Content-Type: multipart/mixed; boundary="-------------0409031604497" This is a multi-part message in MIME format. ---------------0409031604497 Content-Type: text/plain; name="04-273.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-273.keywords" absolutely continuous spectrum, negative eigenvlalues ---------------0409031604497 Content-Type: application/postscript; name="DK.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="DK.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: DK.dvi %%CreationDate: Fri Sep 03 15:43:39 2004 %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Bold Times-Roman CMSY10 CMR12 CMMI12 CMSY8 MSBM10 %%+ CMMI8 CMR8 Times-Italic CMEX10 MSBM7 CMMI6 CMR6 MSAM10 Courier %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf -G0 DK %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2004.09.03:1542 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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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 43 /plus put dup 49 /one put dup 50 /two put dup 52 /four put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523d8c1e5c02115408a 277a0db93878d14fcdfef599913c0cd614d43dc6a08bb4db21730e0c454740fb 6efc542a3a65c0080b19eb0787edb1b37a32e81102ec944c67e6712ba229a7b0 f9e92271d62dad21f274948d3b192dac77c79729bf891b3baa4f1d47ba7b900e e71b90feb7bf7fcfe223a9a69bc9bd354545708209e94c9684039464f9c3260a 5317fb1e6c96e982272909867a7c5b7bf00186e1baeff1a4ced4785b56712833 f194bbcd40a7cc64fdc98d6640c0a6aa6c204d6539c74a67431f44edd1087f62 c3b119d72d6fe805137c77578c33857bde012f38e42dc5a83d4961e6f56c6faf f04fc4dbe862f8a3fae8fae508c701b101126b2ce75829c7c9c97d04fc490762 3cf90c0580ded9c7868d0c9662061602e3e79036abb61f28947c545e13dd65de 9c76d43cd585fe89a1b7d35197c0459045303b0a4fc7bb63a23448b719a06ff1 574ba437bc11c5f5b2373ceb7b9c53b14a46f5bba90e25ab72a87734a16b9e17 a8a0f8386a46c180d03691b79747716e2ccf0b73072d3ee6774b5a04af8996c1 463146ae0fda57802440957d719f1799b1edaaca85fb27ca6cacefc645621727 3e166d2ea5d8d1d055dfe81bc203ef1d3eecfd45d8ed4b8c139b6391c24e380e 0a3f14f4b4454bc23ea67e3b0c2b30f1e20c63875c402e9b46dde773239ccba2 6df2b17edaaa439359ff7137d6e75ef19d1007b705123e5370a9ddcd49f52e4c 1e7e008b96d8f5f4fa5855e28f8755aa7f8dc6dde1ade71958b03975365b34d0 734f387b3d6b4456c11c05338b7cb47aafc4ee312082fca752c0af79e6c1af7a 01fbe29ddfed452bb806f0f1d16acb3097d5b12c7046e9e2cc85a4933e0994de 82311a4d3552daa9e7745fc96e8a9a956520d67e9928365f83cacb72539eb165 4899ab87ec0dbb3b080b23f008171f50 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 61 /slash put dup 100 /d put dup 106 /j put dup 109 /m put dup 114 /r put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425 5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f 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1a547c808df7f1e217d61f22ea5700c4dcc8f15b544d888309a4be99cfbc46fc a70f9338997f16e70221bdafb5a1c7edd59061ba79f08ac3f0fb10a37abf1905 da5decbda51d76267f3e915d7a95db47c850cdaf29ad4a7d560947b07ccad7e5 1466c02df5278a01b0a200394996a52e4b2b9029d64da035129c4d5893860781 4f578d46f7afad82068ecf4c7c189ddefffed9d7b35a8015f993bdf04d324f31 fd897fce5b7cf252627b2c5404595f715ac2295c4cf5dfdc9bdeebe627839a56 6d92e3eba0ab287d0a21492cb0d4ac3d9a78563928c1e8078084f466913e068b 4cfff87bc45e41ee3b4c7fe81d27ec9cce083c7b2f43b4faac33f818a897f809 ca11cfd13675cff7872b3df2735365856d3940fb2e23ef1fb63022d8230a40b3 4546705d09709c2a02f219434e951dfa82a1339c09572310190c4ca5f9b9f981 79382216fe74381a001ab228066dc706493d1267f2263b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 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 readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueXX 5032014 def currentdict end currentfile eexec b5e2457af4a6caaa4536453c498a618ecdce7b5f6f2d5944265309f833bd3d50 3df8bd14c071f404d2177500681a801856cb8c9c9cf0112c9bd17ccba9ab8944 1759a320b2078df0fafdd3e357994bd81740d1a7522ddfafb75d58f5def046f7 084d10fa2f702e570b09a7073d70efe37b48c355a7089772238b7b4538c4912f cf6703a14fa416057ea2e1b94455913dd271b42846ee10d78270a8118e7e4bcb 8deb048bb280c240d59409d47046c890e5f79e5dd4b0be65a28a77aeb53dd33e ac506a6da87bb55e329f433627e06c3c94b078838b908538d93f888e504e25e0 3a8ccf7d2c02122ab3d485525564295390d1154e15fee35edff4eb016fadd32c 26d1b4c09de87943780954cebc4965aa890fe1f80b03eb07103e13d468245c7b c26455f229e8859585c6eeafd9474acdb27290fd62950dc52f893c99a2a614d4 2a7e3618266f3fb0c68a01a30373e048385ffe7dd5844e208a55d1a9263ab2db cb9b19038724f95af00349840157be45cb337871b55a304b87ade64b10ff0eba 21aa0eaeef74aa01f049303a8b25de0acc26bb3a33fcf267f479a2a73f7dece3 2aa23083687322b417fe86e8f5afc2136d045ad6b392364811a17630a94ff097 038eedeedb8da4ebf8fa5a96ce27a2ebf771d14f4a11fb1f9f48cdd207209934 885ef9118463552984b0fd3cf15d55de967fbb051549dd65f60dfe07f299690e 58252f032bca78935b7d2df852ed688bd13dd171b91cf7bd46d5433aef9f50f1 