Content-Type: multipart/mixed; boundary="-------------0702261226961" This is a multi-part message in MIME format. ---------------0702261226961 Content-Type: text/plain; name="07-46.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="07-46.comments" 48 pages ---------------0702261226961 Content-Type: text/plain; name="07-46.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="07-46.keywords" quantum wave guides, quantum graphs, resonances, complex dilation ---------------0702261226961 Content-Type: application/postscript; name="resonances-exner-post.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="resonances-exner-post.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: resonances-exner-post.dvi %%Pages: 48 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMBX12 CMR10 CMCSC10 CMMI10 CMMI7 CMR7 CMR12 CMTI12 %%+ CMTI10 CMR9 CMR8 CMMI12 CMSY10 MSBM10 CMMI8 CMEX10 CMSY8 CMSS12 CMR6 %%+ CMMI6 CMSY7 MSBM7 CMR5 EUFM10 MSAM10 EUFM7 CMSY6 TeX-cmex8 CMBX10 %%+ CMTT10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips resonances-exner-post.dvi -o %+ resonances-exner-post.ps %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2007.02.21:1953 %%BeginProcSet: tex.pro 0 0 %! /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: texps.pro 0 0 %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % 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 (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 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 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 readonly def /FontBBox{-301 -250 1164 946}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: TeX-cmex8 %!PS-AdobeFont-1.0: TeX-cmex8 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex8) def /FullName (TeX\040cmex8\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex8 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 101 /e put readonly def /FontBBox {-29 -2957 1554 772} readonly def currentdict end currentfile eexec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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 78 /N put dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def currentdict end currentfile eexec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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 3 /asteriskmath put dup 15 /bullet put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: EUFM7 %!PS-AdobeFont-1.1: EUFM7 2.1 %%CreationDate: 1992 Nov 20 17:36:25 % Euler fonts were designed by Hermann Zapf. % 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 (EUFM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM7 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 100 /d put dup 104 /h put dup 113 /q put readonly def /FontBBox{0 -250 1193 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163B3DA4F9700DE5807F164169FBB 1458C43CD471029C362871D2FB69E0E5E617BC06F3B8621E3528E4B47E731AE1 0B406A3260424830B3C86A135457A566A1A716189B86883C171DA05829CE2E37 C020AAA2B4E1C2AB63462E7BB571434ED0811B99430919096D08C5F1C659B068 E87DB9366062D68FFD44AAD8A16740DCC214C32CDDDA354637C06EF93BC99352 DF04393C661FFFBF4BA20723ABD9B3E9CA9ABAFEED3C46C638D1A1C726DD7186 51137D23DD526D78AC5284266997E041592776D78B5DD8436571897EFD57A051 F9571E2957B23DF4ADB88D06EAAE9D73ABEC88C934E94205BFDF7115D9E667D6 CD2AFA8DCDA2D49EFC088135417D5D26117B20F923E8F0F5E92E0D8589BE5D93 7D4C3FEEF84B412F8177DE3E3C1711AA06686842AC5A3B3398B098FD06F255F0 2B237EF143FEE4CCC3540EA39B05197D2D9C149A2A71569B8608BA62D982CC7A 4FC2F4170B7A92531E4734A4D1D86FDA1B21AA3683CFC9EA65FB8A91990CEB69 AA62C0F22FDE470FA095FCBE4FB5BD40826BD6FECAA7F8B187412EFDC97E3DAB E2A836F16ED6FFA7F5B5B2714EC5C4A43E4E36D45D9F702CE875B0DFE6E08559 B60BF589C3941BFDAD1392B4D7BCE363E47162D6322FCA12758538A9DB5E4404 56BD008A9DB0E1A2D684F32BDE744F9457C839411F623C0AD633582CAC6FDD79 881E0A4F43DD393738E3CEB1DCAC0CCBAD384E5160BABAA5EF1F46632D05BB7C FC9396D17263BADE1AB2A229367D38F00D7B87124713CD716D9164E64FD1D52C FD6E2226BB350465D3614E241A269ED51FF3283446643AF9F18DCE671611DB2F 5D3EA77EE734D2BED623F973E6840B8DAD1E2C3C2666DD4DD1C1CECEDA9D8BEA 4AD62BA3D1CEC6121BD58420D6CB3257297E10FE60B96601A77A08CA7A6D5B44 A786B602FED3445516C4898C66B56BAFB73EA04B6096150A149C260FA6221ABE CD288026F6C3F3240D704D0F86B3D28AA84BEE35D8B60A10E04E8AA70C58DC8E 76065DCEB58744C7B08A6C767BE184BC37FDE8872682B2511AD5691B39D488CB CD3C8F9DC23EFF62A0CE06B4D9D4DE194641185C2CBCEAD7CCD4EBCC313374AD F8D0092E502DE528A60616E64B1A8DC02EA1FAB114DF5DE32D4A5AE919FACE9E B83C2F027F0766749E43B53517428D6D74B04B63068E64FED95C93525F69ABBB C14B3E3B7F4B2E0C9C0D342CA8B8DF111E80A06972FCE3B578C528B815D2318C 121C002DA8421E69BB6281B7013CD4B4A639339C796526ABD9A0EA803F4B5156 597612B38D81184223A350C9DF997C2D0B3FD5AD58246B0E3F33508BEF3C4B16 CCC9D5B622E36D289DFB96A46F2C4C15038D7C8D16CD96321E11CE69300966D5 1793296E69D25BA317E40B1B66D4C0A1F8C134F2C4FBA3C16E20F7AF054B7BB0 FD46213EE8B9F1184751FC3401B5C058DCDFE14B9F20CC53DB26C8A33D410432 832DFBF332E877B272D608CA7D3DA3F5AF0C65EDB8ECF8E0E96944171C8343D9 A310123F21DDC6E313A46C8621514747C4C46E85C8DC583F07087D92A9391610 1676845226C9D749B34A5C638305E271C108F222C0955680FF2F677ED0CB1338 246078ABFBA7DF317A03BFD2EFCA7240BB327A63E8FA5BD74CC5FDB6D71E5138 DDA27A8DD96A5B88D9750345121F67532D1F788919C60BA3E92286AA42AD0206 7FF8E5967D49994885F87B401005DC12A81C4D8B59919D797E734B8CB4C207F5 D088B2ADA81AA7CB1A13F9BED24334205E4888CCD506F8F9B508737B9D4DCA69 12F57DED65F9CF16F519EF68E54DD4EA385812330D65B98337551ED7CAB8C542 6114884B51DB0CBE7CBF46AA4E48FABD3B6A7AF503218CC26E3FA8C461797872 E96FE7AB3FC45472042D13A5AD27A10F7DE6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % 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 (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 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 3 /square put dup 22 /harpoonupright put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: EUFM10 %!PS-AdobeFont-1.1: EUFM10 2.1 %%CreationDate: 1992 Nov 20 17:36:20 % Euler fonts were designed by Hermann Zapf. % 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 (EUFM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM10 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 100 /d put dup 104 /h put dup 113 /q put readonly def /FontBBox{-26 -224 1055 741}readonly def currentdict end currentfile eexec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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 67 /C put dup 78 /N put dup 82 /R put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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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 8 /circleplus put dup 14 /openbullet put dup 15 /bullet put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 59 /emptyset put dup 65 /A put dup 68 /D put dup 71 /G put dup 72 /H put dup 79 /O put dup 87 /W put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 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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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % 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 (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 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 15 /bullet put dup 48 /prime put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec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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 18 /theta put dup 34 /epsilon put dup 35 /theta1 put dup 59 /comma put dup 101 /e put dup 107 /k put dup 110 /n put dup 118 /v put dup 120 /x put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec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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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 68 /D put dup 101 /e put dup 105 /i put dup 108 /l put dup 110 /n put dup 116 /t put dup 120 /x put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSS12 %!PS-AdobeFont-1.1: CMSS12 1.0 %%CreationDate: 1991 Aug 20 17:33:47 % 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 (CMSS12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS12 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 67 /C put dup 72 /H put dup 76 /L put readonly def /FontBBox{-62 -251 978 758}readonly def currentdict end currentfile eexec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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 3 /asteriskmath put dup 6 /plusminus put dup 15 /bullet put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 63 /perpendicular put dup 71 /G put dup 72 /H put dup 87 /W put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 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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 2 /bracketleftbig put dup 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 40 /braceleftBigg put dup 73 /contintegraldisplay put dup 76 /circleplustext put dup 77 /circleplusdisplay put dup 80 /summationtext put dup 82 /integraltext put dup 83 /uniontext put dup 85 /unionmultitext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 92 /intersectiondisplay put dup 93 /unionmultidisplay put dup 98 /hatwide put dup 99 /hatwider put dup 101 /tildewide put dup 102 /tildewider put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put dup 113 /radicalBig put dup 115 /radicalBigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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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 13 /gamma put dup 18 /theta put dup 19 /iota put dup 21 /lambda put dup 34 /epsilon put dup 35 /theta1 put dup 59 /comma put dup 61 /slash put dup 64 /partialdiff put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 76 /L put dup 78 /N put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 88 /X put dup 96 /lscript 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 109 /m put dup 110 /n put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 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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 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda 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 35 /theta1 put dup 39 /phi1 put dup 44 /arrowhookleft 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 72 /H put dup 74 /J put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 96 /lscript 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 109 /m put dup 110 /n 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 126 /vector put readonly def /FontBBox{-30 -250 1026 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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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 0 /Gamma put dup 8 /Phi 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 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 59 /semicolon put dup 68 /D put dup 78 /N put dup 94 /circumflex put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 105 /i 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 readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict 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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 (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 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 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 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 73 /I 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 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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%%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 11 /ff put dup 12 /fi put dup 13 /fl put dup 19 /acute put dup 39 /quoteright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 58 /colon 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 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 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 127 /dieresis put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec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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 (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 13 /fl put dup 14 /ffi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L 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 85 /U put dup 87 /W 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 readonly def /FontBBox{-36 -251 1103 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % 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 (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 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 19 /acute put dup 20 /caron 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 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 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I 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 122 /z put dup 127 /dieresis put readonly def /FontBBox{14 -250 1077 750}readonly def currentdict end currentfile eexec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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 2 /Theta put dup 4 /Xi put dup 6 /Sigma put dup 8 /Phi put dup 9 /Psi put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 20 /caron put dup 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright 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 47 /slash 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 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent 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 124 /emdash put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec 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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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 48 /zero put dup 49 /one put dup 50 /two put dup 105 /i put dup 110 /n put dup 116 /t put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % 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 (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 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 18 /theta put dup 34 /epsilon put dup 35 /theta1 put