 4974 a(e) p Fm 45 4989 a(2) p Fp 126 4974 a(=) p 243 4974 a(1) p 332 4974 a(on) p 475 4974 a(supp) p Fl 693 4974 a(@) p Fm 744 4989 a(1) p Fl 784 4974 a(e) p Fm 829 4989 a(1) p Fk 896 4974 a(\\) p Fp 990 4974 a(supp) p Fl 1208 4974 a(\037) p Fm 1269 4989 a(11) p Fp 1344 4974 a(,) p 1413 4974 a(so) p 1541 4974 a(that) p Fl 1760 4974 a(e) p Fm 1805 4989 a(2) p Fl 1845 4974 a(\021) p Fm 1893 4989 a(1) p Fi(") p Fl 1965 4974 a(u) p Fm 2021 4989 a(1) p Fi(") p Fp 2134 4974 a(=) p Fl 2251 4974 a(\021) p Fm 2299 4989 a(1) p Fi(") p Fl 2371 4974 a(u) p Fm 2427 4989 a(1) p Fi(") p Fp 2498 4974 a(.) p 2593 4974 a(If) p 2698 4974 a(w) m(e) p 2850 4974 a(mak) m(e) p 3112 4974 a(use) p 3289 4974 a(of) p 3408 4974 a(the) 0 5094 y(relation) 1077 5215 y(\() p Fl(H) p Fi 1196 5230 a(b) p Fk 1252 5215 a(\000) p Fl 1352 5215 a(E) p Fp 1430 5215 a(\)) p Fl(e) p Fi 1513 5174 a(i\022) p Fg 1570 5186 a(b) p Fl 1605 5215 a(e) p Fm 1650 5230 a(2) p Fp 1718 5215 a(=) p Fl 1821 5215 a(e) p Fi 1866 5174 a(i\022) p Fg 1923 5186 a(b) p Fp 1959 5215 a(\() p Fl(H) p Fm 2078 5230 a(0) p Fk 2139 5215 a(\000) p Fl 2239 5215 a(E) p Fp 2317 5215 a(\)) p Fl(e) p Fm 2400 5230 a(2) p Fl 2440 5215 a(;) p Fp 0 5384 a(then) 413 5504 y(\() p Fl(H) p Fi 532 5519 a(b) p Fk 588 5504 a(\000) p Fl 688 5504 a(E) p Fp 766 5504 a(\)) p Fl(e) p Fi 849 5463 a(i\022) p Fg 906 5475 a(b) p Fl 941 5504 a(e) p Fm 986 5519 a(2) p Fl 1026 5504 a(R) p Fp 1101 5504 a(\() p Fl(E) p Fp 1239 5504 a(+) p Fl 1337 5504 a(i) p Fp(0;) p Fl 1463 5504 a(H) p Fm 1544 5519 a(0) p Fp 1583 5504 a(\)) p 1649 5504 a(=) p Fl 1752 5504 a(e) p Fi 1797 5463 a(i\022) p Fg 1854 5475 a(b) p Fl 1890 5504 a(e) p Fm 1935 5519 a(2) p Fp 1997 5504 a(+) p Fl 2095 5504 a(e) p Fi 2140 5463 a(i\022) p Fg 2197 5475 a(b) p Fp 2233 5504 a([) p Fl(H) p Fm 2341 5519 a(0) p Fl 2380 5504 a(;) p 2424 5504 a(e) p Fm 2469 5519 a(2) p Fp 2508 5504 a(]) p Fl(R) p Fp 2610 5504 a(\() p Fl(E) p Fp 2749 5504 a(+) p Fl 2847 5504 a(i) p Fp(0;) p Fl 2973 5504 a(H) p Fm 3054 5519 a(0) p Fp 3093 5504 a(\)) 1723 5753 y(34) p 90 rotate dyy eop %%Page: 35 35 35 34 bop Fp 0 407 a(and) p 190 407 a(hence) p 461 407 a(w) m(e) p 604 407 a(obtain) p 908 407 a(the) p 1076 407 a(rather) p 1368 407 a(formal) p 1675 407 a(represen) m(tation) p Fl 184 627 a(R) p Fp 259 627 a(\() p Fl(E) p Fp 398 627 a(+) p Fl 496 627 a(i) p Fp(0;) p Fl 622 627 a(H) p Fi 703 642 a(b) p Fp 737 627 a(\)) p Fl(e) p Fi 820 586 a(i\022) p Fg 877 598 a(b) p Fl 912 627 a(\021) p Fm 960 642 a(1) p Fi(") p Fl 1032 627 a(u) p 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a(1) p Fk 1546 992 a(\000) p Fl 1645 992 a(d) p Fm 1696 1007 a(2) p Fp 1768 992 a(and) p 1964 992 a(~) p Fl 1958 992 a(y) p Fp 2036 992 a(=) p Fl 2140 992 a(y) p Fm 2188 1007 a(1) p Fk 2249 992 a(\000) p Fl 2349 992 a(d) p Fm 2400 1007 a(1) p Fp 2439 992 a(.) p 2509 992 a(Then) p 2764 992 a(w) m(e) p 2908 992 a(ha) m(v) m(e) p Fk 375 1248 a(j) p Fl(x) p Fk 480 1248 a(\000) p Fl 580 1248 a(y) p Fk 632 1248 a(j) p Fp 742 1248 a(=) p Fj 901 1152 a(\020) p Fp 950 1248 a(\() p Fl(d) p Fm 1039 1263 a(12) p Fp 1136 1248 a(+) p 1240 1248 a(~) p Fl 1234 1248 a(x) p Fk 1311 1248 a(\000) p Fp 1418 1248 a(~) p Fl 1411 1248 a(y) p Fp 1462 1248 a(\)) p Fm 1500 1200 a(2) p Fp 1562 1248 a(+) p 1660 1248 a(\() p Fl(x) p Fm 1753 1263 a(2) p Fk 1815 1248 a(\000) p Fl 1914 1248 a(y) p Fm 1962 1263 a(2) p Fp 2001 1248 a(\)) p Fm 2039 1207 a(2) p Fj 2079 1152 a(\021) p Fm 2128 1175 a(1) p Fi(=) p Fm(2) p Fp 742 1454 a(=) p Fl 901 1454 a(d) p Fj 969 1358 a(\020) p Fp 1018 1454 a(1) p 1089 1454 a(+) p 1187 1454 a(2) p Fl(d) p Fh 1287 1413 a(\000) p Fm(1) p Fp 1397 1454 a(\() p 1441 1454 a(~) p Fl 1435 1454 a(x) p Fk 1512 1454 a(\000) p Fp 1619 1454 a(~) p Fl 1612 1454 a(y) p Fp 1663 1454 a(\)) p 1723 1454 a(+) p Fl 1821 1454 a(d) p Fh 1872 1413 a(\000) p Fm(2) p Fj 1983 1358 a(\020) p Fp 2033 1454 a(\() p 2077 1454 a(~) p Fl 2071 1454 a(x) p Fk 2148 1454 a(\000) p Fp 2254 1454 a(~) p Fl 2248 1454 a(y) p Fp 2299 1454 a(\)) p Fm 2337 1413 a(2) p Fp 2398 1454 a(+) p 2496 1454 a(\() p Fl(x) p Fm 2589 1469 a(2) p Fk 2651 1454 a(\000) p Fl 2751 1454 a(y) p Fm 2799 1469 a(2) p Fp 2838 1454 a(\)) p Fm 2876 1413 a(2) p Fj 2915 1358 a(\021\021) p Fm 3014 1381 a(1) p Fi(=) p Fm(2) p Fl 3141 1454 a(:) p Fp 0 1698 a(Note) p 236 1698 a(that) p Fk 447 1698 a(j) p Fp 481 1698 a(~) p Fl 475 1698 a(x) p Fk(j) p Fp 580 1698 a(+) p