41a2517c4912b837793f84ddcf1116f70f7e9b1e6ec752dbc9183d4791d92602 397bafe29ac6f879ceb72c673c8a1aa0135d6f92d0db7791f9a2f1a5b55347e0 3e63723efd258754f5f4a9ad35873a98d54b6c54b17a39892dc1d38660597448 fdba9258493a0db0d560c01d49f2d889a99eaa8a5b5919cbd33f6b3d97bf27b3 e0b94b48d5d21d6c29aee4faca71bd775bb9defa37ff627f1e4926f10d59313e 77d81a511027ef9a8ed5b7fa9b5bd67758cd13bab6ac18411c974a65d0c90085 67bf5860d0930d7f43e557ee45e76ecb2806d21f4732bb282ac8b591f2b8775d 4b3ce2a37ebb371cb74a3cc513bdd70a0115de4760c21f034f5080d769f7ff83 554af524184702a02e534d1eb98dd3f7c5d51900409354dea37de4ac74a12c3a 69320913de6a728bd887c57f4ee5dcb8772249587ce3190bb662ac853abcff77 d4bd77985a4a805f44f8cc8597416c488866ff8429f65cd0edeec1fe2f0015a3 2bb098b0b3d8c913007f5846ca593c491e1efabc8f420a5fa338c47fd2427813 3279d27f12022195e15827797fe71d898f17b8af955e5bd5ce1da5fae7b3ece8 87aa52db81daa819242c6acb7fbed098d59a27bbcb12dca67e16915a4709fa5e 16311a55ddda46359ab51be5964874f1d3612ec10d2444576c508ae6a285a57f b978458b6f5f93c00882f2227d43d42c648437715a27cefd8d4ffb490e3e9980 1d1b4f1cacbc8b9e59c04c677a04047cc4b655fd8985d8e619a99e71cad67c94 2744577e185ac8b225e5352ae93ef0d804b73b943353266c74677b899d45b286 869cbe8ce9ad231007381de74bd3c6c84958f07ffce0620e42902a01fd15c98a 421ff110e5de48cd65568060afaa1e11e9893e720f22b754c47c334a1f5d0933 9b1b1b91b036b981a6be8a3276634fd4e39af829e2f2ac2b2dde35379abd1bf5 3a1071f07537db5fff44d145fce9713d8a9e2660900c41b83f948e16731d3048 2c8fa2aef8de49e3cf649e8ff62a2748cd9e299c7b 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 0 /parenleftbig put dup 1 /parenrightbig put dup 12 /vextendsingle put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 88 /summationdisplay put dup 90 /integraldisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 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 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83f4d4be6c2568b5f01f2beefd6f5be299e4291b06f7f3711c1bf319787c9b5a b0facbe7be60e131edba9aba14e4c933ef8da9af701890cc0c16681a693e931f 2d7eafb0ff4c379788baa8332d763423eec3e05060d4ad4de98da1ae848435a5 df36e9fdfece4e0632c6bc2597c3d5473426ef06e05b4e345475f222b37a4111 d4a977a1e46783103aab1516ae1fc6cf2ca804e6f567ea8b0e2a155d101d8193 45cfe71664012989e730ddfee32b6afcc9aa22f8961dc17997625d75aaea408c 521ab6bb9ba96409faa7d19b969d0ea6ac32697f6395628beb192bef70742e17 bddaee9277062c3e94890bc279158d8c9cb6d66b7cc6ade36e41cda0136fafcf c09f3bf403379b8e4e6f410752e63b58e30316ad51f6f08779fc8bfd6c1cc477 6a95eccdd3248bcb43480832bb5ec27c46b33848cf713c4f60926f1c5714b9d5 e6aa8f058c7b93196add5953f7fef6f83aaaa393b14d45908adbf4c379501f9f 697a3fbd511dc19ac739287172896c17e8a829862fd343f4ed352afddef647c3 16440f0a9e5c87877aac8ed01e1da8172e24f5a37aeb8a25ba6f2b1e9877f9e3 16c5045c0f6709bdbc4fa7390528ffbd3c4fada6fa388c628457f385a2376294 482fc8bd5ed374434f7aee9f3bc512bb5d22f4c0942980b809cdc6a24f9fd9af bba2d5b3f4d39b988af4a46f8200fba1772a85fb7fa156eedf6d62be2d536073 412be326626659775a5552ff531c71f3149ab74ff0b76fee93435b960453dd66 1697234660e012192d40d31fa36a3b9bba84700dbcdf6655c16771b25712ddac 35c5031e593c7f0bd80182179c8ff390848bcee491710a4eb205ce5081e5abb0 085e52debac498efa4bf24065e277e646ca31edde56cd786a1f3ee74226d52aa 942fbcb1a575c6b0f11c5288456916529bce6984b158482acb9bbac600aeefad 44ca149a2076596b61cf3c244723c8aa3a36afaf8abec84106755147d52e05b5 1dbfc28e0afa127df09ca2a4314816d0ef1fab818dbf4641a78618f09235981e a2bc3d89dc083bfe2326f38cbf36113af5fa7ccd315c9473ac94ee7bdbc32c4e 26afe326fb6d7bc5eb541ee56f9d946d981bf9bb953800a619bfd1d3c9bb2459 0c4dff2546b95925a39348e428f7ae82c2b3295364732c2f144eb620c679e55e 383a356821a3a9e58d29544c39c0691f850d0b0cdd65d91bc19eff3f811e657f 9e74a2bcb1a3b336be59d064fb5aef2a032f37b44f2ca7b79042f4028c3bb104 4c9d9a5b11b87572bdb8147a5b06c2652bec0ddbf6392bb47f8a260f3a71e4a9 9a868e22fa0c72ce580b8cc3eb280b0850a313461646f45edfd89e38b0bbecf2 6bdfda9bf06015a85efd2ba676b5f12b725b017995b7e2bbaed8b4bef714eeb0 ffc81bb47114e9a9f93dda4753610d0dae14b2692fd274eb6a46a886854e7333 f4831c836935abb97e6f9335f31d432d95c22c9e966e76d19d0b08f041f3c0e5 079b4517532c2f07954c0df82bcf7c989900da0b9a7e1dbd50fea30d365de337 56a88798f90519484561592d6ec1e0ad37555f328a67f3643af4e7f0be3cf128 839a0aae529349121632e4a4060e3989168925174ff6b798f2ec0e8b4d58b44a 99444fd2f3dac26d2b76480dbc7a6c21bd650d972d8c8994da30e77f47e950f9 f8f7931787fedd6dc1e6fb484f3757005afc0b6120ac4d6a0f9009bde2d40599 5e3882b9a06820b37af60868dfe6ce67bbd90915ad50df089d642c3a4b969e5f 0628594d5a43edc71569701e3205d1f95709b06fa6 0000000000000000000000000000000000000000000000000000000000000000 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 10 /Omega put 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 61 /equal put dup 99 /c put dup 111 /o put dup 115 /s put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e50bd6bf02070d34a2 