dup 59 /comma put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % 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 (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 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 18 /theta put dup 25 /pi put dup 35 /theta1 put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 64 /partialdiff put dup 67 /C put dup 72 /H put dup 74 /J put dup 83 /S put dup 88 /X put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec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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 11 /ff put dup 12 /fi put dup 14 /ffi put dup 16 /dotlessi put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash 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 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 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 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright 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 125 /hungarumlaut put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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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 12 /fi 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 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 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 85 /U put dup 86 /V put dup 87 /W 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 readonly def /FontBBox{-53 -251 1139 750}readonly def currentdict end currentfile eexec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Ft(e)523 1123 y FC(is)f(the)g(electric)i(p)s(oten)m (tial)e(on)f(the)i(quan)m(tum)g(graph.)53 b(F)-8 b(rom)35 b(these)i(assumptions,)122 1239 y(it)31 b(is)h(clear,)h(that)e(global)g (b)s(ounds)h(on)f(the)h(quan)m(tum)h(graph)e(p)s(oten)m(tials)i Fw(a)e FC(and)h Fw(q)j FC(are)d(enough)122 1355 y(to)g(ensure)i(that)f Fw(\013)819 1370 y Ft(")888 1355 y FC(and)f Fw(q)1120 1370 y Ft(")1190 1355 y FC(are)h(b)s(ounded.)222 1471 y(W)-8 b(e)40 b(de\014ne)h(the)g(magnetic)f(Hamiltonian)h Fw(H)1936 1486 y Ft(")2012 1471 y FC(acting)f(in)g(the)h(the)f(Hilb)s (ert)h(space)g Fv(H)3480 1486 y Ft(")3557 1471 y FC(:=)122 1587 y Fq(L)175 1612 y Fx(2)214 1587 y FC(\()p Fw(X)333 1602 y Ft(")370 1587 y Fw(;)17 b(g)461 1602 y Ft(")497 1587 y FC(\))32 b(\(with)h(the)g(norm)g Fv(k\001k)j FC(and)d(inner)g (pro)s(duct)g Fv(h\001)o Fw(;)17 b Fv(\001i)t FC(\))32 b(via)h(the)g(quadratic)g(form)1288 1747 y Fi(h)1340 1762 y Ft(")1376 1747 y FC(\()p Fw(u)p FC(\))27 b(:=)h Fv(k)p Fw(D)1797 1762 y Ft(";e)1886 1747 y Fw(u)o Fv(k)1991 1706 y Fx(2)2053 1747 y FC(+)22 b Fv(h)p Fw(u;)17 b(q)2333 1762 y Ft(")2369 1747 y Fw(u)o Fv(i)t Fw(;)965 b FC(\(4.4\))122 1906 y(where)32 b Fw(D)483 1921 y Ft(";e)600 1906 y FC(:=)c(\(d)19 b Fv(\000)g FC(i)p Fw(\013)1027 1921 y Ft(")1064 1906 y FC(\).)43 b(Denote)31 b(b)m(y)h Fi(d)1689 1921 y Ft(")1756 1906 y FC(the)f(quadratic)h(form)f(giv)m(en)h(b)m(y)g Fi(h)3025 1921 y Ft(")3093 1906 y FC(without)f(\014eld,)122 2022 y(i.e,)43 b Fw(\013)351 2037 y Ft(")429 2022 y FC(=)e(0)f(and)h Fw(q)876 2037 y Ft(")954 2022 y FC(=)g(0.)67 b(The)41 b(pro)s(of)f(of)g(the)h(follo)m(wing)g(lemma)g(is)g(straigh)m(tforw)m (ard)g(\(cf.)122 2139 y(Lemma)33 b(3.3\):)122 2314 y FI(Lemma)39 b(4.6.)j FA(Assume)35 b(that)h Fw(\013)1361 2329 y Ft(")1426 2314 y Fv(2)28 b Fq(L)1573 2339 y Fr(1)1648 2314 y FC(\()p Fw(T)1757 2278 y Fr(\003)1796 2314 y Fw(X)1877 2329 y Ft(")1913 2314 y FC(\))36 b FA(and)e Fw(q)2219 2329 y Ft(")2284 2314 y Fv(2)29 b Fq(L)2432 2339 y Fr(1)2506 2314 y FC(\()p Fw(X)2625 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FC(for)g(eac)m(h)j(v)m (ertex)g Fw(v)t FC(.)55 b(Clearly)-8 b(,)38 b(w)m(e)g(can)f(estimate)g (the)g(righ)m(t-)122 2244 y(hand)k(side)g(b)m(y)g Fv(k)p Fw(f)11 b Fv(k)879 2259 y Fx(1)p Ft(;\022)1013 2244 y FC(=)41 b Fv(k)p Fw(T)1251 2208 y Ft(\022)1290 2244 y Fw(f)10 b Fv(k)1398 2259 y Fx(1)1478 2244 y FC(and)40 b(w)m(e)i(obtain)e Fv(k)p Fw(J)9 b(f)33 b Fv(\000)23 b Fw(J)2495 2208 y Fx(1)2534 2244 y Fw(f)11 b Fv(k)45 b FC(=)c Fv(O)s FC(\()p Fw(")2971 2208 y Fx(1)p Ft(=)p Fx(2)3080 2244 y FC(\))p Fv(k)p Fw(f)11 b Fv(k)3277 2259 y Fx(1)p Ft(;\022)3411 2244 y FC(where)122 2366 y Fv(O)s FC(\()p Fw(")288 2330 y Fx(1)p Ft(=)p Fx(2)398 2366 y FC(\))32 b(dep)s(ends)i(no)m(w)f(also)g(on)g(Re)16 b Fw(\022)s FC(.)222 2482 y(Next)33 b(w)m(e)h(ha)m(v)m(e)764 2672 y Fv(k)p Fw(J)877 2631 y Fr(0)900 2672 y Fw(u)22 b Fv(\000)g Fw(J)1140 2631 y Fr(0)5 b Fx(1)1203 2672 y Fw(u)p Fv(k)1309 2631 y Fx(2)1376 2672 y FC(=)1479 2577 y Fs(X)1484 2789 y Ft(e)p Fr(2)p Ft(E)1647 2577 y Fs(X)1640 2790 y Ft(v)r Fr(2)p 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FC(=)27 b Fv(O)s FC(\()p Fw(")p FC(\))p Fw(d)1825 3828 y Fx(0)1880 3718 y Fs(X)1882 3930 y Ft(v)r Fr(2)p Ft(V)2041 3813 y Fv(k)p FC(d)p Fw(u)o Fv(k)2250 3772 y Fx(2)2250 3838 y Ft(";v)2371 3813 y FC(=)h Fv(O)s FC(\()p Fw(")p FC(\))p Fv(k)p Fw(u)p Fv(k)2835 3772 y Fx(2)2835 3849 y(1)p Ft(;)p 2890 3794 35 3 v(\022)122 4095 y FC(for)22 b Fw(u)27 b Fv(2)464 4070 y Fs(e)438 4095 y Fv(H)523 4059 y Fx(1)p Ft(;)p 578 4004 V(\022)639 4095 y FC(so)c(that)f Fv(k)p Fw(J)1063 4059 y Fr(0)1087 4095 y Fw(u)f Fv(\000)i Fw(J)1327 4059 y Fr(0)t Fx(1)1390 4095 y Fw(u)o Fv(k)32 b FC(=)27 b Fv(O)s FC(\()p Fw(")1796 4059 y Fx(1)p Ft(=)p Fx(2)1906 4095 y FC(\))p Fv(k)p Fw(u)p Fv(k)2100 4122 y Fx(1)p Ft(;)p 2155 4067 V(\022)2216 4095 y FC(where)c(again)f(the)h(error)f (term)h Fv(O)s FC(\()p Fw(")3512 4059 y Fx(1)p Ft(=)p Fx(2)3622 4095 y FC(\))122 4212 y(dep)s(ends)34 b(also)f(on)f(Re)17 b Fw(\022)s FC(.)222 4328 y(Assumption)34 b(\(B.2\))e(follo)m(ws)h (easily)h(from)f(\(4.12\))o(,)f(i.e.,)1162 4490 y 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FC(\))200 b FA(and)e Fv(k)p Fw(J)2255 1834 y Fr(0)2278 1875 y Fw( )2345 1834 y Ft(\022)2341 1899 y(")2407 1875 y Fv(\000)22 b Fw( )2573 1834 y Ft(\022)2569 1899 y Fx(0)2612 1875 y Fv(k)32 b FC(=)27 b Fv(O)s FC(\()p Fw(")2963 1834 y Fx(1)p Ft(=)p Fx(2)3073 1875 y FC(\))p Fw(:)222 2076 y FC(As)c(a)g(b)m(y-pro)s(duct,)j(w)m(e)f(also)e(ha)m(v)m(e)i(sho)m(wn) f(that)f(the)h(sp)s(ectrum)h(of)e(a)g(magnetic)h(Hamiltonian)122 2192 y(on)g(a)g FA(non-c)-5 b(omp)g(act)32 b FC(manifold)24 b(con)m(v)m(erges)j(to)d(the)g(asso)s(ciated)h(non-compact)g(quan)m (tum)g(graph)122 2309 y(Hamiltonian)42 b(pro)m(vided)i(our)e(uniformit) m(y)i(assumptions)g(are)e(ful\014lled.)73 b(In)43 b(particular,)i(w)m (e)122 2425 y(could)j(appro)m(ximate)h(fractal)e(sp)s(ectra)h(suc)m(h)h (as)f(studied,)53 b(e.g.,)f(in)c([BGP07)o(])g(as)g(w)m(e)h(ha)m(v)m(e) 122 2541 y(men)m(tioned)34 b(in)f(the)g(in)m(tro)s(duction.)122 2742 y FI(Theorem)48 b(6.4.)e FA(Assume)k FC(\(H)1317 2757 y Fx(0)1356 2742 y FC(1\))p FA({)p 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y Fr(\000)p Ft(k)1282 5667 y FC(via)g Fw(f)39 b Fv(7!)27 b(h\001)p Fw(;)17 b(f)11 b Fv(i)t FC(.)40 b(F)-8 b(or)26 b(more)i(details)f(w)m(e)h(refer)f(e.g.)g(to)g([KPS82].)p eop end %%Page: 27 27 TeXDict begin 27 26 bop 747 66 a Fy(CONVER)n(GENCE)33 b(OF)g(RESONANCES)f(ON)g(QUANTUM)h(W)-9 b(A)g(VE)33 b(GUIDES)431 b(27)238 266 y FC(A.2.)49 b FI(Scale)36 b(of)g(Hilb)s(ert)g(spaces)h (asso)s(ciated)g(with)e(a)i(self-adjoin)m(t)g(family)h(of)e(op)s(er-) 238 382 y(ators.)49 b FC(Since)39 b(our)e(dilated)h(op)s(erators)g(are) f(no)h(longer)f(self-adjoin)m(t,)i(w)m(e)g(also)e(need)i(a)e(scale)238 498 y(of)44 b(Hilb)s(ert)h(spaces)g(asso)s(ciated)h(with)e(a)g (particular)h(class)g(of)f(non-self-adjoin)m(t)g(op)s(erators,)238 614 y(namely)i FA(se)-5 b(ctorial)55 b FC(op)s(erators.)82 b(Most)45 b(of)g(the)h(material)f(on)g(suc)m(h)i(op)s(erators)e(is)h (standard)238 731 y(and)f(can)g(b)s(e)g(found)g(e.g.)g(in)g([Ka66)o(].) 