Fk 678 1698 a(j) p Fp 713 1698 a(~) p Fl 706 1698 a(y) p Fk 757 1698 a(j) p Fp 807 1698 a(+) p Fk 905 1698 a(j) p Fl(x) p Fm 988 1713 a(2) p Fk 1027 1698 a(j) p Fp 1077 1698 a(+) p Fk 1175 1698 a(j) p Fl(y) p Fm 1251 1713 a(2) p Fk 1290 1698 a(j) p Fp 1345 1698 a(=) p Fl 1449 1698 a(O) p Fp 1527 1698 a(\() p Fl(d) p Fm 1616 1662 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fp 1822 1698 a(\).) p 1930 1698 a(Since) 1039 1918 y(\(1) p 1148 1918 a(+) p Fl 1246 1918 a(t) p Fp(\)) p Fm 1319 1877 a(1) p Fi(=) p Fm(2) p Fp 1457 1918 a(=) p 1560 1918 a(1) p 1631 1918 a(+) p Fl 1729 1918 a(t=) p Fp(2) p Fk 1884 1918 a(\000) p Fl 1984 1918 a(t) p Fm 2019 1877 a(2) p Fl 2059 1918 a(=) p Fp(8) p 2178 1918 a(+) p Fl 2276 1918 a(O) p Fp 2354 1918 a(\() p Fl(t) p Fm 2427 1877 a(3) p Fp 2466 1918 a(\)) 0 2138 y(as) p Fl 120 2138 a(t) p Fk 183 2138 a(!) p Fp 310 2138 a(0,) p 418 2138 a(a) p 500 2138 a(simple) p 804 2138 a(computation) p 1373 2138 a(yields) p Fk 643 2358 a(j) p Fl(x) p Fk 748 2358 a(\000) p Fl 847 2358 a(y) p Fk 899 2358 a(j) p Fp 954 2358 a(=) p 1057 2358 a(\() p Fl(x) p Fm 1150 2373 a(1) p Fk 1212 2358 a(\000) p Fl 1312 2358 a(y) p Fm 1360 2373 a(1) p Fp 1399 2358 a(\)) p 1459 2358 a(+) p Fl 1557 2358 a(d) p Fh 1608 2317 a(\000) p Fm(1) p Fp 1719 2358 a(\() p Fl(x) p Fm 1812 2373 a(2) p Fk 1874 2358 a(\000) p Fl 1973 2358 a(y) p Fm 2021 2373 a(2) p Fp 2060 2358 a(\)) p Fm 2098 2310 a(2) p Fl 2154 2358 a(=) p Fp(2) p 2274 2358 a(+) p Fl 2372 2358 a(O) p Fp 2450 2358 a(\() p Fl(d) p Fh 2539 2317 a(\000) p Fm(1) p Fi(=) p Fm(2+3) p Fi(\033) p Fp 2836 2358 a(\)) p Fl(:) p Fp 0 2578 a(Th) m(us) p 247 2578 a(the) p 415 2578 a(lemma) p 729 2578 a(is) p 828 2578 a(v) m(eri\014ed) p 1169 2578 a(b) m(y) p 1304 2578 a(ev) p 1393 2578 a(aluating) p 1773 2578 a(the) p 1941 2578 a(Hilb) s(ert{Sc) m(hmidt) p 2676 2578 a(norm.) p Fe 2968 2578 a(2) p Fp 146 2748 a(W) p 238 2748 a(e) p 314 2748 a(apply) p 583 2748 a(the) p 751 2748 a(ab) s(o) m(v) m(e) p 1027 2748 a(lemma) p 1341 2748 a(to) p Fl 1461 2748 a(f) p Fi 1509 2763 a(l) q(m;"") p Fd 1679 2744 a(0) p Fp 1737 2748 a(with) p 1959 2748 a(0) p Fk 2035 2748 a(\024) p Fl 2140 2748 a(l) r(;) p 2248 2748 a(m) p Fk 2361 2748 a(\024) p Fp 2466 2748 a(1.) p 2585 2748 a(Since) p Fj 1223 2884 a(Z) p Fp 1323 3001 a(\() p Fl(@) p Fm 1412 3016 a(1) p Fl 1452 3001 a(e) p Fm 1497 3016 a(1) p Fp 1536 3001 a(\)) p 1591 3001 a(\() p Fl(x) p Fm 1684 3016 a(1) p Fl 1724 3001 a(;) p 1768 3001 a(x) p Fm 1823 3016 a(2) p Fp 1862 3001 a(\)) p Fl 1917 3001 a(dx) p Fm 2023 3016 a(1) p Fp 2090 3001 a(=) p Fk 2194 3001 a(\000) p Fp(1) 0 3246 y(for) p Fl 149 3246 a(x) p Fm 204 3261 a(2) p Fk 272 3246 a(2) p Fp 366 3246 a(supp) p Fl 583 3246 a(\037) p Fm 644 3261 a(11) p Fp 719 3246 a(,) p 779 3246 a(w) m(e) p 922 3246 a(ha) m(v) m(e) 955 3466 y(\() p Fl(K) p Fm 1076 3481 a(+) p Fl 1135 3466 a(\021) p Fm 1183 3481 a(1) p Fi(") p Fl 1255 3466 a(u) p Fm 1311 3481 a(1) p Fi(") p Fl 1383 3466 a(') p Fm 1447 3481 a(0) p Fp 1486 3466 a(\)) p 1541 3466 a(\() p Fl(x) p Fp(\)) p 1700 3466 a(=) p Fk 1803 3466 a(\000) p Fl(e) p Fh 1925 3424 a(\000) p Fi(i"\013) p Ff 2082 3433 a(1) p Fi 2117 3424 a(\031) p Fl 2165 3466 a(\032) p Fm 2215 3481 a(1) p Fi(") p Fp 2287 3466 a(\() p Fl(x) p Fm 2380 3481 a(2) p Fp 2420 3466 a(\)) p Fl(') p Fm 2522 3481 a(0) p Fl 2561 3466 a(;) p Fp 0 3686 a(where) p Fl 282 3686 a(\032) p Fm 332 3701 a(1) p Fi(") p Fp 404 3686 a(\() p Fl(x) p Fm 497 3701 a(2) p Fp 537 3686 a(\)) p 603 3686 a(=) p 706 3686 a(\() p Fl(Y) p 822 3686 a(\021) p Fm 870 3701 a(1) p Fi(") p Fp 942 3686 a(\)) p 997 3686 a(\() p Fl(x) p Fm 1090 3701 a(2) p Fp 1130 3686 a(\),) p 1227 3686 a(and) p Fl 1417 3686 a(Y) p Fp 1528 3686 a(acts) p 1729 3686 a(on) p Fl 1864 3686 a(\021) p Fp 1916 3686 a(\() p Fl(x) p Fm 2009 3701 a(2) p Fp 2049 3686 a(\)) p 2119 3686 a(as) 478 3936 y(\() p Fl(Y) p 594 3936 a(\021) p Fp 646 3936 a(\)) p 700 3936 a(\() p Fl(x) p Fm 793 3951 a(2) p Fp 833 3936 a(\)) p 899 3936 a(=) p Fl 1002 3936 a(c) p Fm 1044 3951 a(+) p Fp 1103 3936 a(\() p Fl(E) p Fp 1219 3936 a(\)) p Fl(d) p Fh 1308 3894 a(\000) p Fm(1) p Fi(=) p Fm(2) p Fj 1489 3818 a(Z) p Fp 1589 3936 a(exp) q(\() p Fl(id) p Fh 1860 3894 a(\000) p Fm(1) p Fk 1954 3847 a(p) p 2037 3847 V Fl 2037 3936 a(E) p Fp 2115 3936 a(\() p Fl(x) p Fm 2208 3951 a(2) p Fk 2270 3936 a(\000) p Fl 2370 3936 a(y) p Fm 2418 3951 a(2) p Fp 2457 