265e57d706e67f56b5c8b536227df3b0c0932037e4774f66bbc4a2108ef5e149 0104a043b438b0ce201eff0951bb25cf04156def138deb42c28b4b4f3e7b085f b7d80c3b993da064739e1e4b9bba4dc66c56766f634844a3bd07f4b9aa01540c 5a83640c40084de610470e1f0824155fae02ea2783bf4312815dadc5b956ebc5 a386aaf5a7b963b2e81a67bb48872dac553206292cfc3e258e035d8e90744cfc f68615f1825be2e00a872ee2dd4736ef86c52b596de807cf0a8c8e2e2f71b3aa cea7983d09bdcdd426537f1839bac4b553676d2f6c6789e80193605ebea72d59 9a46fc15ca2014d0c1b3cc0b7a0bcc19ab24884bdf383a4543c9ed0b804ea840 729d1f6296fb6bc2d69d1a8ff8834c95bebb16f75e8209e6d2923c80296983d2 727dbeb8617837ffadbdbd16cd508139d04c6376227c4a670823ec0e11c582ea 50f1b949cdec3e6602d4c5a215b85caf1db6bf3484505406e53771dfee1ddfbe af456935b628fcbd681380adb03429acbd541d049e26f6290fb28db2b35f6662 c49ccbbb81204ad595cd478a96d3af14a559bdbf2b3be1fc841a022ba3d530fd 748423d33ef6d1f662423859a5e4551cb78176956ce128bf924c0b3ad1f02a78 668fed29f03d36cfbd2d1a92b9effcc4f1fc1ad05f45ae0a3a6aaf141ac2c88a 957a691618b1b0ee84130359e114986e2a8a094e00881b203f87a85a3b4e240f 738f559a4f02c4bacbcc47f987a8f5eda16420b93e2af158d2510b53bbaa265b 1f8213c3871eb25ddd0e1921d8eecff7ae00827dba9c951f56d528122d27a5a4 cc810cd2d6a1b317ac837435bf23e0742b115f2414543bae6787482a86c32e89 583992ad6a884e185869dbc35596bf00d7737582da16e672de5877d175d94469 9ccebdf567748a45a4fddfcde593c06194ace5d720407210b69b89e2f65f9b74 fedd61f326d946c46a3d83da542c699d2068e83f128908c741c7e19fdf2a282b 6543ed0158d2f8b550278e4fad40e5ea4d740239b6d2b4306b72369a274220c4 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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. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 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 78 /N put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812b1188a10f6327c9e8714449de2ae636420f56a44cebd774f0b131c629 818455cc8dd8d40939f3ba8aa5abc54590c7286b172193c23adb1b4f9931a9f7 73b960b1f5b760438028478e4442dc93a567b07e20017c18fca2a1daa2649dee 5a6ec51fd6c3f4b27367c31e95a56ba4bbeda0493bc02306037e2ba69add9b94 373364db316691e73d6811cd76fbc92b0c67ca18dcdf05807f17d1b309456ea9 d113ea0fccd6eb73bd8dfdbd5905a5e38bbf61cfe58fb01ec95a4bdd9565433d 4a7abb8dca6f76c45e50c1c9ba538078a5b7b67307730c84cfc5f62677924a48 28a9bb5be0b65603fd59e525ee6d0fdbef578ed48c15b1a344bd3e748631dc30 08992697b3543551e2a8740b14bdcc1df5780e9b12aed9da00183a46d0f2c727 ba64ce49e2dc7ae49ddec532db0ff9043ad3307040d1c84f4f7904c6250e4190 3f3cc5b97aa240986d464d116eb09e28c4a357bfc705238f21d179c1e8efa07a e338e737da2d04db865b77e9a539e9499aef03ebf58dce169a522fe6d2b43aff 0d806a114cf5af8368256694185c39f8eb6f61376624e3fa5572e82b68906652 e42d01549282e0bed67ed3692a53d6089395fa4e372a7196284f4a37b4aac76a 7d19f6d54519f7a64ae37c7fadbce8df272ee002061751f313f906ad4b82a369 e62e5a44cd30f093041610781e37fe26053bcd33cb4f7c43f8d93f1c72f06351 db9d9094996a34a3a0c3916684e73225589777c316afb196c6103b3293a5b090 804a66ffd0475367489bd6e2841a51e34c58d9ab5dfd4cbab5a936045b0dc8d0 a1373f36ce854c064b92fb8fc747a0ef6b50905a8045c3e021562427bce79ee5 68e5fd5b8628f218ee8ef1356e812a8e074ab2f29ab0a266e311e825bbab8492 b52f3dc748460c5893217f5f86c964d3be470308ca3537d62c1c82725e028163 46b38f244b98524ae1d11643be7b15d34cb7d57a38e1bc8f3661be54c313203a 4033066015c7bc1ae389745acf5f3065a7143d53ec45f32f649d740eb9fa93e2 69b18c2428061d85f694864a2f66c22ca373b939e209cd47756e25aabbd801ca 634ff4c6eaea4eb07dd66e4e712d50ada69be1a022c494a536eab11e8dc947d9 e99ba412496e483e68f76e00dd155ae0f672b13de4b8018370e47abc106a205b c1d2bd518b0e9e3d52e4aa13cd6302d53300c0bc3f7ce08956336987ee0350f5 8236ae1fe20c5ae8575123b72e7434 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 49 /infinity put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a18bfd18d2ff279844b29842a5e4038099fec03d6bd8b54b8032bfa4 a254b5088017073ff3524df950e3f9ff878a0be788cb39580aef5db4fbe9e1f0 e940aeaac02269677cf9c144feb668ba2e2f15cb6388f4bc0e7d96ccd9f85282 2b3ae8cbd0da1b5c642f0b1f0fce43bbdb7537a9f3200089251ca59920182931 f2fbbffcff223956332e7b227af747ca0a5306b479e5b924406f351a5e1fb724 c116087d66a5dc99624a021946d7ccb8d34b5b47dd8372b2ab45bced15c32d66 ea2312b1b02e161fe5da5837ef0cb51742bb60ef71f73b67bd56e13716462119 1b77473d034f6d79b2fa1920cbf45e181cae5cf64474d235c74e3e42350f9927 07023c14bcfa4aa6ab5af75ec20036c01a4cf0c42169aca30618bc41935d6ce5 7e5e34dd12080d3957665bf74aef26ce1932c9c4974b0ed5baf7bda5b9592d29 aae28167d1c0e412a22936d515d3e357b7f61a611a587ee55f717f9c6471e579 0dab88639497770b4494c060a654aa4115167838138d9afc3e93cd8e465aeca6 f7cc93b3129767a51904b1fcc820336d478d8e27fc3c19177d6dab7ba9940126 0a7bec623804de42c84393ef5ae71c6ee403bc93a5d50d1fa412d9283c47dac0 54ee6002d0453b026032f2aa0217fa1afba7506fa70d8c18004ea974aaf3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 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 