Content-Type: multipart/mixed; boundary="-------------0704231038895" This is a multi-part message in MIME format. ---------------0704231038895 Content-Type: text/plain; name="07-99.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="07-99.keywords" Schrodinger operators, Dirichlet conditions, bent waveguides, quantum graphs, threshold resonances ---------------0704231038895 Content-Type: application/postscript; name="dsqueeze3.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="dsqueeze3.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.94a Copyright 2003 Radical Eye Software %%Title: dsqueeze3.dvi %%CreationDate: Mon Apr 23 16:30:15 2007 %%Pages: 16 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMR17 CMR12 CMR10 CMMI10 CMR8 CMTI10 CMBX10 CMBX12 %%+ CMSY8 CMMI12 CMSY10 CMMI8 CMTI12 CMR7 MSBM10 CMEX10 MSBM7 rsfs10 %%+ MSAM10 CMMI6 CMR6 CMSY6 CMTT12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf -G0 dsqueeze3 %DVIPSParameters: dpi=8000 %DVIPSSource: TeX output 2007.04.23:1551 %%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: alt-rule.pro 0 0 %! % 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) 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 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 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 48 /zero put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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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 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 73 /I put dup 76 /L put dup 80 /P put dup 82 /R put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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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 34 /epsilon put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 4391C9DF440285B8FC159D0E98D4258FC57892DDF0342CA1080743A076089583 6AD6FB2DC4C13F077F17789476E48402796E685107AF60A63FB0DE0266D55CF1 8D0AD65B9342CB686E564758C96164FFA711B11C1CE8C726F3C7BB1044BBD283 9AA4675747DF61E130A55E297CA5F0182A3F12F9085AF2F503481071724077A9 387E27879A9649AD5F186F33500FAC8F7FA26634BDCE1221EC0ED0E359E5EA5E 6166526FEB90C30D30099FBDC1BC2F9B62EFEEC48345160804AA98F8D0AA54B7 A480E715426651865C8E444EDB798C7E11040AF6E5A7ED1888653C6DBF5E6169 70BCD9C063B63B561EF165BF3AF11F8E519F37C6FDA2827685739DE2C48B5ADE EE84F067D704D4511DBFA49E166D543CFD9ECD7417055D8A827F51E087CD2927 BAFC7E6CFBD70B0FE969F890A11149D3D44D422C3370495DA9951AEE7253A49F 3A9444C8CD9158D84117299F7F2332FEB0F94E6ED8BC7AA789A3219BC2F227D3 3B5BC75FB53B55D72AF4A6A7BB613FA235B11BB37D059FD87127CEF73D5B3FBF 9F91ABAD78BD9240BD9525EBA78095EA0BDB25D1A19E876F292882EAD5619D46 D20317A345D931F4FF4EAE6216C27044CBA525E3B917CEA25A04C120466C4B93 FC720E6BA832A06CCA0A3916CEF0968D49085AEBD243C41A448289A6F05CE3F5 79148DC112A3CC7E8FF810B8C1A09E05F496C0F1EBA334E42E05C376C98F5F69 C06C71BFC0A2F3AC9951CFBB143C66FB84F9C4ED27DF70869352D61BD5E11508 0797B87C71AC58D7C35AB3247575482E538773F05A104DFCC4C2860B8EF21DF0 626F2EBCDE9E5244262FD52F1C46E3B10E2361ED0F57B1CAEAE26A0A4368DAE4 837A9B3D8756591D2A49B6B14374FC37A0400F0C947BC8516F20B89670D41E15 5ABE7D15B63F57CB03A54D506C38C7C9373F9ACEFE65FD27E0B8A36CC183CB6E 892EDCB469208E4B7EE97A51155B4B82BCE70615D5ECE606BCE1F4283ADB73EB B4048A099C882DA3386A519C7EC7155FB24C17DBB993DABC5C7F0E4D6EEE8E95 A20A17DC943E56C15958219562D201320493EA18F3B6A9B87E8972806BF47177 2DDD137D3A612882EA9D57B89F527D7EF2A3D6EF42B3DB6E7FE95DDC9DAD569C DEC56819F3187D4389BF54554ABD158EEABF5512CFAD688C90E597A239147C12 943FD363DD99507A541D865EBC13428ACFD47E85F35A33D29AB085C9FBE4BF99 FCC1FFA6F4D54660F1F64784D0C1CED519FB3AF5E393709FA17F9769D3C6F076 3CBD202F96D6E1DEB846D0685F2565082574CCF3573CA683EAA096DB64 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 54 /lessorequalslant put dup 62 /greaterorequalslant put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1C87678CE98C24B934A76220 4DD9B2FF3A49786028E35DDE10AD2C926BD30AD47015FFE9469DE1F793D1C53A C8812CBCD402444EAEA7A50EC5FD93D6A04C2783B50EA48059E3E7407537CB8D 4C206846EF0764C05289733920E2399E58AD8F137C229F3CE3E34D2D1EAB2D53 20D44EFAC8EFA4D14A2EFE389D952527F98D0E49BD5BD2C8D58FF9CB9C78D974 75C2AB5467D73D2B5E277A3FDC35909938A9DF0EB91BD9159D3437BE22EE4544 3429AC8E2BFBE34AE54D3BA3AD04BDF3F4F43A2B43992DF88678681B3AB32CFD A23E2C98D1AF00AB206AC95B78BBE6316F7A0AB6BD3236C28C76288B3C25D1EB E9ABB3576C5EC15A71D26177F5883E9B48293D59015615E2EEAF2E9BA04151ED 5497B9A1C41CBA44BAFF13EA218F5EAC11952EE336AD1DBE6CE92F002EAA3B3D 3BE4C3792F3405763C4BD93EFC3B4FC34193439561841BA989DD8D9F9AEE7A7B 24AEB4654B35023C9720B8F31AA9452E29753FB7915CB29977E725611E37C0B7 784BCC26FACF8A7A0EB1E54290D27FFE52B2D87FAD080AD15EE1984C37E0EB30 122C3012D3A16B09C28903D138352AB5462674B6CFB63F1371768D094DDF288C 36FB9B58443F872D61F2CD8CED42FE0EFF3D7E9952A172BB1AFECB60BF79F2B6 04265FDE4F78BC9FD619AA733CD0412F1D9A7C13B271BF827DCBDC8ABAE24FF0 74D3C220621D7FF0EFE62D835A221D0A7C139E2E6681FC2BBA58FA3B80D416EC 3854C63BA040A4262B458340DAA18AA6AEA3BBAC61615CB85982B18664D3D3AF 340C65B969071CF2D0CABEB80E04623D0526F862ECA8280EEE236C535F70561A 854181132E677674AD5E14C6636F57541D3C832D2CCAEC9661F0BCF9863844FD 9167AFD9B08889858AE828CD768583F405D95ACCD7D47194D11587B90753B6FC FEBD10DB17C79C58B8A6927A244E4589D8454B82A6793756730D02B6A50E439F 0E7D1EACEDCB32E425B47A27C6555967F3F7F6C0AEB550F7BA858E9C1F7BF7EC 0D57EA2757FBC117944D3348884B050641A8F42D014D813CFF4712A6D93AFC81 FC4476D3CD7D674593C4605A2E353D8FBA7822D6473C4178FF96E934281D3EA8 B72CFDE186E50AAC2BA9E536B8C53DC44DCFBA4A6885CE21B9C061BB18757D51 9CA8060EA9102DAEF24D789D50C397BD13E57E8F4481A363C8D1EC3C65CBBADA AC056EA5161060A5FA5B6FFDDFEAB5CFC5FCE2D6F79C6CF4646457CAFE5FE0E8 38FD1C4ABF47866CDE061763BEFF09A51178A792264358980FCD65E6A8788C03 8250E2B5D1CCECF0F114E59F43D40F7338317F610E21B8B04305DC581D86E5F4 E2020C2DA7B5BAF1C63C9AAA075EBECEB4B1F083B7C7BD1012A55D417518DB84 