80 b(W)-8 b(e)46 b(also)f(in)m(tro)s(duce)g(a)g(scale)h(of)e(order)h(1) f(whic)m(h)j(is)238 847 y(not)40 b(asso)s(ciated)i(to)e(the)h(natural)f (quadratic)i(form,)g(but)f(easier)g(to)f(handle)i(in)f(the)f(presen)m (t)238 963 y(application.)338 1079 y(Let)f Fv(f)p Fw(H)658 1043 y Ft(\022)696 1079 y Fv(g)746 1094 y Ft(\022)824 1079 y FC(with)g Fw(\022)i Fv(2)e Fw(S)44 b FC(=)38 b Fv(f)17 b Fw(w)40 b Fv(2)f Fu(C)17 b Fv(j)g(j)p FC(Im)e Fw(w)s Fv(j)38 b Fw(<)g(b)17 b Fv(g)38 b FC(b)s(e)h(a)g(family)g(of)f (closed)i(op)s(erators)238 1196 y(acting)33 b(in)g(the)g(Hilb)s(ert)g (space)g Fv(H)q FC(.)238 1374 y FI(De\014nition)38 b(A.1.)k FC(W)-8 b(e)33 b(sa)m(y)g(that)g(the)g(family)g Fv(f)p Fw(H)2159 1338 y Ft(\022)2197 1374 y Fv(g)2247 1389 y Ft(\022)2318 1374 y FC(is)g FA(self-adjoint)2897 1335 y Fx(6)2964 1374 y FC(if)g(\()p Fw(H)3181 1338 y Ft(\022)3219 1374 y FC(\))3257 1338 y Fr(\003)3324 1374 y FC(=)28 b Fw(H)p 3517 1283 40 3 v 3517 1338 a Ft(\022)3555 1374 y FC(.)338 1490 y(The)g(family)g Fv(f)p Fw(H)965 1454 y Ft(\022)1003 1490 y Fv(g)f FC(is)h(called)g 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y FC(\).)338 2241 y(F)-8 b(rom)32 b(no)m(w)h(on)f(w)m(e)i(assume)g(that)e Fv(f)p Fw(H)1763 2205 y Ft(\022)1801 2241 y Fv(g)g FC(is)h(a)f (self-adjoin)m(t,)h(uniformly)g Fw(#)p FC(-sectorial)h(family)238 2357 y(of)e(op)s(erators.)44 b(W)-8 b(e)32 b(start)h(de\014ning)h(the)f (scales)h(of)e(order)g(2,)h(0)f(and)h Fv(\000)p FC(2:)338 2473 y(Let)f Fv(H)597 2437 y Fx(0)665 2473 y FC(:=)27 b Fv(H)q FC(,)33 b Fv(k\001k)1068 2488 y Fx(0)1134 2473 y FC(:=)28 b Fv(k\001k)36 b FC(and)1082 2634 y Fv(H)1167 2593 y Fx(2)p Ft(;\022)1289 2634 y FC(:=)28 b(dom)16 b Fw(H)1709 2593 y Ft(\022)1748 2634 y Fw(;)212 b Fv(k)p Fw(f)11 b Fv(k)2146 2649 y Fx(2)p Ft(;\022)2267 2634 y FC(:=)27 b Fv(k)p FC(\()p Fw(H)2574 2593 y Ft(\022)2635 2634 y FC(+)22 b(1\))p Fw(f)10 b Fv(k)623 b FC(\(A.2\))238 2794 y(b)s(e)31 b(the)f(spaces)i(of)e(order)g(0)g(and)h(2.)42 b(Since)32 b Fw(H)1919 2757 y Ft(\022)1987 2794 y FC(is)f(closed)h(and) e Fv(\000)p FC(1)40 b Fw(=)-61 b Fv(2)28 b Fw(\033)t FC(\()p Fw(H)2990 2757 y Ft(\022)3029 2794 y FC(\),)j Fv(H)3210 2757 y Fx(2)p Ft(;\022)3334 2794 y FC(with)g(norm)238 2910 y Fv(k\001k)366 2925 y Fx(2)p Ft(;\022)492 2910 y FC(is)i(also)g(a)f(Hilb)s(ert)h(space.)44 b(The)34 b(dual)f(space)g(is)h(de\014ned)g(b)m(y)1664 3089 y Fv(H)1749 3048 y Fr(\000)p Fx(2)p Ft(;\022)1925 3089 y FC(:=)28 b(\()p Fv(H)2179 3048 y Fx(2)p Ft(;)p 2234 2993 35 3 v(\022)2273 3089 y FC(\))2311 3048 y Fr(\003)3551 3089 y FC(\(A.3\))238 3246 y(similarly)42 b(as)f(in)g(\(A.1\))o(.)68 b(Note)41 b(the)g(complex)h(conjugation)e(of)g Fw(\022)k FC(in)d(order)g(to)f(comp)s(ensate)238 3362 y(the)33 b(an)m(ti-linearit)m(y)g(in)g(the)f(de\014nition)i(of)d(the)i(dual.)44 b(In)32 b(the)h(next)g(t)m(w)m(o)g(lemmas,)h(w)m(e)f(w)m(an)m(t)h(to) 238 3478 y(assure)g(that)e Fw(H)832 3442 y Ft(\022)903 3478 y FC(and)h(its)g(resolv)m(en)m(t)i(extend)f(to)e(maps)h(on)g(the)g (scale)g(of)f(order)h Fv(\000)p FC(2)p Fw(;)17 b FC(0)p Fw(;)g FC(2:)238 3648 y FI(Lemma)46 b(A.2.)e FA(The)39 b(emb)-5 b(e)g(dding)39 b Fw(\023)11 b FC(:)36 b Fv(H)i(\000)-16 b(!)37 b(H)2080 3612 y Fr(\000)p Fx(2)p Ft(;\022)2229 3648 y FA(,)k Fw(g)g Fv(7!)36 b(h\001)p Fw(;)17 b(g)t Fv(i)43 b FA(is)d(c)-5 b(ontinuous.)60 b(F)-7 b(urther-)238 3764 y(mor)i(e,)47 b Fv(k)p FC(\()p Fw(H)703 3728 y Ft(\022)763 3764 y FC(+)22 b(1\))948 3728 y Fr(\000)p Fx(1)1042 3764 y Fw(g)s Fv(k)50 b FC(=)c Fv(k)p Fw(\023g)s Fv(k)1498 3779 y Fr(\000)p Fx(2)p Ft(;\022)1691 3764 y FA(for)f Fw(g)k Fv(2)d(H)q FA(,)h(i.e.,)g Fv(H)2524 3728 y Fr(\000)p Fx(2)p Ft(;\022)2717 3764 y FA(c)-5 b(an)44 b(b)-5 b(e)45 b(c)-5 b(onsider)g(e)g(d)43 b(as)h(the)238 3883 y(c)-5 b(ompletion)34 b(of)g Fv(H)i FA(in)f(the)g(norm)f Fv(k)p Fw(g)t Fv(k)1656 3898 y Fr(\000)p Fx(2)p Ft(;\022)1831 3883 y FC(:=)28 b Fv(k)p FC(\()p Fw(H)2139 3846 y Ft(\022)2200 3883 y FC(+)22 b(1\))2385 3846 y Fr(\000)p Fx(1)2479 3883 y Fw(g)s Fv(k)t FA(.)238 4052 y(Pr)-5 b(o)g(of.)41 b FC(W)-8 b(e)33 b(ha)m(v)m(e)475 4270 y Fv(k)p Fw(\023g)t Fv(k)660 4285 y Fx(2)p Ft(;)p Fr(\000)p Ft(\022)836 4270 y FC(=)70 b(sup)939 4372 y Ft(f)7 b Fr(2H)1087 4353 y Fp(2)p Fo(;)p 1136 4311 32 3 v(\022)1199 4203 y Fv(jh)p Fw(f)e(;)17 b(g)t Fv(i)t(j)p 1199 4247 285 4 v 1215 4339 a(k)p Fw(f)11 b Fv(k)1374 4365 y Fx(2)p Ft(;)p 1429 4310 35 3 v(\022)1521 4270 y FC(=)28 b(sup)1624 4352 y Ft(h)p Fr(2H)1799 4203 y Fv(jh)p Fw(h;)17 b FC(\()p Fw(H)2093 4167 y Ft(\022)2153 4203 y FC(+)22 b(1\))2338 4167 y Fr(\000)p Fx(1)2432 4203 y Fw(g)s Fv(i)t(j)p 1799 4247 754 4 v 2096 4339 a(k)p Fw(h)p Fv(k)2590 4270 y FC(=)28 b Fv(k)p FC(\()p Fw(H)2871 4229 y Ft(\022)2931 4270 y FC(+)22 b(1\))3116 4229 y Fr(\000)p Fx(1)3210 4270 y Fw(g)t Fv(k)240 b FC(\(A.4\))238 4541 y(where)34 b Fw(h)28 b FC(=)f(\()p Fw(H)p 834 4450 40 3 v 834 4505 a Ft(\022)895 4541 y FC(+)22 b(1\))p Fw(f)43 b FC(and)33 b(the)g(claims)g(follo)m(w.) 1596 b Fh(\003)238 4710 y FI(Lemma)39 b(A.3.)j FA(The)34 b(maps)760 4867 y FC(\()p Fw(H)887 4826 y Ft(\022)947 4867 y FC(+)22 b(1\))11 b(:)34 b Fv(H)1289 4826 y Fx(2)p Ft(;\022)1410 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Ft(\022)2474 777 y Fx(0)2547 752 y FC(=)h Fv(k)p FC(\()p Fw(H)2828 716 y Ft(\022)2888 752 y FC(+)22 b(1\))3073 716 y Fr(\000)p Fx(1)3167 752 y Fv(k)31 b FA(in)c(gener)-5 b(al)122 869 y(dep)g(ends)34 b(on)g Fw(\022)s FA(.)122 1054 y(Pr)-5 b(o)g(of.)41 b FC(The)f(\014rst)f(t)m(w)m(o)h(assertions)h (are)d(almost)i(ob)m(vious.)64 b(The)40 b(last)f(one)g(follo)m(ws)h (from)f(the)122 1170 y(fact)32 b(that)h(since)h Fv(\000)p FC(1)39 b Fw(=)-60 b Fv(2)28 b Fw(\033)t FC(\()p Fw(A)p FC(\),)33 b(w)m(e)g(ha)m(v)m(e)h Fv(k)p Fw(f)11 b Fv(k)32 b(\024)c Fw(C)2022 1134 y Ft(\022)2015 1195 y Fx(0)2061 1170 y Fv(k)p FC(\()p Fw(H)2238 1134 y Ft(\022)2298 1170 y FC(+)22 b(1\))p Fw(f)11 b Fv(k)t FC(,)32 b(and)h(therefore)371 1350 y Fv(k)p Fw(H)510 1309 y Ft(\022)548 1350 y Fw(f)11 b Fv(k)32 b(\024)c(k)p FC(\()p Fw(H)971 1309 y Ft(\022)1031 1350 y FC(+)22 b(1\))p Fw(f)11 b Fv(k)26 b FC(+)c Fv(k)p Fw(f)11 b Fv(k)31 b(\024)d FC(\(1)22 b(+)g Fw(C)2028 1309 y Ft(\022)2021 1375 y Fx(0)2067 1350 y FC(\))p Fv(k)p FC(\()p Fw(H)2282 1309 y Ft(\022)2342 1350 y FC(+)g(1\))p Fw(f)11 b Fv(k)31 b FC(=)d(\(1)22 b(+)g Fw(C)3055 1309 y Ft(\022)3048 1375 y Fx(0)3094 1350 y FC(\))p Fv(k)p Fw(f)11 b Fv(k)3291 1365 y Fx(2)p Ft(;\022)3384 