3936 a(\)) p Fm 2495 3894 a(2) p Fl 2534 3936 a(=) p Fp(2\)) p Fl(\021) p Fp 2722 3936 a(\() p Fl(y) p Fm 2808 3951 a(2) p Fp 2846 3936 a(\)) p Fl 2901 3936 a(dy) p Fm 3000 3951 a(2) p Fl 3039 3936 a(:) p Fp 3343 3936 a(\(7.3\)) 0 4180 y(Similarly) p 415 4180 a(w) m(e) p 558 4180 a(ha) m(v) m(e) 953 4300 y(\() p Fl(K) p Fh 1074 4315 a(\000) p 1133 4248 52 4 v Fl 1133 4300 a(\021) p Fm 1185 4324 a(1) p Fi(") p Fl 1257 4300 a(u) p Fm 1313 4315 a(1) p Fi(") p 1385 4248 64 4 v Fl 1385 4300 a(') p Fm 1449 4324 a(0) p Fp 1488 4300 a(\)) p 1543 4300 a(\() p Fl(x) p Fp(\)) p 1702 4300 a(=) p Fk 1805 4300 a(\000) p Fl(e) p Fh 1927 4259 a(\000) p Fi(i"\013) p Ff 2084 4268 a(1) p Fi 2119 4259 a(\031) p 2166 4248 51 4 v Fl 2166 4300 a(\032) p Fm 2217 4324 a(1) p Fi(") p Fp 2289 4300 a(\() p Fl(x) p Fm 2382 4315 a(2) p Fp 2421 4300 a(\)) p 2459 4248 64 4 v Fl(') p Fm 2523 4324 a(0) p Fl 2563 4300 a(:) p Fp 0 4475 a(The) p 208 4475 a(estimates) p 644 4475 a(obtained) p 1053 4475 a(in) p 1174 4475 a(Lemmas) p 1568 4475 a(6.1) p 1732 4475 a(and) p 1929 4475 a(6.3) p 2094 4475 a(remain) p 2426 4475 a(true) p 2639 4475 a(for) p Fl 2796 4475 a(H) p Fi 2877 4490 a(b) p Fp 2951 4475 a(under) p 3234 4475 a(natural) 0 4595 y(mo) s(di\014cation.) p 599 4595 a(F) p 655 4595 a(or) p 774 4595 a(example,) p 1183 4595 a(w) m(e) p 1326 4595 a(ha) m(v) m(e) p Fk 111 4815 a(kh) p Fl(x) p Fk 277 4815 a(\000) p Fl 377 4815 a(d) p Fm 428 4830 a(2) p Fk 467 4815 a(i) p Fm 506 4774 a(1) p Fi(=) p Fm(2) p Fp 616 4815 a([) p Fl(H) p Fm 724 4830 a(0) p Fl 763 4815 a(;) p 807 4815 a(e) p Fm 852 4830 a(2) p Fp 892 4815 a(]) p Fl(\037) p Fm 980 4830 a(12) p Fp 1069 4789 a(~) p Fl 1055 4815 a(\014) p Fm 1110 4830 a(1) p Fl 1149 4815 a(R) p Fp 1224 4815 a(\() p Fl(E) p Fp 1362 4815 a(+) p Fl 1460 4815 a(i) p Fp(0;) p Fl 1586 4815 a(H) p Fi 1667 4830 a(b) p Fp 1701 4815 a(\)) p Fl(\014) p Fm 1794 4830 a(1) p Fl 1834 4815 a(\037) p Fm 1895 4830 a(12) p Fp 1969 4815 a([) p Fl(H) p Fm 2077 4830 a(0) p Fl 2117 4815 a(;) p 2161 4815 a(e) p Fm 2206 4830 a(2) p Fp 2245 4815 a(]) p Fk(h) p Fl(x) p Fk 2389 4815 a(\000) p Fl 2488 4815 a(d) p Fm 2539 4830 a(2) p Fk 2578 4815 a(i) p Fm 2617 4774 a(1) p Fi(=) p Fm(2) p Fk 2727 4815 a(k) p Fp 2805 4815 a(=) p Fl 2908 4815 a(O) p Fp 2986 4815 a(\() p Fl(d) p Fh 3075 4774 a(\000) p Fm(1) p Fi(=) p Fm(2+) p Fi(c\033) p Fp 3367 4815 a(\)) p Fl(;) p Fp 0 5035 a(whic) m(h) p 287 5035 a(follo) m(ws) p 616 5035 a(from) p 854 5035 a(the) p 1031 5035 a(second) p 1354 5035 a(b) s(ound) p 1663 5035 a(in) p 1785 5035 a(Lemma) p 2141 5035 a(6.3.) p 2361 5035 a(If) p 2467 5035 a(w) m(e) p 2618 5035 a(tak) m(e) p 2838 5035 a(accoun) m(t) p 3207 5035 a(of) p 3326 5035 a(these) 0 5156 y(estimates,) p 456 5156 a(then) p 679 5156 a(Lemma) p 1027 5156 a(7.1) p 1184 5156 a(sho) m(ws) p 1464 5156 a(that) p Fl 1675 5156 a(f) p Fi 1723 5171 a(l) q(m;"") p Fd 1893 5152 a(0) p Fp 1952 5156 a(b) s(eha) m(v) m(es) p 2315 5156 a(lik) m(e) p Fl 99 5376 a(e) p Fh 144 5334 a(\000) p Fi(i"\013) p Ff 301 5343 a(1) p Fi 335 5334 a(\031) p Fl 382 5376 a(e) p Fi 427 5334 a(i") p Fd 484 5311 a(0) p Fi 506 5334 a(\013) p Ff 551 5343 a(1) p Fi 586 5334 a(\031) p Fp 633 5376 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 862 5376 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1057 5376 a(\)\() p Fl(R) p Fp 1208 5376 a(\() p Fl(E) p Fp 1346 5376 a(+) p Fl 1444 5376 a(i) p Fp(0;) p Fl 1570 5376 a(H) p Fi 1651 5391 a(b) p Fp 1685 5376 a(\)) p Fl(e) p Fi 1768 5334 a(i\022) p Fg 1825 5346 a(b) p Fl 1861 5376 a(\037) p Fi 1922 5391 a(l) p Fm 1944 5391 a(2) p Fp 1983 5376 a([) p Fl(H) p Fm 2091 5391 a(0) p Fl 2130 5376 a(;) p 2174 5376 a(e) p Fm 2219 5391 a(2) p Fp 2259 5376 a(]) p Fl(\032) p Fm 2336 5391 a(1) p Fi(") p Fl 2408 5376 a(') p Fm 2472 5391 a(0) p Fl 2512 5376 a(;) p 2556 5376 a(e) p Fi 2601 5334 a(i\022) p Fg 2658 5346 a(b) p Fl 2693 5376 a(\037) p Fi 2754 5391 a(m) p Fm(2) p Fp 2856 5376 a([) p Fl(H) p Fm 2964 5391 a(0) p Fl 3003 5376 a(;) p 3047 5376 a(e) p Fm 3092 5391 a(2) p Fp 3132 5376 a(]) p 3159 5323 51 4 v Fl(\032) p Fm 3209 5399 a(1) p Fi(") p Fd 3277 5380 a(0) p 3303 5323 64 4 v Fl 3303 5376 a(') p Fm 3367 5399 a(0) p Fp 3407 5376 a(\)) 1723 5753 y(36) p 90 rotate dyy eop %%Page: 37 37 37 36 bop Fp 0 407 a(as) p Fl 129 407 a(d) p Fk 223 407 a(!) p 366 407 a(1) p Fp(,) p 536 407 a(when) p 800 407 a(0) p Fk 892 407 a(\024) p Fl 1013 