3BD91D86115057A98B314211E9D9832D32702E56B0E0ACFD30CB2BDE09BCB067 4D2CC3B1E03F8C14F185540984D0BB394BC59A80407707C797379DD2001379A5 B30A0F6746130F7BAB2F4967B07C568684042C50B29D56451B7A5C221B324173 5551FC1F8FDF47AA1201F28B4CC113A6D63FA9E5BE8B109F16549E95D3B74955 8D8972 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: rsfs10 %!PS-AdobeFont-1.0: rsfs10 001.000 %%CreationDate: Sat Mar 21 18:47:14 1998 %%VMusage: 120000 150000 11 dict begin /FontInfo 14 dict dup begin /version (001.001) readonly def /Copyright (Conversion from mf curves by Metafog (c) 1995 Richard Kinch) readonly def /Notice (Copyright (c) Taco Hoekwater, 1998. All rights reserved.) readonly def /FullName (rsfs10) readonly def /FamilyName (rsfs10) readonly def /ItalicAngle -12 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Roman) readonly def end readonly def /FontName /rsfs10 def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 66 /B put dup 68 /D put dup 82 /R put dup 83 /S put dup 84 /T put readonly def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /FontBBox {-2 -300 1240 728} 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 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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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 2 /bracketleftbig put dup 3 /bracketrightbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 101 /tildewide put dup 102 /tildewider put dup 112 /radicalbig put dup 115 /radicalBigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 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 67 /C put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (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 49 /one put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 50 /two put dup 55 /seven put dup 58 /colon put dup 65 /A 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 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 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 readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec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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 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. 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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 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 18 /theta put dup 21 /lambda put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 30 /phi put dup 32 /psi put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 80 /P put dup 81 /Q put dup 82 /R put dup 84 /T put dup 85 /U put dup 86 /V put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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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 1 /Delta put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 16 /dotlessi put dup 19 /acute put dup 20 /caron put dup 22 /macron put dup 24 /cedilla put dup 28 /oslash 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 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 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W 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 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile 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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 14 /delta put dup 59 /comma put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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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 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 46 /period put dup 64 /at put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 106 /j put dup 110 /n put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 122 /z put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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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 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 51 /three 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 71 /G put dup 72 /H put dup 73 /I 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 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 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 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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B10489F464A5B50AF144E23D32 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 readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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 (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 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 58 /colon put dup 68 /D put dup 78 /N put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 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 122 /z put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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cleartomark %%EndFont TeXDict begin 39139632 55387786 1000 8000 8000 (dsqueeze3.dvi) @start /Fa 139[684 3[684 2[684 4[684 6[684 39[684 1[684 684 684 1[684 684 684 684 684 1[684 45[{}15 1328.35 /CMTT12 rf /Fb 207[243 48[{}1 664.176 /CMSY6 rf /Fc 207[406 48[{}1 664.176 /CMR6 rf /Fd 139[581 589 610 1[830 747 830 1245 3[415 830 2[682 3[726 12[1039 3[1021 3[898 19[747 747 747 747 747 747 747 747 747 1[415 46[{}24 1328.35 /CMBX12 rf /Fe 221[390 34[{}1 664.176 /CMMI6 rf /Ff 193[1033 7[1033 54[{}2 1328.35 /MSAM10 rf /Fg 171[992 1153 1129 13[1029 1[1206 66[{}5 1328.35 /rsfs10 rf /Fh 173[640 82[{}1 885.568 /MSBM7 rf /Fi 140[1328 2[1328 9[1328 738 10[738 1[1919 5[627 21[1181 1[1181 1[1181 14[1070 1070 12[996 996 4[701 701 978 978 793 793 12[553 553 609 609{}24 1328.35 /CMEX10 rf /Fj 173[959 14[959 67[{}2 1328.35 /MSBM10 rf /Fk 206[441 49[{}1 774.872 /CMR7 rf /Fl 133[531 631 598 