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 21 /lambda put dup 30 /phi put dup 31 /chi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 76 /L put dup 78 /N put dup 85 /U put dup 86 /V put dup 87 /W put dup 96 /lscript put dup 97 /a put dup 99 /c put dup 100 /d put dup 105 /i put dup 109 /m put dup 110 /n put dup 112 /p put dup 114 /r put dup 117 /u 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 /UniqueXX 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7bcb09b7064e91fa0ded228e42 09aae407a7aaca60b1076299ac4abd23ef02f108765f0e3d91f92f3afbfded37 2fcf6e4b1416901517da8f2fb3c9fe7a87bcbe6fd36cd5b5823fdb74229036a6 3c3346a1093e6b1036902c1bf42fc317c80abf04020a47b344c36de42f05c490 a0ff44ab6d5249e9f552a8707bb7661e242644814001c8430ebd5e5f0b944ceb 666ee64359d663e355b2f17093a964139d17287f6ca6a024767eba4fe4873855 babe2f07b91560f68300b06dfe27264c163195d446980c35bca0b48f7806626a e72636593a05ba403ce1c0f8b2cea3ecd586e90ac17d034ba4af708304f23131 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%%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 1 /Delta put dup 10 /Omega put dup 22 /macron put 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 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 97 /a put dup 100 /d put dup 102 /f put dup 105 /i put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 117 /u put dup 118 /v put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueXX 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204a520640fd7c4d05e35ea5486f a43d0e970787203855daccb1ed0b16325828b13b7c767a1a58c87902f0546ea5 404440fa6526975783c2d7a9572b8e5d5176bac598b8960609f49016aebf3763 89c1adfe6a1ffc0c53b3acd9d168ec3a278fd4f1d9b085dc2df701346c9d0887 3d230a161692b42a45bb5da343b4edd839dd60685a59aaa49fc65cd8e2ad2a9c 5cab953495172a1a9f40d5f38e922443a519dd96f667201a408bd1d89e35f4ab 98e2f68c3366efc14b5afe1018d9c845d808d4f8e07ea8168518a171ab4d6e21 70eeac099eb7ef46eb9781384da1fac3b3133bb718bc80082eaea88759745188 f266b31d0c7e791d633f16ed94e05517a32163e74cbd96dc5db066f2a5313d6d 7f09465608cb404613e0f058073af000e5bdfafbbf9da0c0d5c02a3447f2cdc1 f56481901e34265c26d331ac3f85bdcbc7c51ef9eddf2b9c189c5253f8e74282 d6f053d7d183ae17ea175e5ebc401e67d21a9fea139cbbf3bb1358c713a75843 b39a69aa2b1a7b975f53ff22d1dc3bdf7acd17afa1da21568310c68241b31d3d 03bf404bd30baf9cc19c75b958bce7155f03cb0cfe2cae0327aad4b603284a51 7c26de75b8c6f6aaa9debe4aec08ca4b646d787a9dfac85b2c01760e9c6c6162 fbbc67dbd0796831e00c477d8e23c375ffab46d289be9d2328aec2b7534ae4cd d782ec2453e7787f6e6b4537b46c01545cba6f90b8e9a1bccac1937bceeaa5e7 8e9f368ce067a0a31da98bfbb545be555a7270f0031fadd4f9b186629e5d2c5f d264f8f24cd5a1c0f68399ff4b29fd77c4a54d8296523413c41368d333105653 0d552e9d21486445b09fdd7c0638ee8e6c31a0cebfe9981c99a3b8fbb38316ca a850da5dc690f3aec1627010e64bdade71beadaa9063c977bdf8b1c9681dea54 269dbd9e0732ffcadba50d001cd488898d4255c5833cd2869789d36cdc301df2 7a3278cfbbd4f4fc3b15101e349486dd577a3dffd43936d6c70ab2e1a067e04a c9b53775a33be8580be589333f2a0f01588ea15e144a6ac634c1fec9f99a7d0a 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435f769d6c9c45fb8c6fe873e04cac753e1e830522205f5862e1aa079442060a dd57aa83b046c067c12c7a8e71e554e7bee55503ab49e98f4889740dc206e1e3 8102e3d3243834968d6b935deaf4743f144a66b809e73c898c964193b8fd6881 b296008c3119c5523f30ac9fe70f3f3d1a84e15d91a337db41218ebbd5205e8e e1a5aa714cc867bfd0a655ed84c54e197fb93f0368ec970ca61c173f9151073f 3ec88db9eff311f50f25d42c6f674d1e97700f6c03e8e5231c3d0a8c144da333 98cac3f1356e0280336d1aabe177e5c2f0993423f85ff11a023dabea18cd9c59 c306c06f9885e686e3d462570db71a3b0425e5e5f94002346f5cdd7d91247f63 a6662417bcd442987f4ffe55e0d80663d92fdce9fb6885f966b5a2b6032bf24a 69dad21b694ba4f8930659c4e7176f900d3ea5cfaae65180a6b262ecfe65d7c7 a50aded00cdfaa86bf84ee45e69c7eab103b4b8286fc33325a932a3b77a7ef12 0d360525223804a73ffe5596fb006436a2013ebc15c52f42b87ee170ab3fb2af 941a1582fd440d8668d6a9537a5c7372d30a787136d46f6a34dec4a7699cf056 b1e4729791c82c8052d326d3f23556f3686693d7fbc862b96dbeacb1a9d73647 7e7a46b5b839fa604e8dc24603a1c4ae64cf9081e2aa43baa1791d207336ef0a 154912ceca50937cead4a948f8ae6d18fafc5470d9f77d6acb33f83530d00189 e1f27dbdb9f1bb3918455cf20d05927dc58fc8c1c11ffac95f1ab7e8cedde4e0 a63f869e9b5f43ff28de8bc2a6f4d3ec41a1fba09732c09fc549d5c83fd1141e 0ae1127ce3b690c34c21edbaa7e946edc53ae24c9ae2a8d4cb0deed45511dd09 7e9eea782dc5d11e2397dffb1806e49d91263fb68899a5557da20913f75463f2 47d94faee5a6e598daf9154100ec117d5699a12f468f71d85b15768f841300f1 d4eb284f80ae7431b20f14fa8a16016a29ea3a2d6d8579ec2d3e49119193547f ca1547ea8e3008b366f342f3430868f0df47ee508d6ccf518c1d2949769e95bb dda1bc1213b67e362a6d52579c843eef4e68ac4c403051512ac3c5eac6b8df05 838e5a7c1730e75f6523c7fce358538e4ff4132a79e862672884cdfda868e533 e7c3e613891422e1244bf2e95844c0224789559aa15f519f86ca3b8faeb79225 9ee8b53e6abf19815d9edfa44cefabedecd5761372af3ad6fcd9eb32ec5d1a7e 