407 a(l) r(;) p 1129 407 a(m) p Fk 1258 407 a(\024) p Fp 1378 407 a(1.) p 1525 407 a(W) p 1617 407 a(e) p 1702 407 a(ev) p 1791 407 a(aluate) p 2093 407 a(these) p 2352 407 a(terms.) p 2689 407 a(W) p 2781 407 a(e) p 2866 407 a(use) p 3044 407 a(the) p 3221 407 a(in) m(tegral) 0 527 y(form) m(ula) p Fj 985 530 a(Z) p Fl 1084 648 a(e) p Fh 1129 606 a(\006) p Fi(i\015) t(t) p Ff 1273 583 a(2) p Fl 1329 648 a(dt) p Fp 1443 648 a(=) p 1546 648 a(\() p Fl(\031) t(=\015) p Fp 1748 648 a(\)) p Fm 1786 599 a(1) p Fi(=) p Fm(2) p Fl 1913 648 a(e) p Fh 1958 606 a(\006) p Fi(i\031) r(=) p Fm(4) p Fl 2154 648 a(;) p 2296 648 a(\015) p 2379 648 a(>) p Fp 2483 648 a(0) p Fl(;) p Fp 3343 648 a(\(7.4\)) 0 857 y(to) p 110 857 a(analyze) p 451 857 a(the) p 611 857 a(b) s(eha) m(vior) p 1000 857 a(of) p 1102 857 a(the) p 1262 857 a(term) p 1486 857 a(with) p Fl 1699 857 a(l) p Fp 1758 857 a(=) p Fl 1862 857 a(m) p Fp 1975 857 a(=) p 2078 857 a(0.) p 2195 857 a(Recall) p 2480 857 a(that) p Fl 2683 857 a(\021) p Fm 2731 872 a(1) p Fi(") p Fp 2830 857 a(=) p 2934 857 a(2) p Fl(i) p Fk 3016 773 a(p) p 3099 773 79 4 v Fl 3099 857 a(E) p 3177 857 a(\037) p Fm 3238 872 a(11) p Fi(") p Fp 3345 857 a(\() p Fl(x) p Fm 3438 872 a(2) p Fp 3478 857 a(\).) 0 978 y(W) p 92 978 a(e) p 168 978 a(ha) m(v) m(e) p Fl 65 1170 a(\032) p Fm 115 1185 a(1) p Fi(") p Fp 187 1170 a(\() p Fl(x) p Fm 280 1185 a(2) p Fp 320 1170 a(\)) p 386 1170 a(=) p 489 1170 a(\() p 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1627 a(p) p 2003 1627 V Fl 2003 1716 a(E) p 2081 1716 a(t) p Fm 2116 1675 a(2) p Fl 2155 1716 a(=) p Fp(2\)) p Fl 2308 1716 a(dt) p Fp 2415 1716 a(+) p Fl 2513 1716 a(O) p Fp 2591 1716 a(\() p Fl(d) p Fh 2680 1675 a(\000) p Fm(1) p Fi(=) p Fm(2+) p Fi(\033) p Fp 2942 1716 a(\)) 0 1954 y(and) p 184 1954 a(hence) p 450 1954 a(it) p 542 1954 a(follo) m(ws) p 857 1954 a(from) p 1083 1954 a(form) m(ula) p 1435 1954 a(\(7.4\)) p 1663 1954 a(that) p Fl 1869 1954 a(\032) p Fm 1919 1969 a(1+) p Fp 2013 1954 a(\() p Fl(x) p Fm 2106 1969 a(2) p Fp 2146 1954 a(\)) p 2212 1954 a(=) p Fk 2315 1954 a(\000) p Fp(1) p Fl(=) p Fp(2) p 2550 1954 a(+) p Fl 2637 1954 a(O) p Fp 2715 1954 a(\() p Fl(d) p Fh 2804 1917 a(\000) p Fm(1) p Fi(=) p Fm(2+) p Fi(\033) p Fp 3066 1954 a(\)) p 3131 1954 a(uniformly) 0 2074 y(in) p Fl 106 2074 a(x) p Fm 161 2089 a(2) p Fp 226 2074 a(as) p 339 2074 a(ab) s(o) m(v) m(e.) p 651 2074 a(A) p 749 2074 a(similar) p 1062 2074 a(relation) p 1412 2074 a(is) p 1503 2074 a(true) p 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a(1) p Fk 988 2699 a(!) p 1115 2699 a(\000) p Fl(!) p Fm 1253 2714 a(1) p Fp 1293 2699 a(;) p Fl 1337 2699 a(E) p Fp 1415 2699 a(\)) p 1485 2699 a(is) p 1583 2699 a(calculated) p 2044 2699 a(b) m(y) p 2179 2699 a(summing) p Fj 930 2808 a(X) p Fi 886 2993 a(";") p Fd 972 2974 a(0) p Fh 993 2993 a(2) p Fi(Z) p Fl 1110 2891 a(f) p Fm 1158 2906 a(00) p Fi(;"") p Fd 1314 2888 a(0) p Fk 1367 2891 a(\030) p Fp 1472 2891 a(\(cos) p Fl 1658 2891 a(\013) p Fm 1720 2906 a(1) p Fl 1759 2891 a(\031) p Fp 1818 2891 a(\)) p Fm 1856 2843 a(2) p Fl 1912 2891 a(f) p Fm 1960 2906 a(2) p Fp 1999 2891 a(\() p Fl(!) p Fm 2098 2906 a(1) p Fk 2165 2891 a(!) p 2293 2891 a(\000) p Fl(!) p Fm 2431 2906 a(1) p Fp 2470 2891 a(;) p Fl 2514 2891 a(E) p Fp 2592 2891 a(\)) p Fl(:) p Fp 0 3170 a(W) p 92 3170 a(e) p 179 3170 a(write) p Fl 439 3170 a(\037) p Fm 500 3185 a(12) p Fp 621 3170 a(=) p Fl 744 3170 a(\037) p Fm 805 3185 a(12+) p Fp 934 3170 a(\() p Fl(x) p Fm 1027 3185 a(2) p Fp 1067 3170 a(\)) p 1135 3170 a(+) 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2026 5504 a(a) p Fm 2077 5519 a(0) p Fp 2116 5504 a(\)\)) p Fl 2209 5504 a(=) p Fk(j) p Fl(x) p Fk 2363 5504 a(\000) p Fl 2463 5504 a(a) p Fm 2514 5519 a(0) p Fk 2553 5504 a(j) p Fp 2603 5504 a(+) p Fl 2701 5504 a(O) p Fp 2779 5504 a(\() p Fl(d) p Fh 2868 5463 a(\000) p Fm(2) p Fi(\033) p Fp 3004 5504 a(\)) 1723 5753 y(37) p 90 rotate dyy eop %%Page: 38 38 38 37 bop Fp 0 407 a(for) p Fl 149 407 a(x) p Fk 232 407 a(2) p Fl 326 407 a(F) p Fm 389 422 a(+) p Fp 448 407 a(,) p 508 407 a(and) p 698 407 a(w) m(e) p 841 407 a(ha) m(v) m(e) p Fk 404 634 a(j) p Fl(@) p Fi 488 593 a(\014) 483 659 y(x) p Fp 552 634 a(exp) p Fj 718 538 a(\020) p Fl 768 634 a(i) p Fk 801 545 a(p) p 884 545 79 4 v Fl 884 634 a(E) p Fp 962 634 a(\() p Fk(j) p Fl(x) p Fk 1105 634 a(\000) p Fl 1205 634 a(y) p