863 598 697 432 531 548 598 664 664 731 1063 332 598 399 399 664 598 399 598 664 598 598 664 9[1298 2[930 731 948 996 881 996 966 1165 815 999 682 501 966 1005 848 1[981 930 1[966 6[399 2[664 4[664 1[664 1[399 465 399 2[531 531 20[664 6[731 797 11[{}57 1328.35 /CMTI12 rf /Fm 140[435 425 1[474 1[571 832 281 490 381 320 3[436 484 2[500 12[548 15[772 6[470 1[261 24[434 20[485 1[604 11[{}19 885.568 /CMMI8 rf /Fn 143[1107 1[664 2[664 369 2[664 664 9[886 12[1058 4[900 2[790 15[0 0 3[886 1328 15[1328 6[1033 18[1033 1033 3[1033 369 1033{}21 1328.35 /CMSY10 rf /Fo 133[604 634 739 1[629 740 470 613 586 1[653 1[776 1138 1[676 538 444 2[641 603 676 560 1[683 10[758 883 762 1[990 1030 838 2[1258 885 2[574 1078 1026 1[963 1080 931 988 975 687 1[1012 650 1012 361 361 18[852 4[609 1[846 1[770 2[739 671 738 3[759 2[606 3[576 675 1[827 11[{}53 1328.35 /CMMI12 rf /Fp 149[261 2[470 470 52[941 255 14[941 29[470 1[261 732{}9 885.568 /CMSY8 rf /Fq 128[650 650 2[650 578 686 686 939 686 723 506 513 506 686 723 650 723 1084 361 686 397 361 723 650 397 578 723 578 723 650 2[650 361 650 361 795 975 1[1336 975 975 939 723 957 1012 885 1012 975 1192 813 1011 668 469 975 1021 849 885 993 939 921 975 3[1012 1[361 361 650 650 650 650 650 650 650 650 650 650 1[361 434 361 1012 1[506 506 361 4[650 361 4[650 3[578 1[650 1[650 650 2[361 1[1084 723 723 759 939 1012 7[1084 1[{}93 1328.35 /CMR12 rf /Fr 136[1554 1136 1196 837 849 879 1[1196 1076 1196 1793 598 2[598 1196 1076 658 982 1196 956 1196 1046 12[1497 1[1605 1[1470 6[801 20[1076 1076 1076 1076 2[598 717 45[{}30 1912.83 /CMBX12 rf /Fs 241[539 14[{}1 1212.12 /CMMI10 rf /Ft 139[542 550 574 14[620 774 678 31[1054 65[{}7 1212.12 /CMBX10 rf /Fu 133[496 1[562 2[651 403 496 511 3[681 3[372 372 2[372 558 1[558 1[620 32[929 17[372 1[372 44[{}16 1212.12 /CMTI10 rf /Fv 128[606 4[539 640 640 875 640 673 471 478 475 640 673 606 673 1010 337 640 1[337 673 606 370 539 673 539 673 606 9[1246 1[909 875 673 892 1[825 943 909 1111 3[438 1[951 2[926 875 859 909 7[606 606 606 606 606 1[606 606 606 606 1[337 404 337 23[606 606 19[{}55 1212.12 /CMR10 rf /Fw 194[732 8[470 470 470 470 470 4[732 1[366 366 29[680 10[{}10 885.568 /CMR8 rf /Fx 196[307 59[{}1 1106.96 /CMMI10 rf /Fy 133[492 584 584 799 584 615 430 437 434 584 615 553 615 922 307 584 1[307 615 553 338 492 615 492 615 553 12[799 11[830 6[830 13[553 553 553 2[307 1[307 44[{}33 1106.96 /CMR10 rf /Fz 135[824 1[824 867 607 1[607 1[867 780 867 1[434 2[434 3[694 867 694 1[780 16[1062 10[1062 1[1127 67[{}17 1594.02 /CMR12 rf /FA 133[933 2[1533 1113 1173 813 825 813 1113 1173 1053 1173 1773 573 1113 1[573 1173 1053 633 933 1173 933 1173 1053 18[1592 9[1622 9[573 58[{}26 2295.84 /CMR17 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 2295 13007 a FA(Non)-60 b(trivial)693 b(edge)f(coupling)h(from)g(a)g(Diric)-60 b(hlet)693 b(net)-60 b(w)g(ork)6932 15774 y(squeezing:)933 b(the)693 b(case)g(of)g(a)g(b)60 b(en)-60 b(t)692 b(w)-60 b(a)g(v)g(eguide)11325 19718 y Fz(Claudio)520 b(Cacciapuoti)25198 19139 y Fy(1)26327 19718 y Fz(and)h(P)-43 b(a)g(v)g(el)519 b(Exner)37600 19139 y Fy(2)p Fx(;)p Fy(3)-72 22298 y Fw(1)454 22737 y Fv(Institut)405 b(f)34 b(\177)-640 b(ur)405 b(Angew)-34 b(andte)406 b(Mathematik,)e(Univ)-34 b(ersit\177)-606 b(at)405 b(Bonn,)f(W)-101 b(egelerstr.)537 b(6,)404 b(53115)g(Bonn,)g (German)-34 b(y)4133 23803 y Fw(2)4658 24243 y Fv(Nuclear)404 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Fq(:=)369 b Fn(\000)p Fq(\001)434 b(with)f Fg(D)124 b Fq(\()p Fo(L)42206 44449 y Fw(0)42732 44250 y Fq(\))369 b(:=)g Fo(C)46375 43768 y Fp(1)46280 44578 y Fw(0)47371 44250 y Fq(\(\012\).)945 45855 y(The)485 b(main)g(geometric)h(ob)72 b(ject)486 b(of)g(our)f(study)g(will)h(b)36 b(e)485 b(a)h(family)h(of)e(w)-36 b(a)g(v)g(eguides)486 b(whose)g(shap)36 b(e)485 b(and)-1575 47460 y(width)433 b(dep)36 b(end)433 b(on)g(a)h(scaling)g(parameter)g (0)369 b Fo(<)g(")f Ff(6)h Fq(1)434 b(according)g(to)10399 51247 y Fo(\015)11074 51446 y Fm(")11563 51247 y Fq(\()p Fo(s)p Fq(\))368 b(:=)15431 49188 y Fi(p)p 16759 49188 2380 54 v 1136 x Fo(\025)p Fq(\()p Fo(")p Fq(\))p 15431 50942 3708 54 v 16980 52159 a Fo(")19271 51247 y(\015)20018 49773 y Fi(\020)20944 50349 y Fo(s)p 20944 50942 613 54 v 20946 52159 a(")21690 49773 y Fi(\021)22705 51247 y Fq(;)2823 b Fo(d)26565 51446 y Fm(")27423 51247 y Fq(:=)369 b Fo(")29774 50699 y Fm(\013)30434 51247 y Fo(d)221 b(;)1522 b Fq(with)434 b Fo(\013)377 b(>)369 b 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Fm(")12959 66656 y Fq(of)f(whic)-36 b(h)434 b(c)-36 b(hanges)433 b(sligh)-36 b(tly)435 b(with)e(resp)36 b(ect)434 b(to)f Fo(")p Fq(,)10331 70279 y Fo(\022)10937 70478 y Fm(")11796 70279 y Fq(=)13176 68471 y Fi(Z)13914 71478 y Fh(R)14831 70279 y Fo(\015)15506 70478 y Fm(")15995 70279 y Fq(\()p Fo(s)p Fq(\))221 b Fo(ds)368 b Fq(=)h Fo(\022)21521 69078 y Fi(p)p 22850 69078 V 22850 70279 a Fo(\025)p Fq(\()p Fo(")p Fq(\))f(=)g Fo(\022)27620 68406 y Fi(\022)28598 70279 y Fq(1)296 b(+)30983 69380 y(1)p 30983 69973 651 54 v 30983 71190 a(2)31767 70279 y Fo(\025)32526 70478 y Fw(1)33051 70279 y Fo(")33660 68406 y Fi(\023)34933 70279 y Fq(+)f Fn(O)37 b Fq(\()p Fo(")38450 69730 y Fw(2)38974 70279 y Fq(\))221 b Fo(:)24872 74197 y Fq(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop -1575 7638 a Fq(They)434 b(in)g(turn)e(generate)i (a)g(family)h(of)f(b)36 b(en)-36 b(t)433 b(w)-36 b(a)g(v)g(eguides,)434 b(i.e.)579 b(domains)434 b(\012)36303 7837 y Fm(")37227 7638 y Fq(de\014ned)e(b)-36 b(y)1127 10321 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b(\(2.3\))24872 74197 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop -1575 7638 a Fq(has)603 b(a)h(zero)f(energy)g (resonance)g(if)h(there)e(exist)i(a)f(function)g Fo( )30975 7837 y Fm(r)32138 7638 y Fn(2)657 b Fo(L)34566 7156 y Fp(1)35563 7638 y Fq(\()p Fj(R)p