1350 y Fw(:)122 1526 y FC(Similarly)205 1745 y Fv(jh)p Fw(H)p 361 1649 V 361 1704 a Ft(\022)399 1745 y Fw(f)g(;)17 b(g)t Fv(i)t(j)26 b(\024)i(jh)p FC(\()p Fw(H)p 949 1649 V 949 1704 a Ft(\022)1009 1745 y FC(+)22 b(1\))p Fw(f)10 b(;)17 b(g)t Fv(i)t(j)k FC(+)h Fv(jh)p Fw(f)5 b(;)17 b(g)t Fv(i)t(j)1807 1909 y(\024)28 b FC(\()p Fv(k)p Fw(f)11 b Fv(k)2109 1935 y Fx(2)p Ft(;)p 2164 1880 35 3 v(\022)2225 1909 y FC(+)22 b Fv(k)p Fw(f)11 b Fv(k)t FC(\))p Fv(k)p Fw(g)t Fv(k)30 b(\024)e FC(\(1)22 b(+)g Fw(C)3094 1867 y Ft(\022)3087 1933 y Fx(0)3133 1909 y FC(\))p Fv(k)p Fw(f)11 b Fv(k)3330 1935 y Fx(2)p Ft(;)p 3385 1880 V(\022)3423 1909 y Fv(k)p Fw(g)t Fv(k)122 2099 y FC(and)33 b(therefore)g Fv(k)p Fw(H)860 2062 y Ft(\022)898 2099 y Fw(g)s Fv(k)998 2114 y Fr(\000)p Fx(2)p Ft(;\022)1175 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2816 y FC(and)g(the)g(maps)1443 2992 y Fw(H)1532 2951 y Ft(\022)1581 2992 y FC(:)h Fv(H)1727 2951 y Ft(k)r(;\022)1852 2992 y Fv(\000)-17 b(!)28 b(H)2125 2951 y Ft(k)r Fr(\000)p Fx(2)p Ft(;\022)2312 2992 y Fw(;)1047 b FC(\(A.9a\))1287 3156 y(\()p Fw(H)1414 3114 y Ft(\022)1474 3156 y FC(+)22 b(1\))1659 3114 y Fr(\000)p Fx(1)1764 3156 y FC(:)34 b Fv(H)1910 3114 y Ft(k)r Fr(\000)p Fx(2)p Ft(;\022)2125 3156 y Fv(\000)-16 b(!)27 b(H)2398 3114 y Ft(k)r(;\022)3381 3156 y FC(\(A.9b\))122 3332 y(are)32 b(con)m(tin)m(uous.)222 3448 y(Since)i(in)f(our)h(con)m(text,)g(the)g (domain)g(dom)16 b Fw(H)1946 3412 y Ft(\022)2018 3448 y FC(will)34 b(dep)s(end)h(on)e(the)h FA(c)-5 b(omplex)43 b FC(parameter)122 3564 y Fw(\022)s FC(,)27 b(the)e(natural)g (quadratic)h(form)e(asso)s(ciated)i(to)f Fw(H)2027 3528 y Ft(\022)2090 3564 y FC(is)h(not)f(w)m(ell-adopted)h(to)f(our)g (application)122 3680 y(\(esp)s(ecially)34 b(its)e(natural)g(norm\).)43 b(W)-8 b(e)33 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Fv(k)p Fw(f)11 b Fv(k)2947 4814 y Fx(2)p Ft(;\022)3068 4799 y FC(=:)28 b Fw(C)3276 4758 y Ft(\022)3269 4824 y Fx(3)3315 4799 y Fw(\016)t Fv(k)p Fw(f)11 b Fv(k)3521 4814 y Fx(2)p Ft(;\022)238 4956 y FC(using)35 b(\(B.3\),)d(\(B.7\))g(and)h(De\014nition)g(A.4)g(\(iii\).) 43 b(Similarly)-8 b(,)321 5059 y Fs(\014)321 5119 y(\014)354 5144 y Fv(k)p Fw(J)9 b(f)i Fv(k)576 5103 y Fx(2)637 5144 y Fv(\000)23 b(k)p Fw(f)11 b Fv(k)896 5103 y Fx(2)935 5059 y Fs(\014)935 5119 y(\014)996 5144 y FC(=)1099 5059 y Fs(\014)1099 5119 y(\014)1132 5144 y Fv(h)p FC(\()p Fw(J)1272 5103 y Fr(\003)1312 5144 y Fw(J)31 b Fv(\000)23 b Fd(1)p FC(\))p Fw(f)11 b(;)17 b(f)11 b Fv(i)1798 5059 y Fs(\014)1798 5119 y(\014)623 5308 y Fv(\024)728 5223 y Fs(\014)728 5283 y(\014)761 5308 y Fv(h)p Fw(T)871 5266 y Fr(\000)p Ft(\022)964 5308 y FC(\()p Fw(J)1065 5266 y Fr(\003)1127 5308 y Fv(\000)23 b Fw(J)1290 5266 y Fr(0)1313 5308 y FC(\))p Fw(J)9 b(T)1485 5266 y Ft(\022)1524 5308 y Fw(f)i(;)17 b(T)1698 5266 y Fr(\000)p 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Ft(;\022)3147 5471 y FC(=:)28 b Fw(C)3355 5430 y Ft(\022)3348 5496 y Fx(4)3394 5471 y Fw(\016)t Fv(k)p Fw(f)11 b Fv(k)3600 5430 y Fx(2)3600 5496 y(2)p Ft(;\022)p 238 5568 499 4 v 338 5635 a Fx(8)373 5667 y FH(The)28 b(op)r(erators)d FF(J)965 5637 y FD(1)1030 5667 y FH(and)j FF(J)1246 5637 y Fn(0)t FD(1)1334 5667 y FH(need)g(not)f(to)h(b)r(e)g(b)r(ounded.)p eop end %%Page: 32 32 TeXDict begin 32 31 bop 122 66 a Fy(32)1078 b(P)-6 b(A)d(VEL)25 b(EXNER)g(AND)f(OLAF)h(POST)122 266 y FC(using)36 b(again)e (assumptions)j(in)f(De\014nition)f(A.4,)h(De\014nition)f(B.2)g(and)h (De\014nition)f(B.3.)51 b(The)122 390 y(estimates)34 b(on)713 365 y Fs(e)687 390 y Fv(H)f FC(follo)m(w)g(similarly)-8 b(.)2113 b Fh(\003)222 559 y FC(W)-8 b(e)32 b(can)h(no)m(w)h(state)f (the)g(con)m(v)m(ergence)i(of)d(the)h(resolv)m(en)m(ts:)122 742 y FI(Theorem)d(B.6.)37 b FA(Assume)29 b(that)g(the)g(families)f FC(\()p Fw(H)2008 757 y Ft(\022)2046 742 y FC(\))h FA(and)g FC(\()2357 717 y Fs(e)2335 742 y Fw(H)2416 757 y 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Fw(S)1724 5252 y Fx(ext)1823 5237 y Fw(u)28 b FC(=)f Fw(S)2070 5252 y Fx(ext)2170 5237 y Fw(u)17 b Fv(g)27 b FC(=)g(k)m(er)q(\()p Fv(\000)p Fw(S)2728 5252 y Fx(in)n(t)2839 5237 y FC(+)22 b Fw(S)2997 5252 y Fx(ext)3098 5237 y FC(\))320 b(\(C.12a\))238 5433 y(with)33 b(form)g(giv)m(en)g(b)m(y)1485 5628 y Fi(h)p FC(\()p Fw(u)p FC(\))27 b(:=)h Fi(h)1879 5643 y Fx(in)n(t)1967 5628 y FC(\()p Fw(u)p FC(\))22 b(+)g Fi(h)2271 5643 y Fx(ext)2371 5628 y FC(\()p Fw(u)p FC(\))p Fw(;)921 b FC(\(C.12b\))p eop end %%Page: 38 38 TeXDict begin 38 37 bop 122 66 a Fy(38)1078 b(P)-6 b(A)d(VEL)25 b(EXNER)g(AND)f(OLAF)h(POST)122 266 y FC(where)1090 382 y(\()p Fv(\000)p Fw(S)1265 397 y Fx(in)n(t)1376 382 y FC(+)d Fw(S)1534 397 y Fx(ext)1634 382 y FC(\))p Fw(u)27 b FC(:=)h Fv(\000)p Fw(S)2023 397 y Fx(in)n(t)2112 382 y Fw(u)2168 397 y Fx(in)n(t)2278 382 y FC(+)22 b Fw(S)2436 397 y Fx(ext)2536 382 y Fw(u)2592 397 y Fx(ext)122 518 y FC(for)34 b Fw(u)c FC(=)g Fw(u)521 533 y Fx(in)n(t)632 518 y Fv(\010)24 b Fw(u)789 533 y Fx(ext)889 518 y FC(.)49 b(W)-8 b(e)34 b(will)h(often)g(omit)f(the)h(subscripts)h Fw(u)30 b FC(=)h Fw(u)2675 533 y Fx(in)n(t)2797 518 y FC(etc.)k(if)f(they)h(are)f(clear)122 635 y(from)e(the)h(con)m(text.) 222 751 y(Similarly)-8 b(,)31 b(w)m(e)f(de\014ne)h(the)f FA(dilate)-5 b(d)39 b FC(quadratic)30 b(form)f Fi(h)2265 715 y Ft(\022)2304 751 y FC(,)h(for)f(the)h(momen)m(t)h(for)d FA(r)-5 b(e)g(al)40 b Fw(\022)32 b FC(only)-8 b(,)122 867 y(on)32 b(the)h(space)392 1026 y Fv(H)477 985 y Fx(1)p Ft(;\022)599 1026 y FC(:=)27 b Fv(f)17 b Fw(u)27 b Fv(2)h(H)1058 985 y Fx(1)p Ft(;)p Fx(N)1187 1026 y Fv(j)17 b Fw(S)1292 1041 y Fx(ext)1391 1026 y Fw(u)27 b FC(=)h(e)1621 985 y Fr(\000)p Ft(\022)r(=)p Fx(2)1786 1026 y Fw(S)1846 1041 y Fx(ext)1946 1026 y Fw(u)17 b Fv(g)26 b FC(=)i(k)m(er)q(\()p Fv(\000)p Fw(S)2504 1041 y Fx(in)n(t)2615 1026 y FC(+)22 b(e)2756 985 y Fr(\000)p Ft(\022)r(=)p Fx(2)2921 1026 y Fw(S)2981 1041 y Fx(ext)3081 1026 y FC(\))270 b(\(C.13\))122 1183 y(and)33 b(w)m(e)g(set)1363 1340 y Fi(h)1415 1299 y Ft(\022)1454 1340 y FC(\()p Fw(u)p FC(\))27 b(=)g Fi(h)1768 1355 y Fx(in)n(t)1857 1340 y FC(\()p Fw(u)p FC(\))21 b(+)h Fi(h)2160 1299 y Ft(\022)2160 1365 y Fx(ext)2261 1340 y FC(\()p Fw(u)p FC(\))p Fw(;)920 b FC(\(C.14a\))1222 1504 y Fi(h)1274 1463 y Ft(\022)1274 1529 y Fx(ext)1374 1504 y FC(\()p Fw(u)p FC(\))28 b(=)f(e)1680 1463 y Fr(\000)p Fx(2)p Ft(\022)1810 1504 y Fv(k)p Fw(@)1911 1519 y Fx(ext)2011 1504 y Fw(u)p Fv(k)2117 1463 y Fx(2)2178 1504 y FC(+)22 b Fi(h)2328 1463 y Fr(?)2328 1529 y Fx(ext)2428 1504 y FC(\()p Fw(u)p FC(\))775 b(\(C.14b\))122 1674 y(\(cf.)33 b(\(C.2\)\).)43 b(Note)33 b(that)f(the)h(dilated)g(form)g Fi(h)1846 1638 y Ft(\022)1917 1674 y FC(agrees)g(with)h(the)f(free)g (form)f Fi(h)g FC(if)h Fw(\022)e FC(=)c(0.)222 1790 y(The)38 b(v)-5 b(arious)39 b(quadratic)f(form)g(domains)h(satisfy)g(the)f (follo)m(wing)h(inclusions,)i(also)d(called)122 1907 y FA(Dirichlet-Neumann)33 b(br)-5 b(acketing)p FC(,)32 b(namely)-8 b(,)796 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Fx(1)p Ft(;\022)2373 2569 y(\023)2398 2581 y