Fk 1257 634 a(j) p 1306 634 a(\000) p 1405 634 a(j) p Fl(x) p Fk 1511 634 a(\000) p Fl 1610 634 a(a) p Fm 1661 649 a(0) p Fk 1701 634 a(j) p Fp(\)) p Fj 1767 538 a(\021) p Fk 1833 634 a(j) p 1888 634 a(\024) p Fl 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a(\014nite) p 2626 1808 a(n) m(um) m(b) s(er) p 2991 1808 a(of) p Fl 3112 1808 a(k) p Fp 3208 1808 a(and) p 3408 1808 a(the) 0 1928 y(total) p 237 1928 a(n) m(um) m(b) s(er) p 596 1928 a(is) p 698 1928 a(at) p 821 1928 a(most) p 1064 1928 a(of) p 1179 1928 a(order) p Fl 1438 1928 a(O) p Fp 1516 1928 a(\() p Fl(d) p Fm 1605 1892 a(4) p Fi(\033) p Fp 1686 1928 a(\).) p 1806 1928 a(Let) p Fk 1984 1928 a(f) p Fl(\015) p Fm 2085 1943 a(0) p Fl 2124 1928 a(;) p 2168 1928 a(\015) p Fh 2219 1943 a(\006) p Fk 2278 1928 a(g) p Fp 2364 1928 a(b) s(e) p 2501 1928 a(a) p 2586 1928 a(partition) p 2996 1928 a(of) p 3111 1928 a(unit) m(y) p 3370 1928 a(nor-) 0 2048 y(malized) p 362 2048 a(b) m(y) p Fl 503 2048 a(\015) p Fm 554 2063 a(0) p Fp 593 2048 a(\() p Fl(\030) p Fm 674 2063 a(2) p Fp 713 2048 a(\)) p 776 2048 a(+) p Fl 877 2048 a(\015) p Fm 928 2063 a(+) p Fp 987 2048 a(\() p Fl(\030) p Fm 1068 2063 a(2) p Fp 1107 2048 a(\)) p 1170 2048 a(+) p Fl 1271 2048 a(\015) p Fh 1322 2063 a(\000) p Fp 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p Fm 1318 2522 a(1) p Fp 1374 2507 a(\() p Fl(\015) p Fm 1463 2522 a(0) p Fp 1524 2507 a(+) p Fl 1622 2507 a(\015) p Fm 1673 2522 a(+) p Fp 1754 2507 a(+) p Fl 1852 2507 a(\015) p Fh 1903 2522 a(\000) p Fp 1961 2507 a(\)) p 2022 2507 a(+) p 2120 2507 a(\() o(1) p Fk 2228 2507 a(\000) p Fl 2328 2507 a(\014) p Fm 2383 2522 a(1) p Fp 2423 2507 a(\)) 0 2725 y(and) p 198 2725 a(similarly) p 605 2725 a(for) 776 2699 y(~) p Fl 762 2725 a(\014) p Fm 817 2740 a(1) p Fp 857 2725 a(.) p 952 2725 a(If) p Fl 1057 2725 a(y) p Fp 1150 2725 a(=) p 1268 2725 a(\() p Fl(y) p Fm 1354 2740 a(1) p Fl 1393 2725 a(;) p 1437 2725 a(y) p Fm 1485 2740 a(2) p Fp 1523 2725 a(\)) p Fk 1603 2725 a(2) p Fp 1711 2725 a(supp) p Fl 1928 2725 a(\037) p Fm 1989 2740 a(11) p Fp 2064 2725 a(,) p 2134 2725 a(then) p Fk 2365 2725 a(j) p Fl(y) p Fm 2441 2740 a(2) p Fk 2479 2725 a(j) p Fl 2548 2725 a(<) p Fp 2666 2725 a(6) p Fl(d) p Fm 2766 2689 a(1) p Fi(=) p Fm(2+) p Fi(\033) p Fp 2973 2725 a(.) p 3068 2725 a(Since) p Fl 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932 3958 a(far) p 1087 3958 a(a) m(w) m(a) m(y) p 1337 3958 a(from) p 1574 3958 a(cen) m(ter) p Fl 1871 3958 a(d) p Fm 1922 3973 a(3) p Fp 2000 3958 a(for) p Fl 2155 3958 a(t) p 2229 3958 a(>) p Fp 2344 3958 a(0) p 2432 3958 a(and) p 2628 3958 a(it) p 2732 3958 a(mo) m(v) m(es) p 3029 3958 a(lik) m(e) p 3214 3958 a(the) p 3389 3958 a(free) 0 4079 y(particle.) p 403 4079 a(Hence) p 697 4079 a(the) p 869 4079 a(particle) p 1225 4079 a(do) s(es) p 1449 4079 a(not) p 1627 4079 a(tak) m(e) p 1842 4079 a(momen) m(tum) p 2359 4079 a(around) p Fk 2693 4079 a(\000) 2770 3995 y(p) p 2854 3995 V Fl 2854 4079 a(E) p 2932 4079 a(!) p Fm 2993 4094 a(1) p Fp 3032 4079 a(.) p 3115 4079 a(If) p 3217 4079 a(w) m(e) p 3364 4079 a(tak) m(e) 0 4199 y(accoun) m(t) p 360 4199 a(of) p 471 4199 a(these) p 721 4199 a(facts,) p 979 4199 a(then) p 1201 4199 a(w) m(e) p 1345 4199 a(ha) m(v) m(e) 966 4417 y(\() p Fl(R) p Fp 1079 4417 a(\() p Fl(E) p Fp 1217 4417 a(+) p Fl 1315 4417 a(i) p Fp(0;) p Fl 1441 4417 a(H) p Fi 1522 4432 a(b) p Fp 1556 4417 a(\)) p Fl(\037) p Fm 1655 4432 a(22+) p Fl 1785 4417 a(v) p Fi 1832 4432 a(") p Fl 1869 4417 a(;) p 1913 4417 a(\037) p Fm 1974 4432 a(22+) p Fp 2107 4417 a(~) p Fl 2103 4417 a(v) p Fi 2150 4432 a(") p Fd 2183 4413 a(0) p Fp 2209 4417 a(\)) p 2275 4417 a(=) p Fl 2379 4417 a(o) p Fp(\(1\)) p Fl(:) p Fp 0 4635 a(In) p 134 4635 a(fact,) p 369 4635 a(this) p 572 4635 a(can) p 763 4635 a(b) s(e) p 908 4635 a(sho) m(wn) p 1217 4635 a(in) p 1343 4635 a(almost) p 1670 4635 a(the) p 1851 4635 a(same) p 2107 4635 a(w) m(a) m(y) p 2318 4635 a(as) p 2450 4635 a(used) p 2685 4635 a(to) p 2817 4635 a(pro) m(v) m(e) p 3092 4635 a(\(4.10\)) p 3386 4635 a(and) 0 4755 y(\(4.11\),) p 306 4755 a(and) p 491 4755 a(the) p 655 4755 a(argumen) m(t) p 1087 4755 a(is) p 1181 4755 a(based) p 1448 4755 a(on) p 1580 4755 a(the) p 1743 4755 a(construction) p 2298 4755 a(of) p 2405 4755 a(appro) m(ximation) p 3051 4755 a(to) p 3166 4755 a(resolv) m(en) m(t) p Fl 0 4876 a(R) p Fp 75 4876 a(\() p Fl(E) p Fk 216 4876 a(\006) p Fl 318 4876 a(i) p Fp(0;) p Fl 444 4876 a(H) p Fi 525 4891 a(b) p Fp 558 4876 a(\)) p 632 4876 a(\(see) p 831 4876 a(\(3.29\)) p 1117 4876 a(for) p 1269 4876 a(example\).) p 1737 4876 a(Th) m(us) p 1988 4876 a(it) p 2089 4876 a(follo) m(ws) p 2413 4876 a(that) p 2628 4876 a(the) p 2799 4876 a(terms) p Fl 3074 4876 a(f) p Fi 3122 4891 a(l) q(m;"") p Fd 3292 4872 a(0) p Fp 3354 4876 a(with) p Fl 0 4996 a(l) p Fp 59 4996 a(=) p 162 4996 a(2) p 244 4996 a(or) p Fl 363 4996 a(m) p Fp 476 4996 a(=) p 580 4996 a(2) p 661 4996 a(are) p 823 4996 a(all) p 959 4996 a(negligible.) 