Fq(\),)645 b Fo( )39386 7837 y Fm(r)40704 7638 y Fo(=)-805 b Fn(2)657 b Fo(L)42977 7156 y Fw(2)43503 7638 y Fq(\()p Fj(R)p Fq(\),)646 b(suc)-36 b(h)602 b(that)p -1575 8176 1181 54 v -1575 9243 a Fo(H)102 b( )451 9442 y Fm(r)1326 9243 y Fq(=)369 b(0)434 b(holds)f(in)g(the)h (sense)f(of)h(distributions.)578 b(In)433 b(particular,)h(if)14733 11113 y Fi(Z)15471 14120 y Fh(R)p 16388 11854 1048 54 v 16388 12921 a Fo(V)289 b Fq(\()p Fo(s)p Fq(\))221 b Fo(ds)368 b Fn(6)p Fq(=)h(0)1301 b(and)f Fo(e)28269 12372 y Fm(a)p Fp(j\001j)p 29608 11854 V 29608 12921 a Fo(V)658 b Fn(2)369 b Fo(L)33164 12372 y Fw(1)33689 12921 y Fq(\()p Fj(R)p Fq(\))13635 b(\(2.4\))-1575 16727 y(holds)434 b(for)g(some)g Fo(a)368 b(>)h Fq(0,)434 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b(us)f(stress)h(that)f(the)g(constan)-36 b(ts)1677 34373 y Fo(c)2237 34572 y Fw(1)3196 34373 y Fq(and)433 b Fo(c)6285 34572 y Fw(2)7244 34373 y Fq(de\014ned)f(in)i(\(2.5\))g(coincide)g (with)f(those)h(emplo)-36 b(y)g(ed)433 b(in)h([A)-36 b(CF07)q(].)945 37819 y(Let)364 b(us)g(next)g(in)-36 b(tro)36 b(duce)363 b(a)i(pair)f(of)h(Hamiltonians)g(on)g Fn(G)443 b Fq(b)36 b(oth)364 b(acting)g(as)h Fo(f)511 b Fn(7!)369 b(\000)p Fo(f)42325 37337 y Fp(00)43255 37819 y Fq(but)364 b(di\013ering)g(b)-36 b(y)-1575 39625 y(the)485 b(b)36 b(oundary)484 b(conditions)h(in)f(the)h(v)-36 b(ertex.)732 b(The)485 b(\014rst)f(is)h(the)g(Diric)-36 b(hlet-decoupled)484 b(op)36 b(erator)p 47235 38558 1181 54 v 485 w Fo(H)48415 38803 y Fm(d)49439 39625 y Fq(with)-1575 41432 y(the)519 b(domain)g Fg(D)124 b Fq(\()p 7120 40365 V Fo(H)8300 40609 y Fm(d)8840 41432 y Fq(\))514 b(:=)g Fn(f)p Fo(f)657 b Fn(2)514 b Fo(H)16290 40950 y Fw(2)16815 41432 y Fq(\()p Fj(R)354 b Fn(n)f Fq(0\))h Fn(\\)f Fo(H)23581 40950 y Fw(1)24106 41432 y Fq(\()p Fj(R)p Fq(\))p Fn(j)221 b Fo(f)142 b Fq(\(0\))515 b(=)f(0)p Fn(g)p Fq(.)835 b(The)519 b(other)g(is)g(a)g(p)36 b(oin)-36 b(t-in)g(teraction)-1575 43037 y(Hamiltonian)p 5904 41970 V 435 w Fo(H)7084 42214 y Fm(r)7590 43037 y Fq(,)434 b(whic)-36 b(h)433 b(again)i(acts)e(as)p 19852 41970 V 434 w Fo(H)21033 42214 y Fm(r)21539 43037 y Fo(f)511 b Fq(=)368 b Fn(\000)p Fo(f)25887 42555 y Fp(00)26887 43037 y Fq(but)432 b(on)i(the)f(domain)2878 46833 y Fg(D)124 b Fq(\()p 4537 45766 V Fo(H)5717 46010 y Fm(r)6223 46833 y Fq(\))369 b(:=)8840 44960 y Fi(\032)9836 46833 y Fo(f)511 b Fn(2)369 b Fo(H)13424 46284 y Fw(2)13949 46833 y Fq(\()p Fj(R)295 b Fn(n)h Fq(0\))p Fn(j)221 b Fq(\()p Fo(c)19481 47032 y Fw(1)20302 46833 y Fq(+)295 b Fo(c)22169 47032 y Fw(2)22694 46833 y Fq(\))p Fo(f)142 b Fq(\(0)25139 46284 y Fw(+)25926 46833 y Fq(\))369 b(=)g(\()p Fo(c)29248 47032 y Fw(1)30068 46833 y Fn(\000)296 b Fo(c)31957 47032 y Fw(2)32482 46833 y Fq(\))p Fo(f)142 b Fq(\(0)34927 46284 y Fp(\000)35714 46833 y Fq(\))221 b Fo(;)10682 50709 y Fq(\()p Fo(c)11748 50908 y Fw(1)12569 50709 y Fn(\000)295 b Fo(c)14457 50908 y Fw(2)14983 50709 y Fq(\))p Fo(f)16272 50161 y Fp(0)16582 50709 y Fq(\(0)17738 50161 y Fw(+)18525 50709 y Fq(\))369 b(=)g(\()p Fo(c)21847 50908 y Fw(1)22667 50709 y Fq(+)295 b Fo(c)24534 50908 y Fw(2)25060 50709 y Fq(\))p Fo(f)26349 50161 y Fp(0)26659 50709 y Fq(\(0)27815 50161 y Fp(\000)28602 50709 y Fq(\))g(+)32404 49460 y(^)32350 49811 y Fo(\025)p 30843 50404 3774 54 v 30843 51621 a(c)31403 51820 y Fw(1)32224 51621 y Fq(+)f Fo(c)34090 51820 y Fw(2)34749 50709 y Fo(f)142 b Fq(\(0)36688 50161 y Fp(\000)37475 50709 y Fq(\))37981 48836 y Fi(\033)40278 50709 y Fq(for)369 b Fo(c)42760 50908 y Fw(2)43655 50709 y Fn(6)p Fq(=)g Fn(\000)p Fo(c)46629 50908 y Fw(1)47376 50709 y Fq(;)2878 54586 y Fg(D)124 b Fq(\()p 4537 53519 1181 54 v Fo(H)5717 53763 y Fm(r)6223 54586 y Fq(\))369 b(:=)8840 52713 y Fi(\032)9836 54586 y Fo(f)511 b Fn(2)369 b Fo(H)13424 54037 y Fw(2)13949 54586 y Fq(\()p Fj(R)295 b Fn(n)h Fq(0\))p Fn(j)221 b Fo(f)142 b Fq(\(0)20354 54037 y Fp(\000)21141 54586 y Fq(\))369 b(=)g(0)221 b Fo(;)444 b(f)25856 54037 y Fp(0)26166 54586 y Fq(\(0)27322 54037 y Fw(+)28110 54586 y Fq(\))368 b(=)31041 53337 y(^)30986 53687 y Fo(\025)p 30498 54280 1736 54 v 30498 55497 a Fq(4)p Fo(c)31708 55039 y Fw(2)31708 55823 y(1)32366 54586 y Fo(f)142 b Fq(\(0)34305 54037 y Fw(+)35093 54586 y Fq(\))35599 52713 y Fi(\033)37896 54586 y Fq(for)369 b Fo(c)40378 54785 y Fw(2)41273 54586 y Fq(=)f Fn(\000)p Fo(c)44246 54785 y Fw(1)44993 54586 y Fo(;)-1575 58381 y Fq(where)434 b(w)-36 b(e)434 b(put)17494 60380 y(^)17440 60731 y Fo(\025)369 b Fq(:=)g Fo(\025)21069 60930 y Fw(1)21816 58923 y Fi(Z)22554 61930 y Fh(R)p 23470 59664 1048 54 v 23470 60731 a Fo(V)289 b Fq(\()p Fo(s)p Fq(\))26142 59655 y Fi(\000)26750 60731 y Fo( )27596 60930 y Fm(r)28102 60731 y Fq(\()p Fo(s)p Fq(\))29727 59655 y Fi(\001)30335 59952 y Fw(2)31082 60731 y Fo(ds)221 b(:)16342 b 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b(ends)642 b(on)i(t)-36 b(w)g(o)644 b(real)-1575 70877 y(parameters.)733 b(It)485 b(is)h(a)f(straigh)-36 b(tforw)g(ard)486 b(exercise)g(to)f(c)-36 b(hec)g(k)485 b(that)g(the)g(b)36 b(oundary)484 b(conditions)h(app)36 b(earing)24872 74197 y(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop -1575 7638 a Fq(in)633 b(the)g(de\014nition)f(of) i Fg(D)124 b Fq(\()p 11902 6571 1181 54 v Fo(H)13082 6815 y Fm(r)13588 7638 y Fq(\))633 b(can)g(b)36 b(e)633 b(rewritten)g(in)g(the)g(form)g(\(1.1\))h(with)f(\011)708 b(:=)h(\()p Fo(f)142 b Fq(\(0)45260 7156 y Fw(+)46047 7638 y Fq(\))p Fo(;)221 b(f)142 b Fq(\(0)49074 7156 y Fp(\000)49862 7638 y Fq(\)\))50874 7156 y Fm(T)51607 7638 y Fq(,)-1575 9243 y(\011)-563 8761 y Fp(0)116 9243 y Fq(:=)369 b(\()p Fo(f)3147 8761 y Fp(0)3458 9243 y Fq(\(0)4614 8761 y Fw(+)5401 9243 y Fq(\))p Fo(;)221 b Fn(\000)p Fo(f)8305 8761 y Fp(0)8616 9243 y Fq(\(0)9772 8761 y Fp(\000)10559 9243 y Fq(\)\))11571 8761 y Fm(T)12738 9243 y Fq(and)433 b(the)h(2)295 b Fn(\002)g