Ff(\000)p Fp(1)p Fo(;\022)2371 2638 y Fv(\000)-16 b(!)27 b(H)2644 2597 y Fr(\000)p Fx(1)p Ft(;)p Fx(D)3389 2638 y FC(\(C.16\))122 2795 y(where)34 b Fw(\023)438 2810 y Fr(\000)p Fx(1)p Ft(;\022)615 2795 y FC(=)27 b(\()p Fw(\023)790 2822 y Fx(1)p Ft(;)p 845 2767 35 3 v(\022)885 2795 y FC(\))923 2759 y Fr(\003)962 2795 y FC(.)222 2918 y(The)33 b(follo)m(wing)g(estimate)h(follo)m(ws)f (immediately)h(from)f(\(C.2\):)122 3076 y FI(Lemma)39 b(C.6.)j FA(We)35 b(have)1570 3192 y Fv(k)p Fw(@)1671 3207 y Fr(\017)1711 3192 y Fw(u)p Fv(k)1817 3151 y Fx(2)1884 3192 y Fv(\024)28 b Fi(h)2041 3207 y Fr(\017)2080 3192 y FC(\()p Fw(u)p FC(\))1177 b(\(C.17\))122 3329 y FA(for)35 b(functions)g Fw(u)29 b Fv(2)g(H)967 3293 y Fx(1)966 3354 y Fr(\017)1042 3329 y FA(\(with)35 b(supp)-5 b(ort)36 b(close)e(to)i(the)f(b)-5 b(oundary)36 b(if)f Fv(\017)29 b FC(=)f(in)m(t)q FA(\).)46 b(In)35 b(p)-5 b(articular,)122 3445 y(the)35 b(op)-5 b(er)g(ator)633 3407 y Fx(9)703 3445 y Fw(@)754 3460 y Fr(\017)805 3445 y FC(:)33 b Fv(H)950 3409 y Fx(1)949 3470 y Fr(\017)1017 3445 y Fv(\000)-16 b(!)27 b(H)1289 3460 y Fr(\017)1364 3445 y FA(has)34 b(a)h(norm)f(b)-5 b(ounde)g(d)34 b(by)h FC(1)p FA(.)122 3603 y FI(Asso)s(ciated)43 b(op)s(erators)h(and)g(Sob)s(olev)g(spaces)g (of)f(second)h(order.)49 b FC(W)-8 b(e)37 b(denote)i(the)122 3719 y(Diric)m(hlet)e(op)s(erator)f(on)g Fw(X)1145 3734 y Fr(\017)1221 3719 y FC(corresp)s(onding)i(to)e(the)h(Diric)m(hlet)g (quadratic)g(form)g Fi(h)3280 3683 y Fx(D)3280 3744 y Fr(\017)3374 3719 y FC(b)m(y)g Fw(H)3602 3683 y Fx(D)3594 3744 y Fr(\017)122 3836 y FC(with)c(domain)g Fv(H)776 3800 y Fx(2)p Ft(;)p Fx(D)775 3860 y Fr(\017)889 3836 y FC(.)222 3952 y(If)c(w)m(e)h(are)f(on)g(the)h(exterior)g(part,)f(w)m (e)h(also)g(need)g(the)f(dilated)h(v)m(ersion,)i(namely)e(w)m(e)g (denote)122 4073 y(b)m(y)44 b Fw(H)357 4026 y Ft(\022)r(;)p Fx(D)349 4095 y(ext)513 4073 y FC(the)g(op)s(erator)f(asso)s(ciated)h (to)g(the)g(form)f Fi(h)2174 4026 y Ft(\022)r(;)p Fx(D)2174 4095 y(ext)2330 4073 y FC(whic)m(h)i(is)f(the)g(restriction)h(of)e Fi(h)3560 4037 y Ft(\022)3560 4098 y Fx(ext)122 4199 y FC(\(cf.)d(\(C.14b\)\))f(on)m(to)h Fv(H)1014 4163 y Fx(1)p Ft(;)p Fx(D)1127 4199 y FC(.)64 b(Note)40 b(that)f(the)h (domains)h(of)e Fw(H)2454 4163 y Fx(D)2446 4224 y(ext)2585 4199 y FC(and)h Fw(H)2871 4152 y Ft(\022)r(;)p Fx(D)2863 4222 y(ext)3023 4199 y FC(agree)f(and)h(that)122 4315 y(the)33 b(op)s(erators)g(agree)g(for)f Fw(\022)f FC(=)d(0.)44 b(The)34 b FA(de)-5 b(c)g(ouple)g(d)42 b FC(op)s(erator)32 b Fw(H)2548 4279 y Ft(\022)r(;)p Fx(D)2693 4315 y FC(is)i(then)f(the)g (direct)h(sum,)122 4436 y(namely)g Fw(H)550 4400 y Ft(\022)r(;)p Fx(D)689 4436 y FC(=)28 b Fw(H)882 4400 y Fx(D)874 4461 y(in)n(t)984 4436 y Fv(\010)23 b Fw(H)1173 4389 y Ft(\022)r(;)p Fx(D)1165 4459 y(ext)1285 4436 y FC(.)222 4553 y(Before)30 b(de\014ning)i(the)f FA(c)-5 b(ouple)g(d)40 b FC(dilated)31 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b Fw(H)2101 5345 y Ft(\022)r(;)p Fx(min)2304 5386 y FC(:=)28 b Fw(H)2524 5345 y Fx(min)2516 5410 y(in)n(t)2667 5386 y Fv(\010)23 b Fw(H)2856 5338 y Ft(\022)r(;)p Fx(min)2848 5408 y(ext)3032 5386 y Fw(:)330 b FC(\(C.19\))p 122 5469 499 4 v 222 5535 a Fx(9)257 5567 y FH(Strictly)38 b(sp)r(eaking,)h FF(@)986 5579 y FD(in)n(t)1108 5567 y FH(is)f(de\014ned)g(only)f(on)h (the)g(subset)g(of)g(functions)g(with)g(supp)r(ort)g(close)f(to)h(the) 122 5667 y(b)r(oundary)-7 b(.)p eop end %%Page: 39 39 TeXDict begin 39 38 bop 747 66 a Fy(CONVER)n(GENCE)33 b(OF)g(RESONANCES)f(ON)g(QUANTUM)h(W)-9 b(A)g(VE)33 b(GUIDES)431 b(39)238 266 y FC(The)34 b(corresp)s(onding)f(maximal)g(op)s(erators)g (are)f(de\014ned)i(b)m(y)949 432 y Fw(H)1038 391 y Ft(\022)r(;)p Fx(max)1030 457 y Fr(\017)1255 432 y FC(:=)28 b(\()p Fw(H)1513 391 y Ft(\022)r(;)p Fx(min)1505 457 y Fr(\017)1688 432 y FC(\))1726 391 y Fr(\003)1766 432 y Fw(;)211 b(H)2093 391 y Ft(\022)r(;)p Fx(max)2311 432 y FC(:=)27 b Fw(H)2530 391 y Fx(max)2522 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FC(is)d(b)s(ounded)238 1527 y(indep)s(enden)m(tly)j(of)e Fw(")f FC(b)m(y)h(the)g(sp)s(ectral)h (calculus)g(and)e(the)h(preceding)h(lemma.)497 b Fh(\003)338 1728 y FC(W)-8 b(e)33 b(\014nally)g(c)m(haracterize)h(the)f(domain)g (of)f Fw(H)2055 1692 y Ft(\022)2094 1728 y FC(.)238 1919 y FI(Lemma)g(C.13.)37 b FA(F)-7 b(or)39 b FC(complex)31 b Fw(\022)g Fv(2)d Fw(S)1716 1934 y Ft(#)1762 1919 y FA(,)j(the)e(domain)f(of)h Fw(H)2520 1883 y Ft(\022)2588 1919 y FA(is)g(given)f(by)i Fv(H)3142 1883 y Fx(2)p Ft(;\022)3265 1919 y FA(as)f(in)36 b FC(\(C.22\))238 2036 y FA(and)e Fw(H)516 1999 y Ft(\022)555 2036 y Fw(u)27 b FC(=)h Fw(H)831 1999 y Fx(max)966 2036 y Fw(u)34 b FA(wher)-5 b(e)34 b Fw(H)1420 1999 y Fx(max)1590 2036 y FA(is)h(de\014ne)-5 b(d)34 b(in)42 b FC(\(C.20\))p FA(.)238 2226 y(Pr)-5 b(o)g(of.)41 b FC(Let)33 b Fw(u)27 b FC(=)h Fw(R)973 2190 y Ft(\022)1012 2226 y Fw(v)j Fv(2)d FC(dom)17 b Fw(H)1474 2190 y Ft(\022)1545 2226 y FC(then)925 2345 y Fs(\012)973 2426 y FC(\()p Fw(H)p 1100 2330 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Fx(in)n(t)1846 5374 y FC(\()p Fw(f)5 b(;)17 b(g)t FC(\))k(+)h Fi(h)2241 5333 y Ft(\022)2241 5398 y Fx(ext)2341 5374 y FC(\()p Fw(f)5 b(;)17 b(g)t FC(\))122 5546 y(for)50 b Fw(f)70 b Fv(2)60 b(H)618 5509 y Fx(1)p Ft(;)p 673 5454 V(\022)763 5546 y FC(and)51 b Fw(g)62 b Fv(2)e(H)1291 5509 y Fx(2)p Ft(;\022)1385 5546 y FC(;)g(in)52 b(particular,)k(there)51 b(are)h(no)f(b)s(oundary)g(terms.)100 b(On)122 5662 y(the)42 b(in)m(ternal)h(part,)i(w)m(e)e(ha)m(v)m(e)h Fi(h)1360 5677 y Fx(in)n(t)1448 5662 y FC(\()p Fw(f)5 b(;)17 b(g)t FC(\))43 b Fv(\024)i FC(\()p Fi(h)1927 5677 y Fx(in)n(t)2015 5662 y FC(\()p Fw(f)11 b FC(\))17 b Fi(h)2219 5677 y Fx(in)n(t)2306 5662 y FC(\()p Fw(g)t FC(\)\))2471 5626 y Fx(1)p Ft(=)p Fx(2)2623 5662 y FC(and)42 b Fi(h)2874 5677 y Fx(in)n(t)2962 5662 y FC(\()p Fw(f)11 b FC(\))44 b Fv(\024)g(k)p Fw(f)11 b Fv(k)3421 5626 y Fx(2)3421 5688 y Fg(h)3457 5699 y Fp(in)n(t)3583 5662 y Fv(\031)p eop end %%Page: 45 45 TeXDict begin 45 44 bop 747 66 a Fy(CONVER)n(GENCE)33 b(OF)g(RESONANCES)f(ON)g(QUANTUM)h(W)-9 b(A)g(VE)33 b(GUIDES)431 b(45)238 266 y Fv(k)p Fw(f)11 b Fv(k)397 230 y Fx(2)397 290 y Fg(d)431 301 y Fp(in)n(t)555 266 y FC(=)41 b Fv(k)p Fw(f)770 281 y Fx(in)n(t)859 266 y Fv(k)909 230 y Fx(2)909 292 y(1)p Ft(;\022)1043 266 y FC(using)h(Lemmas)g(3.3)e(and)h(4.6.)68 b(On)41 b(the)g(external)h(part,)h(w)m(e)f(estimate)238 395 y Fv(j)p Fi(h)318 359 y Ft(\022)318 420 y Fx(ext)418 395 y FC(\()p Fw(f)5 b(;)17 b(g)t FC(\))p Fv(j)26 b(\024)j FC(2)17 b(cosh\(Re)f Fw(\022)s FC(\))p Fv(k)p Fw(f)1405 410 y Fx(ext)1506 395 y Fv(k)1556 422 y Fx(1)p Ft(;)p 1611 367 35 3 v(\022)1649 395 y Fv(k)p Fw(g)1746 410 y Fx(ext)1846 395 y Fv(k)1896 410 y Fx(1)p Ft(;\022)2022 395 y FC(and)33 b(the)g(claim)g(follo)m(ws.)745 b Fh(\003)338 568 y FC(Finally)-8 b(,)41 b(w)m(e)f(ha)m(v)m(e)g(to)f(c)m(hec)m(k)j (the)d(em)m(b)s(edding)i(assumption)f(De\014nition)g(A.4)f(\(iii\))g (or)g(the)238 684 y(equiv)-5 b(alen)m(t)32 b(resolv)m(en)m(t)g (estimate)f(\(A.14\).)42 b(W)-8 