146 5166 y(W) p 238 5166 a(e) p 319 5166 a(here) p 535 5166 a(sum) p 746 5166 a(up) p 891 5166 a(the) p 1064 5166 a(results) p 1378 5166 a(whic) m(h) p 1662 5166 a(ha) m(v) m(e) p 1892 5166 a(b) s(een) p 2126 5166 a(obtained) p 2532 5166 a(so) p 2656 5166 a(far.) p 2857 5166 a(W) p 2949 5166 a(e) p 3030 5166 a(use) p 3203 5166 a(the) p 3375 5166 a(new) 0 5286 y(notation) p Fl 399 5504 a(u) p Fm 455 5519 a(2) p Fi(") p Fp 554 5504 a(=) p Fl 657 5504 a(e) p Fh 702 5463 a(\000) p Fi(i") p Ff 814 5472 a(1) p Fi 849 5463 a(\013) p Ff 894 5472 a(1) p Fi 929 5463 a(\031) p Fl 976 5504 a(e) p Fh 1021 5463 a(\000) p Fi(i") p Ff 1133 5472 a(2) p Fi 1167 5463 a(\013) p Ff 1212 5472 a(2) p Fi 1247 5463 a(\031) p Fp 1311 5504 a(\() p Fl(@) p Fm 1400 5519 a(1) p Fl 1439 5504 a(e) p Fm 1484 5519 a(2) p Fp 1524 5504 a(\)) p 1579 5504 a(\() p Fl(x) p Fp(\)) p Fl(;) p 1949 5504 a(\021) p Fm 1997 5519 a(2) p Fi(") p Fp 2097 5504 a(=) p 2200 5504 a(2) p Fl(i) p Fk 2282 5415 a(p) p 2365 5415 V Fl 2365 5504 a(E) p 2443 5504 a(\037) p Fm 2504 5519 a(12) p Fi(") p Ff 2607 5528 a(2) p Fp 2646 5504 a(\() p Fl(x) p Fm 2739 5519 a(2) p Fp 2779 5504 a(\)) p Fl(\032) p Fm 2867 5519 a(1) p Fi(") p Ff 2935 5528 a(1) p Fp 2974 5504 a(\() p Fl(x) p Fm 3067 5519 a(2) p Fp 3107 5504 a(\)) 1723 5753 y(38) p 90 rotate dyy eop %%Page: 39 39 39 38 bop Fp 0 407 a(for) p Fl 149 407 a(") p Fp 222 407 a(=) p 326 407 a(\() p Fl(") p Fm 410 422 a(1) p Fl 449 407 a(;) p 493 407 a(") p Fm 539 422 a(2) p Fp 578 407 a(\)) p Fk 643 407 a(2) p Fl 737 407 a(Z) p Fk 833 407 a(\002) p Fl 933 407 a(Z) p Fp 1007 407 a(.) p 1077 407 a(Then) p Fl 1332 407 a(f) p Fi 1380 422 a(d) p Fp 1453 407 a(b) s(eha) m(v) m(es) p 1817 407 a(lik) m(e) p Fl 322 623 a(f) p Fi 370 638 a(d) p Fk 494 623 a(\030) p Fl 655 623 a(f) p Fm 703 638 a(1) p Fp 742 623 a(\() p Fl(!) p Fm 841 638 a(1) p Fk 908 623 a(!) p 1035 623 a(\000) p Fl(!) p Fm 1173 638 a(1) p Fp 1213 623 a(;) p Fl 1257 623 a(E) p Fp 1335 623 a(\)) p 1395 623 a(+) p 1493 623 a(\(cos) p Fl 1678 623 a(\013) p Fm 1740 638 a(1) p Fl 1779 623 a(\031) p Fp 1838 623 a(\)) p Fm 1876 575 a(2) p Fl 1932 623 a(f) p Fm 1980 638 a(2) p Fp 2020 623 a(\() p Fl(!) p Fm 2119 638 a(1) p Fk 2186 623 a(!) p 2313 623 a(\000) p Fl(!) p Fm 2451 638 a(1) p Fp 2490 623 a(;) p Fl 2534 623 a(E) p Fp 2612 623 a(\)) 495 768 y(+) p 655 768 a(\() p Fl(ic) p Fp(\() p Fl(E) p Fp 884 768 a(\)) p Fl(=) p Fp(4) p Fl(\031) p Fp 1079 768 a(\)) p Fj 1230 685 a(X) p Fi 1133 870 a(";") p Fd 1219 851 a(0) p Fh 1240 870 a(2) p Fi(Z) p Fh 1340 870 a(\002) p Fi(Z) p Fp 1447 768 a(\() p Fl(R) p Fp 1560 768 a(\() p Fl(E) p Fp 1698 768 a(+) p Fl 1796 768 a(i) p Fp(0;) p Fl 1922 768 a(H) p Fm 2003 783 a(3) p Fp 2042 768 a(\)) p Fl(e) p Fi 2125 727 a(i\022) p Ff 2182 736 a(3) p Fl 2221 768 a(\021) p Fm 2269 783 a(2) p Fi(") p Fl 2341 768 a(u) p Fm 2397 783 a(2) p Fi(") p Fl 2468 768 a(') p Fm 2532 783 a(0) p Fl 2572 768 a(;) p 2616 768 a(e) p Fi 2661 727 a(i\022) p Ff 2718 736 a(3) p 2756 716 52 4 v Fl 2756 768 a(\021) p Fm 2808 792 a(2) p Fi(") p Fd 2876 773 a(0) p Fl 2903 768 a(u) p Fm 2959 783 a(2) p Fi(") p Fd 3027 764 a(0) p 3052 716 64 4 v Fl 3052 768 a(') p Fm 3116 792 a(0) p Fp 3156 768 a(\)) p Fl(:) p Fp 3343 768 a(\(7.5\)) 146 1071 y(W) p 238 1071 a(e) p 318 1071 a(pro) s(ceed) p 683 1071 a(to) p 806 1071 a(the) p 978 1071 a(\014nal) p 1199 1071 a(step.) p 1455 1071 a(W) p 1547 1071 a(e) p 1627 1071 a(calculate) p 2038 1071 a(the) p 2210 1071 a(co) s(e\016cien) m(t) p 2669 1071 a(of) p Fl 2784 1071 a(f) p Fm 2832 1086 a(3) p Fp 2872 1071 a(\() p Fl(!) p Fm 2971 1086 a(1) p Fk 3045 1071 a(!) p 3179 1071 a(\000) p Fl(!) p Fm 3317 1086 a(1) p Fp 3357 1071 a(;) p Fl 3401 1071 a(E) p Fp 3479 1071 a(\).) 