Fq(2)434 b(unitary)g(matrix)10616 12516 y Fo(U)508 b Fq(:=)17677 11618 y(1)p 13882 12211 8240 54 v 13882 13643 a(2\()p Fo(c)15598 13186 y Fw(2)15598 13969 y(1)16419 13643 y Fq(+)295 b Fo(c)18286 13186 y Fw(2)18286 13969 y(2)18811 13643 y Fq(\))g(+)g Fo(i)21417 13293 y Fq(^)21363 13643 y Fo(\025)22476 10643 y Fi(\022)24007 11703 y Fn(\000)p Fq(4)p Fo(c)26250 11902 y Fw(1)26776 11703 y Fo(c)27336 11902 y Fw(2)28157 11703 y Fn(\000)g Fo(i)29983 11352 y Fq(^)29929 11703 y Fo(\025)1202 b Fq(2\()p Fo(c)33606 11221 y Fw(2)33606 12031 y(1)34427 11703 y Fn(\000)295 b Fo(c)36315 11221 y Fw(2)36315 12031 y(2)36841 11703 y Fq(\))24619 13457 y(2\()p Fo(c)26335 12975 y Fw(2)26335 13786 y(1)27156 13457 y Fn(\000)g Fo(c)29044 12975 y Fw(2)29044 13786 y(2)29570 13457 y Fq(\))1719 b(4)p Fo(c)33005 13656 y Fw(1)33531 13457 y Fo(c)34091 13656 y Fw(2)34911 13457 y Fn(\000)296 b Fo(i)36738 13107 y Fq(^)36684 13457 y Fo(\025)37996 10643 y Fi(\023)39416 12516 y Fo(:)9518 b Fq(\(2.7\))-1575 15752 y(In)586 b(particular,)623 b(for)586 b Fo(\025)9649 15951 y Fw(1)10802 15752 y Fq(=)628 b(0)585 b(the)g(b)36 b(oundary)585 b(conditions)h(de\014ne)e(the)h(\\scale)i (in)-36 b(v)-72 b(arian)-36 b(t")586 b(Hamiltonian)-1575 17357 y(obtained)440 b(in)g([A)-36 b(CF07)q(].)598 b(Applications)440 b(of)h(this)f(p)36 b(oin)-36 b(t)440 b(in)-36 b(teraction)440 b(w)-36 b(ere)440 b(discussed)f(recen)-36 b(tly)441 b(in)f([HC06)q(],) -1575 18962 y(and)565 b(it)g(is)g(w)-36 b(orth)565 b(men)-36 b(tioning)564 b(that)h(it)g(app)36 b(ears)565 b(also)h(in)e(the)h (theory)g(of)h(regular)f(tree)f(graphs)h([So04)q(].)-1575 20568 y(On)537 b(the)h(other)g(hand,)563 b(in)538 b(distinction)g(to)g ([A)-36 b(CF07)q(])538 b(w)-36 b(e)538 b(ha)-36 b(v)g(e)539 b(here)e(a)i(wider)f(class)g(whic)-36 b(h)538 b(con)-36 b(tains,)565 b(in)-1575 22173 y(particular,)366 b(the)347 b(standard)g Fo(\016)398 b Fq(in)-36 b(teraction)348 b(of)g(coupling)h(strength)31258 21822 y(^)31204 22173 y Fo(\025)468 b Fq([A)-36 b(GHH05])348 b(corresp)36 b(onding)348 b(to)g Fo(c)49043 22372 y Fw(1)49938 22173 y Fq(=)368 b(1)-1575 23778 y(and)375 b Fo(c)1456 23977 y Fw(2)2350 23778 y Fq(=)369 b(0.)559 b(Sp)36 b(ectral)374 b(and)h(scattering)g (prop)36 b(erties)374 b(of)p 26230 22711 1181 54 v 376 w Fo(H)27410 22955 y Fm(r)28291 23778 y Fq(are)h(w)-36 b(ell)375 b(kno)-36 b(wn)375 b([EG99)q(])g(and)f(w)-36 b(e)375 b(recall)h(them)-1575 25383 y(only)434 b(brie\015y:)-1575 27594 y Fd(Prop)42 b(osition)500 b(2.)554 b Fl(F)-100 b(or)466 b(any)f Fn(\0001)371 b Fo(<)17299 27243 y Fq(^)17245 27594 y Fo(\025)e Ff(6)h Fn(1)p Fl(,)466 b(the)f(essential)f(sp)-66 b(e)g(ctrum)465 b(of)p 36400 26527 V 465 w Fo(H)37580 26771 y Fm(r)38551 27594 y Fl(is)g(absolutely)h(c)-66 b(ontinuous)-1575 29199 y(and)481 b(c)-66 b(oincides)478 b(with)i(the)g(interval)f Fq([0)p Fo(;)221 b Fn(1)p Fq(\))p Fl(.)645 b(F)-100 b(urthermor)-66 b(e,)483 b(for)30893 28848 y Fq(^)30838 29199 y Fo(\025)398 b(>)f Fq(0)481 b Fl(ther)-66 b(e)479 b(ar)-66 b(e)480 b(no)g(eigenvalues,)j(while) -1575 30804 y(for)640 30454 y Fq(^)586 30804 y Fo(\025)525 b(<)h Fq(0)550 b Fl(ther)-66 b(e)549 b(is)h(just)f(one)h(ne)-66 b(gative)547 b(eigenvalue)h(given)h(by)g Fo(k)31994 30322 y Fw(2)33046 30804 y Fq(=)526 b Fo(k)35305 30322 y Fw(2)35260 31132 y(0)36357 30804 y Fq(=)f Fn(\000)39060 30281 y Fw(1)p 39060 30499 471 54 v 39060 31262 a(4)39718 30454 y Fq(^)39664 30804 y Fo(\025)40423 30322 y Fw(2)40948 30804 y Fq(\()p Fo(c)42014 30322 y Fw(2)42014 31132 y(1)42898 30804 y Fq(+)357 b Fo(c)44827 30322 y Fw(2)44827 31132 y(2)45353 30804 y Fq(\))45859 30322 y Fp(\000)p Fw(1)47666 30804 y Fl(and)550 b(the)-1575 32409 y(c)-66 b(orr)g(esp)g(onding)463 b(normalize)-66 b(d)464 b(eigenfunction)d(is)3343 36322 y Fo( )4189 36521 y Fw(0)5084 36322 y Fq(=)6464 33628 y Fi(s)p 7793 33628 1763 54 v 7926 35424 a Fn(j)8349 35073 y Fq(^)8295 35424 y Fo(\025)o Fn(j)p 7926 36017 1497 54 v 8349 37234 a Fq(2)11249 35424 y(1)p 9688 36017 3774 54 v 9688 37234 a Fo(c)10248 36776 y Fw(2)10248 37559 y(1)11069 37234 y Fq(+)294 b Fo(c)12935 36776 y Fw(2)12935 37559 y(2)13815 34051 y Fi(\()15107 35287 y Fq(\()p Fo(c)16173 35486 y Fw(1)16993 35287 y Fn(\000)i Fo(c)18882 35486 y Fw(2)19407 35287 y Fq(\))p Fo(e)20516 34739 y Fm(ik)21326 34862 y Fc(0)21787 34739 y Fm(s)25423 35287 y Fo(s)369 b(>)g Fq(0)15107 37375 y(\()p Fo(c)16173 37574 y Fw(1)16993 37375 y Fq(+)295 b Fo(c)18860 37574 y Fw(2)19386 37375 y Fq(\))p Fo(e)20495 36827 y Fp(\000)p Fm(ik)22037 36950 y Fc(0)22498 36827 y Fm(s)25423 37375 y Fo(s)369 b(<)g Fq(0)28436 34051 y Fi(\))29949 36322 y Fo(;)2878 b(k)33864 36521 y Fw(0)34759 36322 y Fq(=)38020 35424 y Fo(i)p Fn(j)38887 35073 y Fq(^)38833 35424 y Fo(\025)p Fn(j)p 36273 36017 5436 54 v 36273 37234 a Fq(2\()p Fo(c)37989 36776 y Fw(2)37989 37559 y(1)38810 37234 y Fq(+)295 b Fo(c)40677 36776 y Fw(2)40677 37559 y(2)41202 37234 y Fq(\))42062 36322 y Fo(;)43363 35972 y Fq(^)43309 36322 y Fo(\025)369 b(<)f Fq(0)221 b Fo(:)-1575 40110 y Fl(Final)66 b(ly,)440 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Fq(\()p Fo(c)17477 45335 y Fw(2)17477 46146 y(1)18298 45817 y Fn(\000)295 b Fo(c)20186 45335 y Fw(2)20186 46146 y(2)20712 45817 y Fq(\))p 13648 46410 8961 54 v 13648 47843 a(2)p Fo(k)45 b Fq(\()p Fo(c)16085 47385 y Fw(2)16085 48168 y(1)16906 47843 y Fq(+)295 b Fo(c)18773 47385 y Fw(2)18773 48168 y(2)19299 47843 y Fq(\))g(+)f Fo(i)21904 47492 y Fq(^)21850 47843 y Fo(\025)22963 46716 y(;)2879 b Fg(R)27415 46167 y Fp(f)p Fm(l)11 b(;r)26 b Fp(g)29414 46716 y Fq(\()p Fo(k)45 b Fq(\))369 b(=)g Fn(\006)35359 45817 y Fq(4)p Fo(k)45 b(c)37290 46016 y Fw(1)37816 45817 y Fo(c)38376 46016 y Fw(2)39197 45817 y Fn(\007)295 b Fo(i)41023 45467 y Fq(^)40969 45817 y Fo(\025)p 34063 46410 V 34063 47843 a Fq(2)p Fo(k)45 b Fq(\()p Fo(c)36500 47385 y Fw(2)36500 48168 y(1)37321 47843 y