7ee59a78b74e3a1771d9f7a46b092d6ff02458dbffab79e69ac51121bad7406c 5b360f4e680729ffef592973fd4e0d4330b01a0fa45df873c3a3d23009aa3490 e15306b2326fd662a31d261e3bba745bc0442e99ca3c33f8b537a54d87aa8f2d 06a9d465c4a08a1ad9541b4d67d5a5972f261b4f3b067ed16a0ef3a9cd406043 6e4f924ea8f68836328766260842c2370c109236f92dceec412302751037a0a7 a83389ce2262e65be969fdce6d886ca95b457615b8902e6bdd752e6f74d14d5a 30211785e2843db26f8da6dffe72f56de143c916a3b51ab73867b93c77d24adb 8c736c59ea764360ab93510b3f485952be8978292eee61092f46c7c01d24fc09 fd1909f2bc36e4d378120c1772bf5c5627a886138e8d85fb37cc1496b808c670 9d468f3989f78bedd26469edd8669e0efa0406a6c814a2ed835ebe1130b7e4d1 738728795fd11a1705fb2381dc7f52b3aa46791ae9361a8ced51bae07b2abff8 1c3932eeb271b28c483d78804f5fa519e8c441b996780e103211d3458d84ea0f 99df80f86405812f3cb5632bc95d469940defe71bd084ffed480ab7d2d343972 510d0129a0ea4d15733321dd5fdbd324f4c4bd39566a6fcc81ae6d210b074c8b 5cf35fcd72474833789f04103879960e4eb4dfb2364fe5be3e1c4be1093ced9a 9cc52fae5b25ae6cc856b99aa919ec756039bd7fa3c8c52fbd5be4a8d3f5b866 3ae20df9aeb1ba9cb1b902570769a243146a36c0d274eb8d0827b8173148871d f6746cf3033faace24d15d54d157e2520e1d5a20d35e979d83df4cb7936a6682 616a599a6fdd08120fcf958c3eec3a2ceb163eff722b51f76a8e6bdd6ec7a4b1 a9be7a26acd32227f5ca73255bb49c52770a9a6122fbbec4dd46e58098e9a2d7 103925f0797d4e3b97e1cf0c026650a34a6fdcbaba657694d00383ab3546296e 3690c1d8eb0ae9018a4abd55594710b1ef7649eba3aec10120b9965e2a38a7c2 34cc4f136b9e8eb12ef333dba520539e72bbd9a59285fd486f72afb029bcd9eb 93c5172b0880497dd5bb530da9c04b3e3fb2326558d055afdd919c614cd84e1b 29bc00fe594e78216f716c81bc279159d225a0771410d3b76714dfd97b21fb7e f086200e9887518ee1e9ff83c95176764d646873a2e48965a5056aa5217f8b1e 2f4b11a48e818d694c4d4b1323edb22691cd3ae3810c52255bb71061d774237d 8d1505fbe1cd37a73053a90f4af8485587bada0732130ef5533ec98ef7da615d af2d4a7bf4cb3e5ee53447aae5196160be55e9d739ac7223015cb863f2598d15 57ee8191c63304461c16a5aabcceee1564004b98a964536339729db881cc7579 0680d6cdb02e617991b3e9f4 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 6 /plusminus put dup 7 /minusplus put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a 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Ft(Consider)344 b(positi)-33 b(v)-20 b(e)344 b(smooth)h(functions)g Fp(\020)27152 41809 y Fm(n)28168 41610 y Fr(\024)390 b Fq(1)344 b Ft(supported)h(in)f Fp(B)38533 41809 y Fm(n)p Fl(+1)40665 41610 y Fr(n)304 b Fp(B)42621 41809 y Fl(1)43490 41610 y Ft(such)6075 43160 y(that)12486 44837 y Fp(\020)13054 45036 y Fm(n)13681 44837 y Fq(\()p Fp(x)p Fq(\))368 b(=)h(1)p Fp(;)886 b Fq(for)443 b(2)370 b Fp(<)e Fr(j)p Fp(x)p Fr(j)h Fp(<)g(n;)1550 b Fq(and)443 b Fr(jr)p Fp(\020)33971 45036 y Fm(n)34597 44837 y Fq(\()p Fp(x)p Fq(\))p Fr(j)369 b(\024)g Fp(C)6075 46824 y Ft(Put)319 b Fp(\021)8808 47023 y Fm(n)9434 46824 y Fq(\()p Fp(x)p Fq(\))369 b(=)g Fr(j)p Fp(x)p Fr(j)14412 46342 y Fl(\(1)p Fo(\000)p Fm(d)p Fl(\))p Fm(=)p Fl(2)17826 46824 y Fp(\020)18394 47023 y Fm(n)19021 46824 y Fq(\()p Fp(x)p Fq(\))p Ft(.)407 b(Assume)320 b(that)g(on)g(the)g(support)h(of)f Fp(\021)38387 47023 y Fm(n)39333 46824 y Ft(the)g(potential)6075 48373 y Fp(V)507 b Fq(+)218 b Fp(W)491 b Ft(is)312 b(of)f(the)h(form)g Fp(V)508 b Fq(+)218 b Fp(W)549 b Fq(=)368 b(div)19 b Fp(A)218 b Fq(+)g Fr(j)p Fp(A)p Fr(j)29310 47891 y Fl(2)29835 48373 y Ft(,)316 b(where)311 b Fp(A)g Ft(is)g(a)g(locally)h(bounded) 6075 49923 y(v)-20 b(ector)332 b(function.)414 b(Since)331 b Fr(\000)p Fq(\001)296 b Fr(\000)f Fp(V)584 b Fq(+)295 b Fp(W)550 b Fr(\025)369 b Fq(0)p Ft(,)332 b(we)g(ha)-27 b(v)-20 b(e)333 b(the)f(estimate)7269 50890 y Fj(Z)8818 52698 y Fq(div)19 b Fp(A)p Fr(j)p Fp(\021)12593 52897 y Fm(n)13219 52698 y Fr(j)13588 52150 y Fl(2)14114 52698 y Fp(dx)295 b Fq(+)17131 50890 y Fj(Z)18680 52698 y Fr(j)p Fp(A)p Fr(j)20393 52150 y Fl(2)20919 52698 y Fr(j)p Fp(\021)21930 52897 y Fm(n)22556 52698 y Fr(j)22925 52150 y Fl(2)23451 52698 y Fp(dx)369 b Fr(\024)26637 50890 y Fj(Z)28187 52698 y Fr(jr)p Fp(\021)30305 52897 y Fm(n)30931 52698 y Fr(j)31300 52150 y Fl(2)31826 52698 y Fp(dx)295 b Fq(+)f(2)35713 50890 y Fj(Z)37264 52698 y Fp(W)181 b Fq(\()p Fp(x)p Fq(\))p Fr(j)p Fp(\021)41435 52897 y Fm(n)42060 52698 y Fr(j)42429 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65390 y Fp(dx)369 b Fr(\024)33008 64314 y Fj(\000)33617 65390 y Fq(1)295 b(+)36002 64491 y(1)p 36002 65084 V 36065 66301 a Fp(\017)36785 64314 y Fj(\001)37615 63582 y(Z)39165 65390 y Fr(jr)p Fp(\021)41283 65589 y Fm(n)41909 65390 y Fr(j)42278 64841 y Fl(2)42804 65390 y Fp(dx)7781 68840 y Fq(+2)9664 67032 y Fj(Z)11215 68840 y Fp(W)181 b Fq(\()p Fp(x)p Fq(\))p Fr(j)p Fp(\021)15386 69039 y Fm(n)16011 68840 y Fr(j)16380 68291 y Fl(2)16906 68840 y Fp(dx)369 b Fr(\024)20092 67764 y Fj(\000)20701 68840 y Fq(1)295 b(+)23086 67941 y(1)p 