0 1191 y(If) p 98 1191 a(w) m(e) p 241 1191 a(mak) m(e) p 496 1191 a(use) p 664 1191 a(of) p 775 1191 a(the) p 943 1191 a(relation) 1085 1407 y(\() p Fl(H) p Fm 1204 1422 a(3) p Fk 1265 1407 a(\000) p Fl 1365 1407 a(E) p Fp 1443 1407 a(\)) p Fl(e) p Fi 1526 1366 a(i\022) p Ff 1583 1375 a(3) p Fl 1621 1407 a(e) p Fm 1666 1422 a(3) p Fp 1734 1407 a(=) p Fl 1837 1407 a(e) p Fi 1882 1366 a(i\022) p Ff 1939 1375 a(3) p Fp 1978 1407 a(\() p Fl(H) p Fm 2097 1422 a(0) p Fk 2159 1407 a(\000) p Fl 2258 1407 a(E) p Fp 2336 1407 a(\)) p Fl(e) p Fm 2419 1422 a(3) p Fp 0 1624 a(and) p 190 1624 a(if) p 279 1624 a(w) m(e) p 423 1624 a(rep) s(eat) p 723 1624 a(the) p 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4624 a(\)) p Fk 640 4624 a(2) p Fl 734 4624 a(Z) p Fk 823 4624 a(\002) p Fl 915 4624 a(Z) p Fp 989 4624 a(.) p 1060 4624 a(Assume) p 1418 4624 a(that) p Fk 1626 4624 a(j) p Fl(x) p Fm 1709 4639 a(2) p Fk 1748 4624 a(j) p Fl 1804 4624 a(<) p 1907 4624 a(cd) p Fi 2000 4588 a(\033) p Fp 2076 4624 a(for) p 2222 4624 a(some) p Fl 2463 4624 a(c) p 2533 4624 a(>) p Fp 2636 4624 a(0.) p 2754 4624 a(If) p Fl 2848 4624 a(") p Fp 2922 4624 a(=) p 3025 4624 a(\(+) p Fl(;) p Fp 3183 4624 a(+\),) p 3354 4624 a(then) p Fl 0 4745 a(\032) p Fm 50 4760 a(2) p Fi(") p Fp 122 4745 a(\() p Fl(x) p Fm 215 4760 a(2) p Fp 255 4745 a(\)) p 326 4745 a(b) s(eha) m(v) m(es) p 689 4745 a(lik) m(e) 81 4998 y(\(2) p Fl(i) p Fk 201 4910 a(p) p 284 4910 V Fl 284 4998 a(E) p Fp 362 4998 a(\)) p Fm 400 4957 a(2) p Fl 440 4998 a(c) p Fm 482 5013 a(+) p Fp 541 4998 a(\() p Fl(E) p Fp 657 4998 a(\)) p Fm 695 4957 a(2) p Fl 734 4998 a(d) p Fh 785 4957 a(\000) p Fm(1) p Fj 896 4881 a(Z) p Fh 979 4908 a(1) p Fm 942 5070 a(0) p Fl 1070 4998 a(e) p Fi 1115 4957 a(id) p Fd 1175 4934 a(\000) p Ff(1) p Fh 1258 4901 a(p) p 1317 4901 56 3 v Fi 1317 4957 a(E) s(y) p Ff 1409 4934 a(2) 1407 4979 y(2) p Fi 1444 4957 a(=) p Fm(2) p Fj 1535 4877 a(\022) 1597 4881 y(Z) p Fh 1680 4908 a(1) p Fm 1643 5070 a(0) p Fl 1771 4998 a(e) p Fi 1816 4957 a(id) p Fd 1876 4934 a(\000) p Ff(1) p Fh 1959 4901 a(p) p 2018 4901 V Fi 2018 4957 a(E) p Fm 2073 4957 a(\() p Fi(z) p Ff 2133 4966 a(2) p Fh 2168 4957 a(\000) p Fi(y) p Ff 2258 4966 a(2) p Fm 2293 4957 a(\)) p Ff 2320 4934 a(2) p Fi 2355 4957 a(=) p Fm(2) p Fl 2446 4998 a(dz) p Fm 2542 5013 a(2) p Fj 2581 4877 a(\023) p Fl 2676 4998 a(dy) p Fm 2775 5013 a(2) p Fp 2835 4998 a(+) p Fl 2933 4998 a(O) p Fp 3011 4998 a(\() p Fl(d) p Fh 3100 4957 a(\000) p Fm(1) p Fi(=) p Fm(2+2) p Fi(\033) p Fp 3397 4998 a(\)) p Fl(:) p Fp 0 5247 a(Hence) p 290 5247 a(w) m(e) p 434 5247 a(ha) m(v) m(e) p Fl 232 5475 a(\032) p Fm 282 5490 a(2) p Fi(") p Fp 354 5475 a(\() p Fl(x) p Fm 447 5490 a(2) p Fp 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407 a(making) p 489 407 a(c) m(hange) p 816 407 a(of) p 931 407 a(v) p 977 407 a(ariables,) p 1369 407 a(so) p 1493 407 a(that) p Fl 1709 407 a(\032) p Fm 1759 422 a(2) p Fi(") p Fp 1867 407 a(=) p 1978 407 a(3) p Fl(=) p Fp(8) p 2149 407 a(+) p Fl 2251 407 a(O) p Fp 2329 407 a(\() p Fl(d) p Fh 2418 371 a(\000) p Fm(1) p Fi(=) p Fm(2+2) p Fi(\033) p Fp 2714 407 a(\)) p 2789 407 a(b) m(y) p 2929 407 a(use) p 3102 407 a(of) p 3218 407 a(form) m(ula) 0 527 y(\(7.4\).) p 270 527 a(Similarly) p Fl 682 527 a(\032) p Fm 732 542 a(2) p Fi(") p Fp 832 527 a(=) p 935 527 a(3) p Fl(=) p Fp(8) p 1098 527 a(+) p Fl 1190 527 a(O) p Fp 1268 527 a(\() p Fl(d) p Fh 1357 491 a(\000) p Fm(1) p Fi(=) p Fm(2+2) p Fi(\033) p Fp 1653 527 a(\)) p 1720 527 a(for) p Fl 1866 527 a(") p Fp 1940 527 a(=) p 2043 527 a(\() p Fk(\000) p Fl(;) p Fk 2202 527 a(\000) p Fp(\)) p 2347 527 a(and) p Fl 2534 527 a(\032) p Fm 2584 542 a(2) p Fi(") p Fp 2684 527 a(=) p 2788 527 a(1) p Fl(=) p Fp(8) p 2951 527 a(+) p Fl 3043 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Fp 92 2605 a([1]) p 244 2605 a(R.) p 381 2605 a(Adami) p 704 2605 a(and) p 900 2605 a(A.) p 1038 2605 a(T) p 1100 2605 a(eta,) p 1298 2605 a(On) p 1466 2605 a(the) p 1640 2605 a(Aharono) m(v{Bohm) p 2395 2605 a(Hamiltonian,) p Fo 3037 2605 a(L) p 3093 2605 a(ett.) p 3294 2605 a(Math.) 244 2725 y(Phys.) p Fq 523 2725 a(43) p Fp 668 2725 a(\(1998\),) p 999 2725 a(43{53.) 92 2929 y([2]) p 244 2929 a(G.) p 392 2929 a(N.) p 536 2929 a(Afanasiev,) p Fo 1025 2929 a(T) p 1088 2929 a(op) p 1183 2929 a(olo) p 1303 2929 a(gic) p 1418 2929 a(al) p 1536 2929 a(E\013e) p 1702 2929 a(cts) p 1865 2929 a(in) p 1995 2929 a(Quantum) p 2436 2929 a(Me) p 2563 2929 a(chanics) p Fp(,) p 2998 2929 a(Klu) m(w) m(er) p 3346 2929 a(Aca-) 244 3049 y(demic) p 526 3049 a(Publishers,) p 1027 3049 a(1999.) 