Fq(+)295 b Fo(c)39188 47385 y Fw(2)39188 48168 y(2)39713 47843 y Fq(\))g(+)g Fo(i)42319 47492 y Fq(^)42265 47843 y Fo(\025)43378 46716 y(:)945 49952 y Fq(Let)487 b(no)-36 b(w)487 b Fo(G)7118 50151 y Fm(k)8174 49952 y Fq(b)36 b(e)487 b(the)g(resolv)-36 b(en)g(t)488 b(of)g(the)e(free)i(Laplacian)g(on)f Fj(R)p Fq(,)501 b(it)488 b(is)f(a)h(b)36 b(ounded)486 b(op)36 b(erator-v)-72 b(alued)-1575 51557 y(analytical)436 b(function)d(of)h Fo(k)11683 51075 y Fw(2)12643 51557 y Fq(for)g Fo(k)15351 51075 y Fw(2)16246 51557 y Fn(2)368 b Fj(C)p Fn(n)p Fj(R)20082 51075 y Fw(+)21304 51557 y Fq(and)433 b(Im)443 b Fo(k)414 b(>)368 b Fq(0,)435 b(with)e(the)g(in)-36 b(tegral)434 b(k)-36 b(ernel)434 b(giv)-36 b(en)434 b(b)-36 b(y)10917 54513 y Fo(G)11943 54712 y Fm(k)12511 54513 y Fq(\()p Fo(s)295 b Fn(\000)g Fo(s)15866 53964 y Fp(0)16177 54513 y Fq(\))368 b(=)19029 53614 y Fo(i)p 18565 54207 1372 54 v 18565 55424 a Fq(2)p Fo(k)20069 54513 y(e)20672 53964 y Fm(ik)24 b Fp(j)p Fm(s)p Fp(\000)p Fm(s)23369 53652 y Fb(0)23667 53964 y Fp(j)26585 54513 y Fo(k)27306 53964 y Fw(2)28201 54513 y Fn(2)369 b Fj(C)p Fn(n)p Fj(R)32038 53964 y Fw(+)32826 54513 y Fo(;)591 b Fq(Im)443 b Fo(k)414 b(>)368 b Fq(0)221 b Fo(:)-1575 57716 y Fq(By)443 b(Krein's)g(form)-36 b(ula)443 b([ABD95)r(,)g(EG99])g(the)f(in)-36 b(tegral)443 b(k)-36 b(ernel)443 b(of)g(the)f(resolv)-36 b(en)g(t)p 39156 56649 1001 54 v 443 w Fo(R)40157 56894 y Fm(d)40696 57716 y Fq(\()p Fo(k)41923 57234 y Fw(2)42449 57716 y Fq(\))384 b(:=)h(\()p 45603 56649 1181 54 v Fo(H)46783 56894 y Fm(d)47624 57716 y Fn(\000)301 b Fo(k)49679 57234 y Fw(2)50205 57716 y Fq(\))50711 57234 y Fp(\000)p Fw(1)-1575 59322 y Fq(is)p 5423 59860 1001 54 v 5423 60927 a Fo(R)6424 60104 y Fm(d)6964 60927 y Fq(\()p Fo(k)8191 60378 y Fw(2)8716 60927 y Fo(;)221 b(s;)g(s)11106 60378 y Fp(0)11418 60927 y Fq(\))369 b(=)f Fo(G)14699 61126 y Fm(k)15268 60927 y Fq(\()p Fo(s)295 b Fn(\000)g Fo(s)18623 60378 y Fp(0)18933 60927 y Fq(\))g(+)g(2)p Fo(ik)45 b(G)23882 61126 y Fm(k)24451 60927 y Fq(\()p Fo(s)p Fq(\))p Fo(G)27102 61126 y Fm(k)27670 60927 y Fq(\()p Fo(s)28789 60378 y Fp(0)29099 60927 y Fq(\))369 b Fo(;)1522 b(k)32578 60378 y Fw(2)33473 60927 y Fn(2)369 b Fj(C)p Fn(n)p Fj(R)37310 60378 y Fw(+)38319 60927 y Fo(;)591 b Fq(Im)443 b Fo(k)414 b(>)368 b Fq(0)221 b Fo(;)-1575 63001 y Fq(while)434 b(the)f(in)-36 b(tegral)434 b(k)-36 b(ernel)434 b(of)g(the)f(resolv)-36 b(en)g(t)p 21808 61934 V 434 w Fo(R)22809 62178 y Fm(r)23315 63001 y Fq(\()p Fo(k)24542 62519 y Fw(2)25068 63001 y Fq(\))369 b(:=)g(\()p 28191 61934 1181 54 v Fo(H)29371 62178 y Fm(r)30172 63001 y Fn(\000)295 b Fo(k)32221 62519 y Fw(2)32747 63001 y Fq(\))33253 62519 y Fp(\000)p Fw(1)34944 63001 y Fq(equals)p 16 65292 1001 54 v 16 66359 a Fo(R)1017 65536 y Fm(r)1523 66359 y Fq(\()p Fo(k)2750 65811 y Fw(2)3276 66359 y Fq(;)221 b Fo(s;)g(s)5666 65811 y Fp(0)5977 66359 y Fq(\))369 b(=)p Fo(G)8890 66558 y Fm(k)9458 66359 y Fq(\()p Fo(s)295 b Fn(\000)h Fo(s)12814 65811 y Fp(0)13124 66359 y Fq(\))f(+)g(2)p Fo(ik)19029 65460 y Fq(2)p Fo(k)45 b(c)20960 64978 y Fw(2)20960 65789 y(2)21781 65460 y Fq(+)295 b Fo(i)23586 65110 y Fq(^)23532 65460 y Fo(\025)p 17179 66053 8961 54 v 17179 67486 a Fq(2)p Fo(k)45 b Fq(\()p 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Fm(")p Fp(!)p Fw(0)p 15032 28175 1001 54 v 15032 29242 a Fo(R)16033 28419 y Fm(")16033 29570 y(n;m)17753 29242 y Fq(\()p Fo(k)18980 28693 y Fw(2)19506 29242 y Fq(\))368 b(=)h Fo(\016)22337 29441 y Fm(n;m)p 24057 28175 V 24057 29242 a Fo(R)25058 28419 y Fm(r)25564 29242 y Fq(\()p Fo(k)26791 28693 y Fw(2)27317 29242 y Fq(\))2656 b Fo(k)31200 28693 y Fw(2)32095 29242 y Fn(2)369 b Fj(C)p Fn(n)p Fj(R)p Fo(;)886 b Fq(Im)443 b Fo(k)414 b(>)369 b Fq(0)221 b Fo(;)1677 33041 y Fl(wher)-66 b(e)650 b(the)g(c)-66 b(onstants)650 b Fo(c)14334 33240 y Fw(1)14859 33041 y Fl(,)697 b Fo(c)16515 33240 y Fw(2)17691 33041 y Fl(and)20455 32691 y Fq(^)20400 33041 y Fo(\025)p Fl(,)f(de\014ne)-66 b(d)650 b(in)749 b Fq(\(2.5\))651 b Fl(and)788 b Fq(\(2.6\))p Fl(,)697 b(ar)-66 b(e)650 b(obtaine)-66 b(d)649 b(by)h(setting)p 1677 33579 1048 54 v 1677 34647 a Fo(V)658 b Fq(=)369 b Fn(\000)5640 34124 y Fw(1)p 5640 34341 471 54 v 5640 35105 a(4)6243 34647 y Fo(\015)6990 34165 y Fw(2)7981 34647 y Fl(and)465 b Fo(\016)11081 34846 y Fm(n;m)13265 34647 y Fl(indic)-66 b(ates)464 b(the)g(Kr)-66 b(one)g(cker)463 b(symb)-66 b(ol,)464 b Fo(\016)32242 34846 y Fm(n;m)34331 34647 y Fq(=)368 b(0)466 b Fl(if)e Fo(n)369 b Fn(6)p Fq(=)g Fo(m)464 b Fl(and)h Fo(\016)45317 34846 y Fm(n;n)47145 34647 y Fq(=)368 b(1)p Fl(.)-1575 39408 y Fr(3)2152 b(The)716 b(limit)h(of)g(short)f(range)h(p)60 b(oten)-60 b(tials)715 b(in)i(dimension)e(one)-1575 42436 y Fq(The)531 b(main)g(ingredien)-36 b(t)530 b(in)g(the)g(pro)36 b(of)531 b(of)h(Theorem)e(2.1)i(is)f(the)f (analysis)i(of)f(scaling)h(prop)36 b(erties)530 b(of)i(one)-1575 44041 y(dimensional)434 b(Hamiltonians.)579 b(Sp)36 b(eci\014cally)-108 b(,)435 b(w)-36 b(e)433 b(will)i(\014nd)e(the)g(limiting)h(b)36 b(eha)-36 b(viour)434 b(as)g Fo(")368 b Fn(!)i Fq(0)433 b(for)p 14278 46780 1181 54 v 14278 47848 a Fo(H)15459 48047 y Fm(")16318 47848 y Fq(:=)368 b Fn(\000)19532 46949 y Fo(d)20208 46467 y Fw(2)p 19225 47542 1815 54 v 19225 48759 a Fo(ds)20514 48375 y Fw(2)21468 47848 y Fq(+)22907 46949 y Fo(\025)p Fq(\()p Fo(")p Fq(\))p 22907 47542 2380 54 v 23530 48759 a Fo(")24139 48375 y Fw(2)p 25419 46780 1048 54 v 25419 47848 a Fo(V)26467 46373 y Fi(\020)27393 46949 y Fo(s)p 27393 47542 613 54 v 27395 48759 a(")28138 46373 y Fi(\021)29153 47848 y Fo(;)2823 b(s)369 b Fn(2)f Fj(R)221 b Fo(:)-1575 51278 y Fq(Recall)553 b(that)e(this)g(problem)g(is)h(w)-36 b(ell)552 b(studied)e(if)i(the)f(limit)h(is)g(considered,)580 b(roughly)552 b(sp)36 b(eaking,)582 b(around)-1575 52883 y(the)464 b(free)g(op)36 b(erator)464 