23086 68534 V 23149 69751 a Fp(\017)23869 67764 y Fj(\001)24699 67032 y(Z)26249 68840 y Fr(jr)p Fp(\021)28367 69039 y Fm(n)28993 68840 y Fr(j)29362 68291 y Fl(2)29888 68840 y Fp(dx)g Fq(+)g(2)33776 67032 y Fj(Z)35326 68840 y Fr(j)p Fp(W)181 b Fq(\()p Fp(x)p Fq(\))p Fr(jj)p Fp(x)p Fr(j)40701 68291 y Fl(1)p Fo(\000)p Fm(d)42442 68840 y Fp(dx:)6075 62951 y Ft(\(3.3\))p eop %%Page: 5 5 5 4 bop 16614 3345 a Ff(ABSOLUTEL)-100 b(Y)323 b(CONTINUOUS)i(SPECTR) -40 b(UM)10039 b(5)6075 6001 y Ft(Note)332 b(that)h(the)f(right)h(hand) g(side)f(is)g(bounded)h(uniformly)h(in)f Fp(n)f Ft(and)g(therefore)6075 8896 y(\(3.4\))18735 7088 y Fj(Z)19472 10095 y Fl(2)p Fm(<)p Fo(j)p Fm(x)p Fo(j)p Fm()g(N)139 b Ft(.)766 b(The)450 b(e)-20 b(xistence)451 b(of)g Fp(A)24440 22897 y Fm(N)25787 22698 y Ft(w)-13 b(as)449 b(pro)-20 b(v)g(en)452 b(in)f(the)g(proposition)h (of)f(this)6075 24248 y(section.)412 b(In)332 b(order)h(to)g(apply)f (Theorem)h(2.1)f(we)g(put)9399 26862 y Fp(V)10157 27061 y Fm(n)10783 26862 y Fq(\()p Fp(x)p Fq(\))369 b(=)g(div)16072 25387 y Fj(\020)16865 26862 y Fp(w)17795 27061 y Fm(n)18421 26862 y Fq(\()p Fp(x)p Fq(\))p Fp(A)21147 27061 y Fm(N)22044 26862 y Fq(\()p Fp(x)p Fq(\))23795 25387 y Fj(\021)24588 26862 y Fp(;)1550 b Fq(and)442 b Fp(U)29920 27061 y Fm(n)30547 26862 y Fq(\()p Fp(x)p Fq(\))368 b(=)h Fr(j)p Fp(w)35346 27061 y Fm(n)35972 26862 y Fq(\()p Fp(x)p Fq(\))p Fp(A)38698 27061 y Fm(N)39594 26862 y Fq(\()p Fp(x)p Fq(\))p Fr(j)41714 26313 y Fl(2)42240 26862 y Fp(:)6075 29430 y Ft(Then)332 b(clearly)-86 b(,)11151 32325 y Fr(\000)p Fq(\001)295 b Fr(\006)g Fp(V)15649 32524 y Fm(n)16571 32325 y Fq(+)g Fp(U)18761 32524 y Fm(n)19757 32325 y Fr(\025)369 b Fq(0)p Fp(;)2878 b Fq(sup)25742 33380 y Fm(n)27228 30517 y Fj(Z)28778 32325 y Fr(j)p Fp(U)30030 32524 y Fm(n)30656 32325 y Fq(\()p Fp(x)p Fq(\))p Fr(jj)p Fp(x)p Fr(j)34253 31776 y Fl(1)p Fo(\000)p Fm(d)35995 32325 y Fp(dx)369 b(<)g Fr(1)p Fp(:)6075 35219 y Ft(Here)312 b(the)h(second)g(bound)g(follo)-33 b(ws)314 b(from)g(\(3.4\))q(.)405 b(It)314 b(remains)f(to)g(pro)-20 b(v)g(e)314 b(that)f Fp(V)42331 35418 y Fm(n)43181 35219 y Fq(+)223 b Fp(U)45299 35418 y Fm(n)6075 36769 y Ft(con)-53 b(v)-20 b(er)c(ges)300 b(to)g Fp(W)355 b Fq(+)175 b Fp(V)589 b Ft(in)300 b Fp(L)19331 36287 y Fl(2)19331 37114 y Fm(l)11 b(oc)20540 36769 y Fq(\()p Fn(R)22005 36287 y Fm(d)22719 36769 y Fr(n)175 b Fp(B)24546 36968 y Fl(1)25072 36769 y Fq(\))300 b Ft(.)401 b(But)300 b(this)g(follo)-33 b(ws)300 b(from)h(the)f(simple)g(f)-13 b(act)6075 38319 y(that)11347 40014 y Fp(W)181 b Fq(\()p Fp(x)p Fq(\))294 b(+)h Fp(V)289 b Fq(\()p Fp(x)p Fq(\))369 b(=)g Fp(V)21414 40213 y Fm(n)22040 40014 y Fq(\()p Fp(x)p Fq(\))295 b(+)g Fp(U)26276 40213 y Fm(n)26903 40014 y Fq(\()p Fp(x)p Fq(\))p Fp(;)2878 b Fq(for)443 b(1)369 b Fp(<)g Fr(j)p Fp(x)p Fr(j)g Fp(<)g(n:)20752 43065 y Ft(4.)698 b(S)66 b Fs(E)g(C)g(O)g(N)g(D)397 b(P)66 b(R)23 b(O)66 b(O)g(F)7403 45390 y Ft(There)354 b(is)h(a)f(f)-13 b(amily)356 b(of)f(non-ne)-20 b(g)-7 b(ati)-33 b(v)-20 b(e)356 b(functions)f Fp(\021)31461 45589 y Fm(n)32498 45390 y Fr(2)410 b Fp(C)34820 44908 y Fo(1)34725 45718 y Fl(0)35816 45390 y Fq(\()p Fn(R)37281 44908 y Fm(d)38133 45390 y Fr(n)312 b Fp(B)40097 45589 y Fl(1)40623 45390 y Fq(\))p Ft(,)360 b Fp(\021)42463 45589 y Fm(n)43499 45390 y Fr(\024)411 b Fq(1)p Ft(,)6075 46940 y(and)332 b(a)g(positi)-33 b(v)-20 b(e)333 b(constant)f Fp(c)19052 47139 y Fl(1)19947 46940 y Fp(>)368 b Fq(0)p Ft(,)333 b(such)f(that)g Fp(\021)28375 47139 y Fm(n)29333 46940 y Ft(is)g(supported)h(in)g(the)f(set)19044 49190 y Fr(f)p Fp(x)370 b Fr(2)e Fn(R)23030 48641 y Fm(d)23939 49190 y Fq(:)812 b Fp(n)369 b(<)g Fr(j)p Fp(x)p Fr(j)g Fp(<)g Fq(4)p Fp(n)p Fr(g)6075 51428 y Ft(and)332 b(such)g(that)11015 53666 y Fp(\021)11657 53865 y Fm(n)12283 53666 y Fq(\()p Fp(x)p Fq(\))369 b(=)f(1)p Fp(;)1551 b Fq(for)443 b(2)p Fp(n)370 b(<)e Fr(j)p Fp(x)p Fr(j)h Fp(<)g Fq(3)p Fp(n;)1551 b Fq(and)442 b Fr(jr)p Fp(\021)34738 53865 y Fm(n)35364 53666 y Fr(j)369 b(\024)g Fp(c)38064 53865 y Fl(1)38590 53666 y Fp(n)39366 53117 y Fo(\000)p Fl(1)40624 53666 y Fp(:)6075 55903 y Ft(One)264 b(can)f(e)-33 b(v)-20 b(en)264 b(assume)f(that)h Fp(\021)20450 56102 y Fm(n)21076 55903 y Fq(\()p Fp(x)p Fq(\))369 b(=)g Fp(\021)48 b Fq(\()p Fp(x=n)p Fq(\))p Ft(.)389 b(Then)263 b(there)h(is)g(a)f(positi)-33 b(v)-20 b(e)265 b(constant)6075 57453 y Fp(C)464 b(>)368 b Fq(0)333 b Ft(such)f(that)6075 60096 y(\(4.1\))19760 58288 y Fj(Z)21310 60096 y Fr(jr)p Fp(\021)23428 60295 y Fm(n)24054 60096 y Fr(j)24423 59547 y Fl(2)24949 60096 y Fp(dx)368 b(<)h(C)316 b(n)30136 59547 y Fm(d)p Fo(\000)p Fl(2)31879 60096 y Fp(:)6075 62946 y Ft(Assume)377 b(that)h(on)g(the)f (support)i(of)f Fp(\021)23297 63145 y Fm(n)24300 62946 y Ft(the)g(potential)g Fp(V)618 b Fq(+)329 b