b(e)31 b(can)f(pro)m(v)m(e)h(ev)m(en)h (more,)e(namely)h(the)g(stronger)238 800 y(resolv)m(en)m(t)42 b(estimate)e(\(A.15\).)63 b(Again,)41 b(the)f(pro)s(ofs)f(di\013er)h (sligh)m(tly)g(in)g(the)g(quan)m(tum)g(graph)238 916 y(and)33 b(manifold)g(case.)238 1087 y FI(Lemma)i(C.15.)j FA(Ther)-5 b(e)31 b(exists)g(a)g(c)-5 b(onstant)31 b Fw(C)2007 1051 y Ft(\022)2000 1111 y Fx(2)2077 1087 y FA(dep)-5 b(ending)30 b(only)h(on)g FC(Re)17 b Fw(\022)s FA(,)32 b Fv(k)p Fw(a)p Fv(k)3264 1102 y Fr(1)3369 1087 y FA(and)f Fv(k)p Fw(q)t Fv(k)3702 1102 y Fr(1)238 1217 y FA(such)i(that)h(the)f(r)-5 b(esolvent)32 b Fw(R)1296 1181 y Ft(\022)1369 1217 y FA(extends)g(to)h(a)g(b)-5 b(ounde)g(d)33 b(map)2511 1192 y Fs(b)2493 1217 y Fw(R)2568 1181 y Ft(\022)2619 1217 y FC(:)g Fv(H)2764 1181 y Fr(\000)p Fx(1)p Ft(;\022)2940 1217 y Fv(\000)-16 b(!)28 b(H)3214 1181 y Fx(1)p Ft(;\022)3341 1217 y FA(with)33 b(norm)238 1333 y(b)-5 b(ounde)g(d)34 b(by)h Fw(C)813 1297 y Ft(\022)806 1358 y Fx(2)852 1333 y FA(.)45 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y Fv(k)p Fw(q)331 4199 y Ft(")368 4184 y Fv(k)418 4199 y Fr(1)492 4184 y FA(,)66 b(and)j FC(not)59 b FA(on)h Fw(")p FA(,)65 b(such)59 b(that)h(the)f(r)-5 b(esolvent)59 b Fw(R)2481 4148 y Ft(\022)2580 4184 y FA(extends)f(to)i(a)f(b)-5 b(ounde)g(d)59 b(map)256 4289 y Fs(b)238 4314 y Fw(R)313 4278 y Ft(\022)363 4314 y FC(:)34 b Fv(H)509 4278 y Fr(\000)p Fx(1)p Ft(;\022)685 4314 y Fv(\000)-16 b(!)27 b(H)958 4278 y Fx(1)p Ft(;\022)1087 4314 y FA(with)35 b(norm)f(b)-5 b(ounde)g(d)34 b(by)2076 4289 y Fs(e)2057 4314 y Fw(C)2134 4278 y Ft(\022)2127 4339 y Fx(2)2173 4314 y FA(.)45 b(In)34 b(p)-5 b(articular,)35 b(we)f(have)1634 4485 y Fv(k)p Fw(u)p Fv(k)1790 4444 y Fx(2)1790 4510 y(1)p Ft(;\022)1910 4485 y Fv(\024)2035 4460 y Fs(e)2016 4485 y Fw(C)2093 4444 y Ft(\022)2086 4510 y Fx(2)2132 4485 y Fv(k)p Fw(u)p Fv(k)2288 4444 y Fx(2)2288 4510 y(2)p Ft(;\022)3505 4485 y FC(\(C.45\))238 4654 y FA(for)h(al)5 b(l)34 b Fw(u)27 b Fv(2)i(H)796 4618 y Fx(2)p Ft(;\022)924 4654 y FA(on)35 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begin 46 45 bop 122 66 a Fy(46)1078 b(P)-6 b(A)d(VEL)25 b(EXNER)g(AND)f(OLAF)h(POST)122 266 y FC(map)34 b Fw(\023)374 281 y Fx(1)p Ft(;\022)502 266 y FC(dep)s(ends)h(on)e Fv(k)p Fw(\013)1128 281 y Ft(")1165 266 y Fv(k)1215 281 y Fr(1)1323 266 y FC(and)g Fv(k)p Fw(q)1606 281 y Ft(")1643 266 y Fv(k)1693 281 y Fr(1)1768 266 y FC(,)h(but)f(can)h(b)s(e)g(b)s (ounded)g FA(indep)-5 b(endently)41 b FC(on)34 b Fw(")f FC(b)m(y)122 382 y(our)f(assumptions.)2741 b Fh(\003)222 553 y FC(Summarizing)36 b(the)h(results)g(of)e(Lemmas)i(C.12)f(and)g (C.13)f(and)h(Lemmas)h(C.15)f(and)g(C.16)122 669 y(w)m(e)e(ha)m(v)m(e)f (sho)m(wn)h(the)f(follo)m(wing)g(theorem:)122 845 y FI(Theorem)f(C.17.) 37 b FA(The)29 b(family)h Fv(f)p Fw(H)1508 809 y Ft(\022)1546 845 y Fv(g)1596 860 y Ft(\022)r Fr(2)p Ft(S)1721 872 y Fo(#)1796 845 y FA(is)g(a)g(self-adjoint,)f(analytic)h(family)f(of)g (op)-5 b(er)g(ators)122 963 y(with)37 b(domain)e(given)h(by)46 b FC(\(C.22\))p FA(.)51 b(In)36 b(addition,)g Fv(fH)2109 927 y Fx(1)p 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1612 y FI(Ac)m(kno)m(wledgmen)m(ts.)49 b FC(The)28 b(researc)m(h)g(w)m(as)f(supp)s(orted)h(in)e(part)h(b)m(y)g (the)g(Czec)m(h)h(Academ)m(y)g(of)122 1728 y(Sciences)c(and)e(Ministry) h(of)e(Education,)k(Y)-8 b(outh)22 b(and)g(Sp)s(orts)g(within)g(the)h (pro)5 b(jects)22 b(A100480501)122 1844 y(and)43 b(LC06002,)h(and)e(b)m (y)i(the)f(ESF)f(pro)5 b(ject)44 b(\\Sp)s(ectral)e(Theory)i(and)f(P)m (artial)f(Di\013eren)m(tial)122 1961 y(Equations)26 b(\(SPECT\)".)h (The)f(second)g(author)f(w)m(as)h(partly)f(supp)s(orted)h(b)m(y)g(the)f (DF)m(G)f(through)122 2077 y(the)j(Gran)m(t)g(P)m(o)h(1034/1-1,)e(and)h (appreciates)i(the)e(hospitalit)m(y)i(extended)g(to)e(him)g(in)h(the)f (Isaac)122 2193 y(Newton)34 b(Institute)g(\(Cam)m(bridge\))g(during)f (the)h(programme)f(\\Analysis)h(on)f(Graphs)g(and)g(its)122 2309 y(Applications")g(where)h(this)g(w)m(ork)f(w)m(as)g(\014nished.) 1600 2518 y FB(References)122 2676 y FH([A)n(C71])192 b(J.)57 b(Aguilar)e(and)h(J.)g(M.)h(Com)n(b)r(es,)63 b Fz(A)56 b(class)h(of)g(analytic)g(p)l(erturb)l(ations)f(for)h(one-b)l (o)l(dy)564 2775 y(Schr\177)-42 b(odinger)32 b(Hamiltonians)p FH(,)c(Comm.)g(Math.)g(Ph)n(ys.)e Fb(22)i FH(\(1971\),)e(269{279.)122 2875 y([ASvK)362 2845 y FD(+)417 2875 y FH(01])40 b(C.)32 b(Albrec)n(h)n(t,)g(J.)f(H.)h(Smet,)g(K.)f(v)n(on)g(Klitzing,)h(D.)g(W) -7 b(eiss,)32 b(V.)g(Umansky)-7 b(,)32 b(and)f(H.)g(Sc)n(h)n(w)n (eizer,)564 2975 y Fz(Evidenc)l(e)38 b(of)g(Hofstadter's)g(fr)l(actal)f (ener)l(gy)g(sp)l(e)l(ctrum)f(in)h(the)g(quantize)l(d)f(Hal)t(l)i(c)l (onductanc)l(e)p FH(,)564 3074 y(Ph)n(ys.)27 b(Rev.)h(Lett.)g Fb(86)f FH(\(2001\),)f(147{150.)122 3174 y([Aub76])158 b(Th.)35 b(Aubin,)j Fz(Esp)l(ac)l(es)f(de)g(Sob)l(olev)g(sur)f(les)h (vari)n(\023)-40 b(et)n(\023)g(es)37 b(riemanniennes)p FH(,)g(Bull.)e(Sci.)g(Math.)g(\(2\))564 3273 y Fb(100)27 b FH(\(1976\),)g(no.)g(2,)g(149{173.)122 3373 y([BC71])193 b(E.)27 b(Balslev)e(and)i(J.)g(M.)f(Com)n(b)r(es,)h Fz(Sp)l(e)l(ctr)l (al)i(pr)l(op)l(erties)h(of)g(many-b)l(o)l(dy)f(Schr\177)-42 b(odinger)31 b(op)l(er)l(ators)564 3473 y(with)g(dilatation-analytic)h (inter)l(actions)p FH(,)c(Comm.)g(Math.)g(Ph)n(ys.)e Fb(22)h FH(\(1971\),)g(280{294.)122 3572 y([BCD89])130 b(Ph.)35 b(Briet,)i(J.-M.)e(Com)n(b)r(es,)h(and)f(P)-7 b(.)35 b(Duclos,)i Fz(Sp)l(e)l(ctr)l(al)g(stability)g(under)g (tunneling)p FH(,)f(Comm.)564 3672 y(Math.)28 b(Ph)n(ys.)f Fb(126)g FH(\(1989\),)f(no.)h(1,)h(133{156.)122 3772 y([BGP07])131 b(J.)40 b(Br)r(\177)-44 b(uning,)42 b(V.)e(Geyler,)i(and) d(K.)h(P)n(ankrashkin,)g Fz(Cantor)h(and)g(b)l(and)g(sp)l(e)l(ctr)l(a)g (for)h(p)l(erio)l(dic)564 3871 y(quantum)29 b(gr)l(aphs)i(with)f (magnetic)h(\014elds)p FH(,)d(Comm.)f(Math.)h(Ph)n(ys.)f Fb(269)g FH(\(2007\),)f(no.)h(1,)h(87{105.)122 3971 y([CDKS87])78 b(J.-M.)23 b(Com)n(b)r(es,)g(P)-7 b(.)22 b(Duclos,)i(M.)f(Klein,)g(and) g(R.)f(Seiler,)i Fz(The)i(shap)l(e)g(r)l(esonanc)l(e)p FH(,)e(Comm.)f(Math.)564 4070 y(Ph)n(ys.)k Fb(110)g FH(\(1987\),)f(no.) i(2,)f(215{236.)122 4170 y([C69])252 b(J.-M.)37 b(Com)n(b)r(es,)h Fz(R)l(elatively)h(c)l(omp)l(act)f(inter)l(actions)g(in)g(many)g(p)l (article)i(systems)p FH(,)e(Comm)n(un.)564 4270 y(Math.)28 b(Ph)n(ys.)f Fb(12)g FH(\(1969\),)f(283{295.)122 4369 y([CT73])192 b(J.