b([A)-36 b(GHH05].)670 b(The)464 b(case)g(whic)-36 b(h)464 b(in)-36 b(v)g(olv)g(es)465 b(threshold)e(resonances)g(is)i(di\013eren)-36 b(t)462 b(and)i(in)-1575 54488 y(a)456 b(sense)f(similar)h(to)f(appro)-36 b(ximations)456 b(of)g(p)36 b(oin)-36 b(t)455 b(in)-36 b(teractions)455 b(in)g(dimension)g(t)-36 b(w)g(o)455 b(and)g(three)f(men)-36 b(tioned)-1575 56093 y(ab)36 b(o)-36 b(v)g(e.)716 b(It)480 b(is)f(useful)h(to)f(discuss)g(this)g (issue)h(separately)g(b)36 b(ecause)479 b(in)g(our)g(opinion)h(it)f(is) h(of)g(indep)36 b(enden)-36 b(t)-1575 57699 y(in)g(terest)483 b(as)h(appro)-36 b(ximation)483 b(of)i(a)e(class)h(of)g(p)36 b(oin)-36 b(t)483 b(p)36 b(erturbations)483 b(of)h(the)e(Laplacian)i (in)f(dimension)h(one)-1575 59304 y(with)443 b(scaled)g(p)36 b(oten)-36 b(tials.)606 b(Let)442 b(us)h(stress)f(that)h(the)f Fo(\016)25073 58822 y Fp(0)25383 59304 y Fq(-t)-36 b(yp)36 b(e)443 b(in)-36 b(teractions)442 b(do)h(not)f(b)36 b(elong)443 b(to)g(this)g(class)g({)-1575 60909 y(a)463 b(w)-36 b(a)g(y)463 b(to)f(appro)-36 b(ximate)463 b(them)f(b)-36 b(y)462 b(regular)g(p)36 b(oten)-36 b(tials)463 b(can)f(b)36 b(e)462 b(found)g(in)g([ENZ01)q(].)665 b(The)462 b(main)g(idea)h(of) -1575 62514 y(our)433 b(analysis)i(comes)f(from)g(the)f(w)-36 b(ork)435 b([BGW85)q(].)945 64172 y(In)413 b(the)g(follo)-36 b(wing)416 b(w)-36 b(e)413 b(supp)36 b(ose)413 b(that)g(the)g (conditions)g(\(2.4\))i(are)e(satis\014ed.)572 b(As)413 b Fo(\025)p Fq(\()p Fo(")p Fq(\))g(is)g(real)h(analytic)-1575 65777 y(near)353 b(the)f(origin)h(b)-36 b(y)352 b(assumption)g(w)-36 b(e)353 b(can)g(mak)-36 b(e)353 b(the)f(expansion)h(\(2.2\))g(for)g (small)h Fo(")e Fq(more)h(sp)36 b(eci\014c)352 b(writing)19335 69880 y Fo(\025)p Fq(\()p Fo(")p Fq(\))368 b(=)h(1)295 b(+)26205 68220 y Fp(1)25716 68618 y Fi(X)25789 71408 y Fm(n)p Fw(=1)27856 69880 y Fo(\025)28615 70079 y Fm(n)29241 69880 y Fo(")29850 69332 y Fm(n)30697 69880 y Fo(:)18237 b Fq(\(3.1\))24872 74197 y(8)p eop end %%Page: 9 9 TeXDict begin 9 8 bop -1575 7638 a Fq(F)-108 b(or)468 b(ev)-36 b(ery)470 b Fo(")428 b(>)h Fq(0)469 b(the)f(resolv)-36 b(en)g(t)469 b(of)p 17144 6571 1181 54 v 469 w Fo(H)18324 7837 y Fm(")19283 7638 y Fq(is)g(a)g(b)36 b(ounded)467 b(op)36 b(erator-v)-72 b(alued)468 b(analytical)j(function)d(of)i Fo(k)49811 7156 y Fw(2)50805 7638 y Fq(as)-1575 9243 y(long)487 b(as)f Fo(k)3666 8761 y Fw(2)4650 9243 y Fn(2)458 b Fj(C)p Fn(n)p Fj(R)8576 8761 y Fw(+)9364 9243 y Fq(,)499 b Fo(k)10945 8761 y Fw(2)12084 9243 y Fo(=)-805 b Fn(2)458 b Fo(\033)14012 9442 y Fm(p)14541 9243 y Fq(\()p 15047 8176 V Fo(H)16227 9442 y Fm(")16717 9243 y Fq(\))486 b(and)f(Im)443 b Fo(k)503 b(>)458 b Fq(0,)500 b(where)485 b Fo(\033)30994 9442 y Fm(p)31524 9243 y Fq(\()p 32030 8176 V Fo(H)33210 9442 y Fm(")33700 9243 y Fq(\))g(denotes)h(the)f(p)36 b(oin)-36 b(t)486 b(sp)36 b(ectrum)485 b(of)p -1575 9781 V -1575 10848 a Fo(H)-395 11047 y Fm(")95 10848 y Fq(.)579 b(As)433 b(usual)h(w)-36 b(e)434 b(factorize)g(the)f(in)-36 b(teraction)434 b(using)f(the)g(functions)11783 13898 y Fo(v)48 b Fq(\()p Fo(s)p Fq(\))367 b(:=)i Fn(j)p 16563 12831 1048 54 v Fo(V)289 b Fq(\()p Fo(s)p Fq(\))p Fn(j)19604 13350 y Fw(1)p Fm(=)p Fw(2)21292 13898 y Fo(;)1522 b(u)p Fq(\()p Fo(s)p Fq(\))369 b(:=)g(sgn)221 b([)p 30119 12831 V Fo(V)290 b Fq(\()p Fo(s)p Fq(\)])p Fn(j)p 33522 12831 V Fo(V)e Fq(\()p Fo(s)p Fq(\))p Fn(j)36562 13350 y Fw(1)p Fm(=)p Fw(2)38250 13898 y Fo(;)-1575 16949 y Fq(whic)-36 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Fo(uG)19443 26042 y Fm("k)20446 25843 y Fo(v)21123 24767 y Fi(\003)21676 25064 y Fp(\000)p Fw(1)25756 25843 y Fq(Im)443 b Fo(k)414 b Ff(>)369 b Fq(0)p Fo(;)591 b(k)414 b Fn(6)p Fq(=)369 b(0)p Fo(;)591 b(k)36640 25295 y Fw(2)37689 25843 y Fo(=)-804 b Fn(2)368 b Fo(\033)39528 26042 y Fm(p)40058 25843 y Fq(\()p 40564 24776 1568 54 v Fo(H)41642 26042 y Fm(")42131 25843 y Fq(\))-1575 28304 y(and)628 b Fo(A)2124 28503 y Fm(")2614 28304 y Fq(\()p Fo(k)45 b Fq(\))p Fo(;)649 b(C)6288 28503 y Fm(")6778 28304 y Fq(\()p Fo(k)45 b Fq(\))628 b(are)h(de\014ned)e (via)i(their)f(in)-36 b(tegral)629 b(k)-36 b(ernels,)678 b Fo(A)32656 28503 y Fm(")33146 28304 y Fq(\()p Fo(k)45 b Fq(;)221 b Fo(s;)g(s)36763 27822 y Fp(0)37074 28304 y Fq(\))701 b(=)f Fo(G)41019 28503 y Fm(k)41588 28304 y Fq(\()p Fo(s)427 b Fn(\000)h Fo("s)45817 27822 y Fp(0)46127 28304 y Fq(\))p Fo(v)48 b Fq(\()p Fo(s)48429 27822 y Fp(0)48739 28304 y Fq(\))628 b(and)-1575 29909 y Fo(C)-644 30108 y Fm(")-154 29909 y Fq(\()p Fo(k)45 b Fq(;)221 b Fo(s;)g(s)3463 29427 y Fp(0)3774 29909 y Fq(\))638 b(=)f Fo(u)p Fq(\()p Fo(s)p Fq(\))p Fo(G)9958 30108 y Fm(k)10527 29909 y Fq(\()p Fo("s)401 b Fn(\000)i Fo(s)14705 29427 y Fp(0)15016 29909 y Fq(\),)631 b(resp)36 b(ectiv)-36 b(ely)-108 b(.)1053 b(W)-108 b(e)592 b(are)f(in)-36 b(terested)591 b(in)h(the)f(b)36 b(eha)-36 b(viour)591 b(of)i Fo(T)47991 30108 y Fm(")48481 29909 y Fq(\()p Fo(k)45 b Fq(\))591 b(as)-1575 31514 y Fo(")369 b Fn(!)g Fq(0.)579 b(T)-108 b(o)434 b(this)f(aim)h(w)-36 b(e)434 b(de\014ne)e(the)h(op)36 b(erators)434 b Fo(P)615 b Fq(and)433 b Fo(Q)h Fq(b)-36 b(y)15850 35083 y Fo(P)550 b Fq(:=)20293 34184 y(1)p 19112 34777 3012 54 v 19112 35994 a(\()p Fo(v)48 b(;)221 b(u)p Fq(\))22256 35083 y(\()p Fo(v)48 b(;)221 b Fn(\001)g Fq(\))p Fo(u)370 b(;)1522 b(Q)369 b Fq(:=)g(1)296 b Fn(\000)f Fo(P)-1575 38935 y Fq(where)420 b(\()p Fn(\001)221 b Fo(;)g Fn(\001)p Fq(\))421 b(denotes)e(the)h(standard)f(scalar)i(pro)36 b(duct)419 b(in)h Fo(L)28405 38453 y Fw(2)28930 38935 y Fq(\()p Fj(R)p Fq(\);)425 b(let)420 b(us)g(notice)g(that)g(b)-36 b(y)420 b(assumption)f(w)-36 b(e)-1575 40540 y(ha)g(v)g(e)434 b(\()p Fo(v)48 b(;)221 b(u)p Fq(\))369 b(=)6185 39470 y Fi(R)6812 41001 y Fh(R)p 7728 39473 1048 54 v 7728 40540 a Fo(V)289 b Fq(\()p Fo(s)p Fq(\))p Fo(ds)368 b Fn(6)p Fq(=)h(0.)579 b(The)433 b(op)36 