Fp(W)558 b Ft(is)377 b(of)h(the)g(form)h Fp(V)618 b Fq(+)6075 64496 y Fp(W)751 b Fq(=)570 b(div)19 b Fp(A)376 b Fq(+)f Fr(j)p Fp(A)p Fr(j)15876 64014 y Fl(2)16402 64496 y Ft(,)468 b(where)442 b Fp(A)f Ft(is)g(a)f(locally)i(bounded)g(v)-20 b(ector)442 b(function.)740 b(Since)6075 66046 y Fr(\000)p Fq(\001)295 b Fr(\000)g Fp(V)585 b Fq(+)295 b Fp(W)549 b Fr(\025)369 b Fq(0)p Ft(,)333 b(we)f(ha)-27 b(v)-20 b(e)7269 67032 y Fj(Z)8818 68840 y Fq(div)19 b Fp(A)p Fr(j)p Fp(\021)12593 69039 y Fm(n)13219 68840 y Fr(j)13588 68291 y Fl(2)14114 68840 y Fp(dx)295 b Fq(+)17131 67032 y Fj(Z)18680 68840 y Fr(j)p Fp(A)p Fr(j)20393 68291 y Fl(2)20919 68840 y Fr(j)p Fp(\021)21930 69039 y Fm(n)22556 68840 y Fr(j)22925 68291 y Fl(2)23451 68840 y Fp(dx)369 b Fr(\024)26637 67032 y Fj(Z)28187 68840 y Fr(jr)p Fp(\021)30305 69039 y Fm(n)30931 68840 y Fr(j)31300 68291 y Fl(2)31826 68840 y Fp(dx)295 b Fq(+)f(2)35713 67032 y Fj(Z)37264 68840 y Fp(W)181 b Fq(\()p Fp(x)p Fq(\))p Fr(j)p Fp(\021)41435 69039 y Fm(n)42060 68840 y Fr(j)42429 68291 y Fl(2)42955 68840 y Fp(dx:)p eop %%Page: 6 6 6 5 bop 6075 3345 a Ff(6)16303 b(O.)250 b(SAFR)-40 b(ONO)-50 b(V)6075 6001 y Ft(Inte)-20 b(gration)334 b(by)e(parts)g(leads)g(to) 11629 7929 y Fj(\014)11629 8726 y(\014)12072 7250 y(Z)13622 9058 y Fq(div)18 b Fp(A)p Fr(j)p Fp(\021)17396 9257 y Fm(n)18022 9058 y Fr(j)18391 8510 y Fl(2)18917 9058 y Fp(dx)20332 7929 y Fj(\014)20332 8726 y(\014)21144 9058 y Fr(\024)369 b Fp(\017)23292 7250 y Fj(Z)24842 9058 y Fr(j)p Fp(A)p Fr(j)26555 8510 y Fl(2)27081 9058 y Fr(j)p Fp(\021)28092 9257 y Fm(n)28718 9058 y Fr(j)29087 8510 y Fl(2)29613 9058 y Fp(dx)295 b Fq(+)32763 8160 y(1)p 32763 8753 651 54 v 32826 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b(Theorem)h(1.1)f(with)h Fp(V)659 b Fq(=)368 b(div)19 b Fp(A)332 b Ft(and)g Fp(W)549 b Fq(=)369 b Fr(j)p Fp(A)p Fr(j)30932 33244 y Fl(2)31458 33726 y Ft(.)1519 b Fd(\003)22280 36886 y Ft(R)66 b Fs(E)g(F)g(E)g(R)g(E)g(N)g(C)g(E)g(S) 6628 38989 y Fu([1])553 b(A.)483 b(Mohammed,)537 b Fg(W)-102 b(eak)485 b(Harnac)-22 b(k')-44 b(s)484 b(inequality)h(for)e(non-ne)-44 b(gative)486 b(solutions)d(of)g(elliptic)8472 40317 y(equations)279 b(with)e(potential)p Fu(.)h(Proc.)f(Amer)-61 b(.)277 b(Math.)h(Soc.)g Fc(129)g Fu(\(2001\),)f(no.)h(9,)f(2617-2621)6628 41645 y([2])553 b(H.)322 b(Behnck)-11 b(e,)335 b Fg(Absolute)323 b(continuity)g(of)f(Hamiltonians)h(with)e(von)i(Neumann-W)-61 b(igner)325 b(poten-)8472 42974 y(tials.)276 b Fu(Proc.)i(Amer)-61 b(.)277 b(Math.)g(Soc.)h Fc(111)g Fu(\(1991\),)g(373-384.)6628 44302 y([3])553 b(H.)322 b(Behnck)-11 b(e,)335 b Fg(Absolute)323 b(continuity)g(of)f(Hamiltonians)h(with)e(von)i(Neumann-W)-61 b(igner)325 b(poten-)8472 45631 y(tials.)276 b(II.)g Fu(Manuscripta)i(Math.)f Fc(71)h Fu(\(1991\),)g(163-181.)6628 46959 y([4])553 b(M.)341 b(Christ,)356 b(A.)340 b(Kisele)-28 b(v)342 b(and)g(C.)f(Remling,)357 b Fg(The)342 b(absolutely)h (continuous)g(spectrum)e(of)g(one-)8472 48287 y(dimensional)514 b(Sc)-17 b(hr)16497 48294 y(\250)16407 48287 y(oding)-11 b(er)515 b(oper)-17 b(ator)-11 b(s)513 b(with)g(decaying)i(potentials)p Fu(.)d(Math.)h(Res.)f(Lett.)g Fc(4)8472 49616 y Fu(\(1997\),)278 b(719-723.)6628 50944 y([5])553 b(M.)547 b(Christ)g(and)h(A.)g(Kisele) -28 b(v)-72 b(,)615 b Fg(Absolutely)549 b(continuous)g(spectrum)f(for)f (one-dimensional)8472 52272 y(Sc)-17 b(hr)10573 52279 y(\250)10483 52272 y(oding)-11 b(er)274 b(oper)-17 b(ator)-11 b(s)271 b(with)g(slowly)f(decaying)k(potentials:)340 b(some)271 b(optimal)g(r)-41 b(esults)p Fu(.)270 b(J.)f(Am.)8472 53601 y(Math.)278 b(Soc.)g Fc(11)f Fu(\(1998\),)h(771-797.)6628 54929 y([6])553 b(S.)319 b(Denisso)-17 b(v)-72 b(,)331 b Fg(On)319 b(the)h(absolutely)g(continuous)h(spectrum)f(of)f(Dir)-17 b(ac)320 b(oper)-17 b(ator)p Fu(,)330 b(to)319 b(appear)i(in)8472 56257 y(Commun.PDE.)6628 57586 y([7])553 b(S.)369 b(Denisso)-17 b(v)-72 b(,)393 b Fg(Absolutely)371 b(continuous)g(spectrum)f(of)f(Sc) -17 b(hr)32461 57593 y(\250)32371 57586 y(oding)-11 b(er)372 b(oper)-17 b(ator)-11 b(s)370 b(with)f(slowly)8472 58914 y(decaying)280 b(potentials)e Fu(,)e(to)h(appear)i(in)e(IRMN)6628 60242 y([8])553 b(D.)307 b(Damanik)h(and)g(R.)f(Killip,)p Fg(Half-line)e(Sc)-17 b(hr)26710 60249 y(\250)26620 60242 y(oding)-11 b(er)310 b(oper)-17 b(ator)-11 b(s)308 b(with)e(no)i(bound) h(states)d Fu(,)313 b(to)8472 61571 y(appear)279 b(in)e(Acta)h(Math.) 6628 62899 y([9])553 b(P)-123 b(.)376 b(Deift)e(and)i(R.)f(Killip,)399 b Fg(On)375 b(the)h(absolutely)g(continuous)i(spectrum)e(of)f(one)h (-dimensional)8472 64227 y(Sc)-17 b(hr)10573 64234 y(\250)10483 64227 y(oding)-11 b(er)295 b(oper)-17 b(ator)-11 b(s)292 b(with)f(squar)-41 b(e)292 b(summable)h(potentials)p Fu(,)i(Commun.)e(Math.)f(Ph)-6 b(ys.)292 b Fc(203)8472 65556 y Fu(\(1999\),)278 b(341-347.)6075 66884 y([10])553 b(V)-143 b(.)277 b(Jaksic)g(and)i(Y)-143 b(.)276 b(Last,)h Fg(Corrugated)i(surfaces)e(and)h(a.c.)g(spectrum)p Fu(,)f(submitted) 6075 68213 y([11])553 b(R.)251 b(Killip)f(and)i(B.)f(Simon,)257 b Fg(Sum)252 b(rules)e(for)h(J)-39 b(acobi)253 b(matrices)e(and)h (their)e(applications)j(to)e(spec-)8472 69541 y(tr)-17 b(al)277 b(theory)p Fu(,)h(Annals)g(of)e(Math.