-M.)19 b(Com)n(b)r(es)f(and)g(L.)h(Thomas,)g Fz(Asymptotic)j(b)l(ehaviour)h(of)g(eigenfunctions)f(for)g(multip)l (article)564 4469 y(Schr\177)-42 b(odinger)32 b(op)l(er)l(ators)p FH(,)d(Comm.)e(Math.)h(Ph)n(ys.)f Fb(34)g FH(\(1973\),)f(251{270.)122 4569 y([DEM01])116 b(P)-7 b(.)33 b(Duclos,)i(P)-7 b(.)33 b(Exner,)g(and)g(B.)g(Meller,)h Fz(Op)l(en)h(quantum)f(dots:)49 b(r)l(esonanc)l(es)35 b(fr)l(om)g(p)l(erturb)l(e)l(d)564 4668 y(symmetry)j(and)g(b)l(ound)f(states)g(in)g(str)l(ong)g(magnetic)h (\014elds)p FH(,)g(Rep.)e(Math.)g(Ph)n(ys.)f Fb(47)g FH(\(2001\),)564 4768 y(no.)28 b(2,)f(253{267.)122 4867 y([EL06])203 b(P)-7 b(.)23 b(Exner)e(and)i(J.)f(Lip)r(o)n(vsk)q(\023) -43 b(y,)23 b Fz(Equivalenc)l(e)j(of)h(r)l(esolvent)e(and)h(sc)l (attering)f(r)l(esonanc)l(es)g(on)g(quan-)564 4967 y(tum)k(gr)l(aphs)p FH(,)g(Preprin)n(t)e(\(math-ph/0610065\))d(\(2006\).)122 5067 y([EP05])198 b(P)-7 b(.)27 b(Exner)g(and)g(O.)g(P)n(ost,)f Fz(Conver)l(genc)l(e)k(of)g(sp)l(e)l(ctr)l(a)g(of)g(gr)l(aph-like)h (thin)f(manifolds)p FH(,)f(Journal)d(of)564 5166 y(Geometry)h(and)h(Ph) n(ysics)e Fb(54)h FH(\(2005\),)g(77{115.)122 5269 y([E)204 5248 y(\024)202 5269 y(S89])209 b(P)-7 b(.)25 b(Exner)e(and)h(P)-7 b(.)1160 5248 y(\024)1158 5269 y(Seba,)25 b Fz(Bound)i(states)f(in)h (curve)l(d)h(quantum)d(wave)l(guides)p FH(,)i(J.)d(Math.)h(Ph)n(ys.)f Fb(30)564 5368 y FH(\(1989\),)j(no.)g(11,)g(2574{2580.)122 5468 y([ETV01])133 b(P)-7 b(.)20 b(Exner,)h(M.)g(T)-7 b(ater,)21 b(and)f(D.)h(V)-7 b(an)n(\024)-39 b(ek,)20 b Fz(A)j(single-mo)l(de)h(quantum)e(tr)l(ansp)l(ort)h(in)g (serial-structur)l(e)564 5567 y(ge)l(ometric)31 b(sc)l(atter)l(ers)p FH(,)c(J.)h(Math.)g(Ph)n(ys.)e Fb(42)h FH(\(2001\),)g(4050{4078.)122 5667 y([E97])255 b(P)-7 b(.)20 b(Exner,)g Fz(Magnetor)l(esonanc)l(es)k (on)e(a)h(lasso)g(gr)l(aph)p FH(,)g(F)-7 b(ound.)20 b(Ph)n(ys.)f Fb(27)g FH(\(1997\),)h(no.)f(2,)i(171{190.)p eop end %%Page: 47 47 TeXDict begin 47 46 bop 747 66 a Fy(CONVER)n(GENCE)33 b(OF)g(RESONANCES)f(ON)g(QUANTUM)h(W)-9 b(A)g(VE)33 b(GUIDES)431 b(47)238 266 y FH([F96])259 b(M.)35 b(F)-7 b(reidlin,)36 b Fz(Markov)i(pr)l(o)l(c)l(esses)f(and)g(di\013er)l(ential)g(e)l (quations:)52 b(asymptotic)37 b(pr)l(oblems)p FH(,)h(Lec-)681 365 y(tures)27 b(in)h(Mathematics)f(ETH)g(Z)r(\177)-44 b(uric)n(h,)27 b(Birkh\177)-42 b(auser)26 b(V)-7 b(erlag,)27 b(Basel,)f(1996.)238 465 y([FW93])174 b(M.)35 b(I.)h(F)-7 b(reidlin)35 b(and)g(A.)h(D.)g(W)-7 b(en)n(tzell,)37 b Fz(Di\013usion)g(pr)l(o)l(c)l(esses)h(on)e(gr)l(aphs)i(and)g(the)f (aver)l(aging)681 565 y(principle)p FH(,)29 b(Ann.)g(Probab.)d Fb(21)h FH(\(1993\),)f(no.)i(4,)f(2215{2245.)238 664 y([GY83])186 b(S.)19 b(Gra\016)f(and)g(K.)h(Y)-7 b(a)5 b(jima,)20 b Fz(Exterior)i(c)l(omplex)g(sc)l(aling)h(and)f(the)g(A)n (C-Stark)f(e\013e)l(ct)g(in)h(a)g(Coulomb)681 764 y(\014eld)p FH(,)28 b(Comm.)f(Math.)h(Ph)n(ys.)f Fb(89)g FH(\(1983\),)f(no.)i(2,)f (277{301.)238 863 y([HeM87])138 b(B.)36 b(Hel\013er)h(and)f(A.)h (Martinez,)i Fz(Comp)l(ar)l(aison)h(entr)l(e)d(les)i(diverses)g (notions)f(de)h(r)n(\023)-40 b(esonanc)l(es)p FH(,)681 963 y(Helv.)27 b(Ph)n(ys.)g(Acta)h Fb(60)f FH(\(1987\),)f(no.)i(8,)f (992{1003.)238 1063 y([HP06])194 b(P)-7 b(.)43 b(Hislop)g(and)g(O.)g(P) n(ost,)j Fz(Exp)l(onential)e(lo)l(c)l(alization)i(for)f(r)l(adial)h(r)l (andom)f(quantum)e(tr)l(e)l(es)p FH(,)681 1162 y(Preprin)n(t)26 b(\(math-ph/0611022\))e(\(2006\).)238 1262 y([HS89])205 b(P)-7 b(.)37 b(D.)h(Hislop)f(and)g(I.)g(M.)h(Sigal,)h Fz(Semiclassic)l(al)i(the)l(ory)e(of)h(shap)l(e)g(r)l(esonanc)l(es)f (in)f(quantum)681 1362 y(me)l(chanics)p FH(,)29 b(Mem.)e(Amer.)h(Math.) g(So)r(c.)f Fb(78)h FH(\(1989\),)e(no.)h(399,)g(123.)238 1461 y([HS96])205 b(P)-7 b(.)36 b(D.)i(Hislop)e(and)h(I.)g(M.)g(Sigal,) i Fz(Intr)l(o)l(duction)f(to)g(sp)l(e)l(ctr)l(al)g(the)l(ory)p FH(,)i(Springer-V)-7 b(erlag,)37 b(New)681 1561 y(Y)-7 b(ork,)27 b(1996.)238 1660 y([Ka66])206 b(T.)27 b(Kato,)g Fz(Perturb)l(ation)j(the)l(ory)g(for)h(line)l(ar)f(op)l(er)l(ators)p FH(,)f(Springer-V)-7 b(erlag,)25 b(Berlin,)i(1966.)238 1760 y([KPS82])145 b(S.)36 b(G.)g(Kre)-9 b(\025)-32 b(\020n,)37 b(Y)-7 b(u.)1330 1739 y(\026)1335 1760 y(I.)37 b(P)n(etun)-9 b(\026)-32 b(\020n,)37 b(and)f(E.)f(M.)i(Sem)n(\177)-39 b(eno)n(v,)36 b Fz(Interp)l(olation)j(of)f(line)l(ar)g(op)l(er)l(ators) p FH(,)681 1860 y(T)-7 b(ranslations)29 b(of)i(Mathematical)g (Monographs,)f(v)n(ol.)h(54,)g(American)g(Mathematical)f(So)r(ciet)n(y) -7 b(,)681 1959 y(Pro)n(vidence,)25 b(R.I.,)j(1982,)e(T)-7 b(ranslated)27 b(from)g(the)h(Russian)f(b)n(y)g(J.)h(Sz)r(})-44 b(ucs.)238 2059 y([KoS99])160 b(V.)38 b(Kostrykin)e(and)i(R.)g(Sc)n (hrader,)h Fz(Kir)l(chho\013)9 b('s)41 b(rule)e(for)i(quantum)d(wir)l (es)p FH(,)j(J.)d(Ph)n(ys.)e(A)j Fb(32)681 2159 y FH(\(1999\),)26 b(no.)h(4,)h(595{630.)238 2258 y([KoS03])160 b(V)-7 b(adim)28 b(Kostrykin)e(and)i(Rob)r(ert)g(Sc)n(hrader,)e Fz(Quantum)j(wir)l(es)h (with)h(magnetic)f(\015uxes)p FH(,)d(Comm.)681 2358 y(Math.)g(Ph)n(ys.) g Fb(237)g FH(\(2003\),)f(no.)i(1-2,)e(161{179,)e(Dedicated)k(to)g (Rudolf)g(Haag.)238 2457 y([Ku04])202 b(P)-7 b(.)31 b(Kuc)n(hmen)n(t,)i Fz(Quantum)f(gr)l(aphs:)48 b(I.)34 b(Some)g(b)l(asic)h(structur)l(es)p FH(,)d(W)-7 b(a)n(v)n(es)30 b(Random)i(Media)g Fb(14)681 2557 y FH(\(2004\),)26 b(S107{S128.)238 2657 y([KuZ01])151 b(P)-7 b(.)32 b(Kuc)n(hmen)n(t)h(and)f(H.)i(Zeng,)f Fz(Conver)l(genc)l (e)j(of)f(sp)l(e)l(ctr)l(a)g(of)g(mesosc)l(opic)i(systems)d(c)l(ol)t (lapsing)681 2756 y(onto)29 b(a)i(gr)l(aph)p FH(,)e(J.)e(Math.)h(Anal.) f(Appl.)i Fb(258)e FH(\(2001\),)f(no.)h(2,)h(671{700.)238 2856 y([Moi98])172 b(Moisey)n(ev,)47 b Fz(Quantum)c(the)l(ory)j(of)g(r) l(esonanc)l(es:)69 b(c)l(alculating)46 b(ener)l(gies,)k(widths)c(and)f (cr)l(oss-)681 2956 y(se)l(ctions)30 b(by)g(c)l(omplex)g(sc)l(aling)p FH(,)f(Ph)n(ys.)d(Rep.)i Fb(302)f FH(\(1998\),)f(211{293.)238 3055 y([MV06])175 b(S.)27 b(Molc)n(hano)n(v)f(and)h(B.)g(V)-7 b(ain)n(b)r(erg,)26 b Fz(Sc)l(attering)k(solutions)f(in)h(a)g(network)f (of)h(thin)g(\014b)l(ers:)38 b(smal)t(l)681 3155 y(diameter)31 b(asymptotics)p FH(,)d(Preprin)n(t)f(\(math-ph/0609021\))d(\(2006\).) 238 3254 y([Ned97])168 b(L.)21 b(Nedelec,)i Fz(Sur)h(les)g(r)n(\023)-40 b(esonanc)l(es)25 b(de)g(l'op)n(\023)-40 b(er)l(ateur)25 b(de)g(Dirichlet)g(dans)g(un)e(tub)l(e)p FH(,)g(Comm.)e(P)n(artial)681 3354 y(Di\013eren)n(tial)27 b(Equations)g Fb(22)g FH(\(1997\),)f(no.)i (1-2,)e(143{163.)238 3454 y([P05])256 b(O.)31 b(P)n(ost,)g Fz(Br)l(anche)l(d)j(quantum)f(wave)h(guides)g(with)f(Dirichlet)i(b)l (oundary)f(c)l(onditions:)47 b(the)33 b(de-)681 3553 y(c)l(oupling)39 b(c)l(ase)p FH(,)h(Journal)c(of)h(Ph)n(ysics)e(A:)j 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y(strips.)c(I.)f(Basic)i(estimates)e(and)h(c)l (onver)l(genc)l(e)f(of)h(the)g(Laplacian)h(sp)l(e)l(ctrum)p FH(,)d(Arc)n(h.)g(Ration.)681 4550 y(Mec)n(h.)27 b(Anal.)h Fb(160)f FH(\(2001\),)f(no.)h(4,)h(271{308.)238 4649 y([S72])267 b(Barry)38 b(Simon,)43 b Fz(Quadr)l(atic)e(form)h(te)l (chniques)f(and)h(the)f(Balslev-Comb)l(es)i(the)l(or)l(em)p FH(,)g(Comm.)681 4749 y(Math.)27 b(Ph)n(ys.)g Fb(27)g FH(\(1972\),)g(1{9.)238 4848 y([S79])267 b(B.)40 b(Simon,)j Fz(The)f(de\014nition)g(of)g(mole)l(cular)g(r)l(esonanc)l(e)g(curves)f (by)g(the)h(metho)l(d)g(of)g(exterior)681 4948 y(c)l(omplex)30 b(sc)l(aling)p FH(,)f(Ph)n(ys.)d(Lett.)i(A)g Fb(71)f FH(\(1979\),)g(211{214.)238 5048 y([U76])251 b(K.)26 b(Uhlen)n(b)r(ec)n(k,)h Fz(Generic)j(pr)l(op)l(erties)g(of)g (eigenfunctions)p FH(,)e(Amer.)f(J.)f(Math.)h Fb(98)f FH(\(1976\),)g(no.)h(4,)681 5147 y(1059{1078.)p eop end %%Page: 48 48 TeXDict begin 48 47 bop 122 66 a Fy(48)1078 b(P)-6 b(A)d(VEL)25 b(EXNER)g(AND)f(OLAF)h(POST)222 266 y FG(Dep)-6 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