92 3252 y([3]) p 244 3252 a(Y.) p 384 3252 a(Aharono) m(v) p 839 3252 a(and) p 1037 3252 a(D.) p 1179 3252 a(Bohm,) p 1502 3252 a(Signi\014cance) p 2041 3252 a(of) p 2159 3252 a(electromagnetic) p 2866 3252 a(p) s(oten) m(tial) p 3286 3252 a(in) p 3408 3252 a(the) 244 3373 y(quan) m(tum) p 656 3373 a(theory) p 921 3373 a(,) p Fo 981 3373 a(Phys.) p 1259 3373 a(R) p 1325 3373 a(ev.) p Fq 1491 3373 a(115) p Fp 1691 3373 a(\(1959\),) p 2022 3373 a(485{491.) 92 3576 y([4]) p 244 3576 a(L.) p 358 3576 a(Dabro) m(wski) p 834 3576 a(and) p 1017 3576 a(P) p 1075 3576 a(.) p 1129 3576 a(Sto) m(vicek,) p 1539 3576 a(Aharono) m(v{Bohm) p 2282 3576 a(e\013ect) p 2533 3576 a(with) p Fl 2749 3576 a(\016) p Fp 2796 3576 a({t) m(yp) s(e) p 3058 3576 a(in) m(teraction,) p Fo 244 3697 a(J.) p 360 3697 a(Math.) p 654 3697 a(Phys.) p Fq 933 3697 a(39) p Fp 1078 3697 a(\(1998\),) p 1409 3697 a(47{62.) 92 3900 y([5]) p 244 3900 a(H.) p 372 3900 a(Isozaki) p 694 3900 a(and) p 879 3900 a(H.) p 1008 3900 a(Kitada,) p 1357 3900 a(A) p 1458 3900 a(remark) p 1788 3900 a(on) p 1919 3900 a(the) p 2083 3900 a(micro{lo) s(cal) p 2596 3900 a(resolv) m(en) m(t) p 3002 3900 a(estimates) p 3427 3900 a(for) 244 4020 y(t) m(w) m(o) p 436 4020 a(b) s(o) s(dy) p 690 4020 a(Sc) m(hr\177) p 876 4020 a(odinger) p 1231 4020 a(op) s(erators,) p Fo 1699 4020 a(Publ.) p 1959 4020 a(RIMS,) p 2282 4020 a(Kyoto) p 2578 4020 a(Univ.) p Fq 2856 4020 a(21) p Fp 3008 4020 a(\(1985\),) p 3348 4020 a(889{) 244 4141 y(910.) 92 4344 y([6]) p 244 4344 a(H.) p 381 4344 a(Isozaki) p 711 4344 a(and) p 905 4344 a(H.) p 1042 4344 a(Kitada,) p 1400 4344 a(Scattering) p 1870 4344 a(matrices) p 2265 4344 a(for) p 2418 4344 a(t) m(w) m(o{b) s(o) s(dy) p 2870 4344 a(Sc) m(hr\177) p 3056 4344 a(odinger) p 3408 4344 a(op-) 244 4465 y(erators,) p Fo 597 4465 a(Sci.) p 791 4465 a(Pap) p 952 4465 a(ers) p 1112 4465 a(Col) p 1262 4465 a(l.) p 1351 4465 a(of) p 1466 4465 a(A) n(rts) p 1684 4465 a(and) p 1873 4465 a(Sci.,) p 2098 4465 a(T) p 2161 4465 a(okyo) p 2387 4465 a(Univ.) p Fq 2665 4465 a(35) p Fp 2809 4465 a(\(1985\),) p 3140 4465 a(81{107.) 92 4668 y([7]) p 244 4668 a(H.) p 381 4668 a(T.) p 515 4668 a(Ito) p 673 4668 a(and) p 867 4668 a(H.) p 1004 4668 a(T) p 1066 4668 a(am) m(ura,) p 1399 4668 a(Aharono) m(v{Bohm) p 2153 4668 a(e\013ect) p 2414 4668 a(in) p 2532 4668 a(scattering) p 2986 4668 a(b) m(y) p 3126 4668 a(p) s(oin) m(t{lik) m(e) 244 4788 y(magnetic) p 661 4788 a(\014elds) p 911 4788 a(at) p 1030 4788 a(large) p 1269 4788 a(separation,) p Fo 1814 4788 a(A) n(nn.) p 2059 4788 a(H.) p 2196 4788 a(Poinc) p 2437 4788 a(ar) n(\023) p 2529 4788 a(e) p Fq 2651 4788 a(2) p Fp 2740 4788 a(\(2001\),) p 3070 4788 a(309{359.) 92 4992 y([8]) p 244 4992 a(V.) p 378 4992 a(Kostrykin) p 835 4992 a(and) p 1026 4992 a(R.) p 1159 4992 a(Sc) m(hrader,) p 1592 4992 a(Cluster) p 1935 4992 a(prop) s(erties) p 2395 4992 a(of) p 2508 4992 a(one) p 2688 4992 a(particle) p 3042 4992 a(Sc) m(hr\177) p 3228 4992 a(odinger) 244 5112 y(op) s(erators,) p 702 5112 a(I) s(I,) p Fo 835 5112 a(R) p 901 5112 a(ev.) p 1056 5112 a(Math.) p 1340 5112 a(Phys.) p Fq 1619 5112 a(10) p Fp 1764 5112 a(\(1998\),) p 2094 5112 a(627{683.) 92 5315 y([9]) p 244 5315 a(Y.) p 403 5315 a(Nam) m(bu,) p 804 5315 a(The) p 1031 5315 a(Aharono) m(v{Bohm) p 1806 5315 a(problem) p 2212 5315 a(revisited,) p Fo 2712 5315 a(Nucle) p 2946 5315 a(ar) p 3096 5315 a(Phys.) p Fq 3375 5315 a(579) p Fp 244 5436 a(\(2000\),) p 574 5436 a(590{616.) 1723 5753 y(40) p 90 rotate dyy eop %%Page: 41 41 41 40 bop Fp 43 407 a([10]) p 244 407 a(M.) p 387 407 a(Reed) p 626 407 a(and) p 809 407 a(B.) p 932 407 a(Simon,) p Fo 1252 407 a(Metho) p 1511 407 a(ds) p 1630 407 a(of) p 1739 407 a(Mo) p 1871 407 a(dern) p 2091 407 a(Mathematic) p 2587 407 a(al) p 2691 407 a(A) n(nalysis) p Fp(,) p 3102 407 a(I) s(I,) p Fo 3228 407 a(F) p 3285 407 a(ourier) 244 527 y(A) n(nalysis,) p 665 527 a(Self{A) p 937 527 a(djointness) p Fp(,) p 1469 527 a(Academic) p 1916 527 a(Press,) p 2200 527 a(1976.) 43 731 y([11]) p 244 731 a(S.) p 381 731 a(N.) p 536 731 a(M.) p 708 731 a(Ruijsenaars,) p 1289 731 a(The) p 1513 731 a(Aharono) m(v{Bohm) p 2285 731 a(e\013ect) p 2565 731 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