\(2003\))p eop %%Page: 9 9 9 8 bop 16614 3345 a Ff(ABSOLUTEL)-100 b(Y)323 b(CONTINUOUS)i(SPECTR) -40 b(UM)10039 b(9)6075 6001 y Fu([12])553 b(R.)434 b(Killip,)472 b Fg(P)-89 b(erturbations)435 b(of)f(one-dimensional)i(Sc)-17 b(hr)30957 6008 y(\250)30867 6001 y(oding)-11 b(er)437 b(oper)-17 b(ator)-11 b(s)435 b(pr)-41 b(eserving)435 b(the)8472 7330 y(absolutely)279 b(continuous)g(spectrum)p Fu(,)e(Int.)g(Math.)g(Res.)g(Not.)g(\(2002\),)g(2029-2061.)6075 8658 y([13])553 b(A.)411 b(Kisele)-28 b(v)-72 b(,)444 b(Y)-143 b(.)410 b(Last)h(and)g(B.)g(Simon)g Fg(Modi\002ed)h(Pr)29898 8665 y(\250)29808 8658 y(ufer)f(and)h(EFGP)f(tr)-17 b(ansforms)410 b(and)i(the)8472 9986 y(spectr)-17 b(al)228 b(analysis)e(of)h (one-dimensional)i(Sc)-17 b(hr)26897 9993 y(\250)26807 9986 y(oding)-11 b(er)229 b(oper)-17 b(ator)-11 b(s)p Fu(,)238 b(Comm.)227 b(Math.)f(Ph)-6 b(ys.)228 b Fc(194)8472 11315 y Fu(\(1998\),)278 b(1-45.)6075 12643 y([14])553 b(K.)252 b(K)-17 b(urata,)257 b Fg(Continuity)c(and)g(Harnac)-22 b(k')-44 b(s)252 b(inequality)i(for)d(solutions)g(of)h(elliptic)f (partial)h(dif)-20 b(fer)e(-)8472 13971 y(ential)278 b(equations)g(of)f(second)i(or)-41 b(der)p Fu(,)277 b(Indiana)i(Uni)-28 b(v)-72 b(.)277 b(Math.)h(J.)e Fc(43)i Fu(\(1994\),)f(no.)h(2,)f (411-440.)6075 15300 y([15])553 b(A.)791 b(Lapte)-28 b(v)-72 b(,)920 b(S.)791 b(Nabok)-11 b(o)792 b(and)g(O.Safrono)-17 b(v)-72 b(,)921 b Fg(Absolutely)791 b(continuous)i(spectrum)e(of)8472 16628 y(Sc)-17 b(hr)10573 16635 y(\250)10483 16628 y(oding)-11 b(er)238 b(oper)-17 b(ator)-11 b(s)235 b(with)f(slowly)g(decaying)k (and)d(oscillating)g(potentials)p Fu(,)243 b(Comm.)235 b(Math.)8472 17957 y(Ph)-6 b(ys.)278 b(to)f(appear)-61 b(.)6075 19285 y([16])553 b(C.)437 b(Remling,)478 b Fg(The)439 b(absolutely)f(continuous)h(spectrum)f(of)f(one-dimensional)j(Sc)-17 b(hr)42581 19292 y(\250)42491 19285 y(oding)-11 b(er)8472 20613 y(oper)-17 b(ator)-11 b(s)278 b(with)f(decaying)j(potentials)p Fu(,)e(Comm.)f(Math.)h(Ph)-6 b(ys.)277 b Fc(193)i Fu(\(1998\),)e (151-170.)6075 21942 y([17])553 b(O.)321 b(Safrono)-17 b(v)-72 b(,)334 b Fg(The)323 b(spectr)-17 b(al)322 b(measur)-41 b(e)322 b(of)f(a)g(J)-39 b(acobi)324 b(matrix)d(in)g(terms)f(of)h(the)h (F)-116 b(ourier)321 b(tr)-17 b(ans-)8472 23270 y(form)277 b(of)g(the)h(perturbation)p Fu(,)g(Arki)-28 b(v)277 b(Matematik,)h(to)f (appear)-61 b(.)6075 24598 y([18])553 b(O.)238 b(Safrono)-17 b(v)-72 b(,)248 b Fg(On)239 b(the)f(absolutely)i(continous)g(spectrum)f (of)f(multi-dimensional)h(Sc)-17 b(hr)42581 24605 y(\250)42491 24598 y(oding)-11 b(er)8472 25927 y(oper)-17 b(ator)-11 b(s)278 b(with)f(slowly)g(decaying)j(potentials)p Fu(,)e(Comm.Math.)g (Ph)-6 b(ys.)278 b(to)f(appear)6075 27255 y([19])553 b(O.)505 b(Safrono)-17 b(v)508 b(and)e(G.)f(Stolz,)562 b Fg(Absolutely)507 b(continuous)g(spectrum)f(of)f(multi-dimensional) 8472 28583 y(Sc)-17 b(hr)10573 28590 y(\250)10483 28583 y(oding)-11 b(er)280 b(oper)-17 b(ator)-11 b(s)278 b(with)f(potentials) h(decaying)i(only)e(in)f(a)g(cone)p Fu(,)h(in)f(preparation)6075 29912 y([20])553 b(M.)213 b(Reed)h(and)g(B.)e(Simon,)226 b Fg(Methods)214 b(of)f(modern)h(mathematical)h(physics)p Fu(,)225 b Fc(3)p Fu(,)h(Academic)215 b(Press,)8472 31240 y(San)279 b(Francisco,)f(London)h(\(1978\).)6075 32568 y([21])553 b(B.)277 b(Simon,)h Fg(Sc)-17 b(hr)15310 32575 y(\250)15220 32568 y(oding)-11 b(er)280 b(semigr)-50 b(oups)p Fu(,)278 b(Bull.)e(Amer)-61 b(.)278 b(Math.)f(Soc.)h Fc(7)f Fu(\(1982\),)h(no.)f(3,)g(447-526)6075 33897 y([22])553 b(J.)240 b(v)-22 b(on)241 b(Neumann)i(and)e(E.P)-123 b(.)241 b(W)-44 b(igner)g(,)23679 33658 y Fg(\250)23398 33897 y(Uber)241 b(merkw)28953 33904 y(\250)28863 33897 y(ur)-41 b(dig)-11 b(e)242 b(diskr)-41 b(ete)241 b(Eig)-11 b(enwerte)p Fu(,)249 b(Z.Ph)-6 b(ys.)241 b Fc(30)8472 35225 y Fu(\(1929\),)278 b(465-467.)7431 37716 y(D)56 b Fb(E)g(P)-25 b(A)56 b(R)q(T)g(M)g(E)g(N)g(T)453 b(O)56 b(F)461 b(M)56 b(A)-43 b(T)56 b(H)g(E)g(M)g(A)-43 b(T)56 b(I)g(C)e(S)i Fu(,)484 b(U)12 b(A)56 b(B)g(,)461 b(1)56 b(3)g(0)g(0)462 b(U)56 b Fb(N)g(I)g(V)g(E)g(R)e(S)i(I)g(T)g(Y)453 b Fu(B)56 b Fb(O)g(U)g(L)g(E)g(V)-64 b(A)56 b(R)e(D)i Fu(,)487 b(B)56 b Fb(I)g(R)e(M)i Fu(-)6103 39044 y Fb(I)g(N)g(G)g(H)g (A)g(M)g Fu(,)326 b(A)56 b(L)332 b(3)56 b(5)g(2)g(9)g(4)7403 40372 y Fg(E-mail)277 b(addr)-41 b(ess)p Fu(:)344 b Fa (oleg@math.uab.edu)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0409031604497--