b(erator)434 b Fo(T)23702 40739 y Fm(")24192 40540 y Fq(\()p Fo(k)45 b Fq(\))433 b(can)h(b)36 b(e)433 b(written)h(as)g(in)f([BGW85)q(],) 15462 44703 y Fo(T)16224 44902 y Fm(")16715 44703 y Fq(\()p Fo(k)45 b Fq(\))368 b(=)20197 42830 y Fi(\024)20898 44703 y Fq(1)295 b(+)23283 43805 y Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 23283 44398 3455 54 v 24020 45614 a(2)p Fo("k)26871 44703 y(P)476 b Fq(+)29634 44367 y Fi(f)29492 44703 y Fo(M)30750 44902 y Fm(")31240 44703 y Fq(\()p Fo(k)45 b Fq(\))32973 42830 y Fi(\025)33674 43128 y Fp(\000)p Fw(1)49295 44703 y Fq(\(3.3\))-1575 48853 y(where)2395 48517 y Fi(f)2252 48853 y Fo(M)3510 49052 y Fm(")4000 48853 y Fq(\()p Fo(k)g Fq(\))487 b Fn(2)f Fg(B)54 b Fq(\()p Fo(L)10243 48371 y Fw(2)10769 48853 y Fo(;)221 b(L)12236 48371 y Fw(2)12762 48853 y Fq(\),)521 b(the)502 b(Banac)-36 b(h)503 b(space)g(of)g(b)36 b(ounded)502 b(op)36 b(erators)503 b(from)g Fo(L)41493 48371 y Fw(2)42019 48853 y Fq(\()p Fj(R)p Fq(\))g(to)g Fo(L)47037 48371 y Fw(2)47562 48853 y Fq(\()p Fj(R)p Fq(\),)521 b(for)-1575 50628 y(ev)-36 b(ery)517 b Fo(")509 b(>)h Fq(0)516 b(and)g(Im)443 b Fo(k)554 b(>)510 b Fq(0.)826 b(F)-108 b(urthermore,)535 b(if)517 b Fo(e)24818 50146 y Fm(a)p Fp(j\001j)p 26157 49561 1048 54 v 26157 50628 a Fo(V)799 b Fn(2)509 b Fo(L)29994 50146 y Fw(1)30520 50628 y Fq(\()p Fj(R)p Fq(\))516 b(holds)g(for)h (some)g Fo(a)509 b(>)g Fq(0)517 b(then)48973 50292 y Fi(f)48830 50628 y Fo(M)50088 50827 y Fm(")51094 50628 y Fq(is)-1575 52233 y(analytic)442 b(with)e(resp)36 b(ect)440 b(to)g Fo(")g Fq(for)h Fo(")380 b(>)g Fn(\000)p Fo(a=)p Fq(\(2)221 b(Im)444 b Fo(k)45 b Fq(\))440 b(and)g(the)f(follo)-36 b(wing)443 b(series)d(expansion)h(con)-36 b(v)g(erges)441 b(in)-1575 53838 y(the)433 b Fg(B)54 b Fq(\()p Fo(L)3316 53356 y Fw(2)3842 53838 y Fo(;)221 b(L)5309 53356 y Fw(2)5835 53838 y Fq(\)-norm,)18997 56237 y Fi(f)18854 56572 y Fo(M)20112 56771 y Fm(")20603 56572 y Fq(\()p Fo(k)45 b Fq(\))368 b(=)24574 54912 y Fp(1)24085 55310 y Fi(X)24158 58100 y Fm(n)p Fw(=0)26225 56572 y Fo(")26834 56024 y Fm(n)27660 56572 y Fi(e)-938 b Fo(m)28598 56771 y Fm(n)29224 56572 y Fq(\()p Fo(k)45 b Fq(\))221 b Fo(;)-1575 60122 y Fq(where)4978 62524 y Fi(e)-938 b Fo(m)5916 62723 y Fm(n)6542 62524 y Fq(\()p Fo(k)45 b Fq(\))368 b(:=)h(\()p Fo(ik)45 b Fq(\))12562 61975 y Fm(n)13188 62524 y Fo(m)14326 62723 y Fm(n)15247 62524 y Fq(+)16687 61625 y Fo(i\025)17890 61824 y Fm(n)p Fw(+1)19718 61625 y Fq(\()p Fo(v)j(;)221 b(u)p Fq(\))p 16687 62218 6043 54 v 19022 63435 a(2)p Fo(k)22862 62524 y(P)476 b Fq(+)26156 60863 y Fm(n)25483 61262 y Fi(X)25625 64061 y Fm(j)51 b Fw(=0)27623 62524 y Fo(\025)28382 62723 y Fm(n)p Fp(\000)p Fm(j)30171 62524 y Fq(\()p Fo(ik)45 b Fq(\))32348 61975 y Fm(j)32834 62524 y Fo(m)33972 62723 y Fm(j)37060 62524 y Fo(n)370 b Fq(=)e(0)p Fo(;)221 b Fq(1)p Fo(;)g Fq(2)p Fo(;)g(:)g(:)g(:)448 b(:)-1575 66255 y Fq(The)535 b(op)36 b(erators)534 b Fo(m)8190 66454 y Fm(n)9351 66255 y Fq(are)h(Hilb)36 b(ert-Sc)-36 b(hmidt)532 b(and)i(do)h(not)f(dep)36 b(end)533 b(on)i Fo(k)45 b Fq(,)560 b(their)534 b(in)-36 b(tegral)535 b(k)-36 b(ernels)534 b(b)36 b(eing)-1575 67860 y(giv)-36 b(en)434 b(b)-36 b(y)434 b(the)f(expressions)15362 70298 y Fo(m)16500 70497 y Fm(n)17126 70298 y Fq(\()p Fo(s;)221 b(s)19440 69749 y Fp(0)19750 70298 y Fq(\))369 b(=)g Fn(\000)p Fo(u)p Fq(\()p Fo(s)p Fq(\))25758 69399 y Fn(j)p Fo(s)294 b Fn(\000)i Fo(s)28976 68917 y Fp(0)29286 69399 y Fn(j)29655 68917 y Fm(n)p Fw(+1)p 25758 69992 5726 54 v 26095 71209 a Fq(2\()p Fo(n)f Fq(+)g(1\)!)31838 70298 y Fo(v)48 b Fq(\()p Fo(s)33634 69749 y Fp(0)33943 70298 y Fq(\))221 b Fo(:)24872 74197 y Fq(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop -1575 7638 a Fq(The)328 b(b)36 b(eha)-36 b(viour)329 b(of)g Fo(T)9060 7837 y Fm(")9550 7638 y Fq(\()p Fo(k)45 b Fq(\))328 b(as)g Fo(")369 b Fn(!)g Fq(0)329 b(dep)36 b(ends)326 b(strongly)j(on)f(the)g(presence)f (of)i(a)g(zero)f(energy)h(resonance)f(for)-1575 9243 y(the)365 b(Hamiltonian)p 8008 8176 1181 54 v 367 w Fo(H)102 b Fq(.)556 b(Under)365 b(the)g(assumptions)g(\(2.4\))h(the)f(presence)g (of)i(suc)-36 b(h)364 b(a)i(resonance)g(is)g(equiv)-72 b(alen)-36 b(t)-1575 10848 y(to)434 b(the)f(existence)h(of)g(a)g (function)f Fo(')16301 11047 y Fw(0)17196 10848 y Fn(2)369 b Fo(L)19336 10366 y Fw(2)19862 10848 y Fq(\()p Fj(R)p Fq(\))433 b(whic)-36 b(h)433 b(satis\014es)h(the)f(relation)19604 13756 y Fo(')20456 13955 y Fw(0)21278 13756 y Fq(+)294 b Fo(QM)24872 13955 y Fw(0)25399 13756 y Fo(Q')27281 13955 y Fw(0)28176 13756 y Fq(=)368 b(0)221 b Fo(:)18507 b Fq(\(3.4\))-1575 16664 y(F)-108 b(urthermore,)477 b(if)470 b(suc)-36 b(h)469 b(a)h Fo(')12534 16863 y Fw(0)13529 16664 y Fq(exists,)479 b(it)470 b(can)f(b)36 b(e)469 b(c)-36 b(hosen)469 b(real,)480 b(in)469 b(whic)-36 b(h)469 b(case)h(the)f(constan)-36 b(ts)469 b Fo(c)46953 16863 y Fw(1)47478 16664 y Fq(,)479 b Fo(c)48878 16863 y Fw(2)49873 16664 y Fq(and)-1521 17918 y(^)-1575 18269 y Fo(\025)433 b Fq(de\014ned)g(in)g(\(2.5\))h(and)f(\(2.6\))q(,)h(resp)36 b(ectiv)-36 b(ely)-108 b(,)434 b(are)g(related)f(to)h Fo(')31006 18468 y Fw(0)31966 18269 y Fq(b)-36 b(y)9985 21909 y Fo(c)10545 22108 y Fw(1)11440 21909 y Fq(=)12953 21010 y(\()p Fo(v)48 b(;)221 b(m)15856 21209 y Fw(0)16382 21010 y Fo(')17234 21209 y Fw(0)17759 21010 y Fq(\))p 12953 21603 5313 54 v 14104 22820 a(\()p Fo(v)48 b(;)221 b(u)p Fq(\))18767 21909 y Fo(;)1522 b(c)21210 22108 y Fw(2)22105 21909 y Fq(=)23618 21010 y(1)p 23618 21603 651 54 v 23618 22820 a(2)24402 21909 y(\(\()p Fn(\001)p Fq(\))p Fo(v)48 b(;)221 b(')28400 22108 y Fw(0)28925 21909 y Fq(\))369 b Fo(;)31737 21558 y Fq(^)31683 21909 y Fo(\025)g Fq(=)f Fo(\025)34950 22108 y Fw(1)35476 21909 y Fq(\()209 b(~)-859 b Fo(')36834 22108 y Fw(0)37360 21909 y Fo(;)221 b(')38794 22108 y Fw(0)39320 21909 y Fq(\))g Fo(:)-1575 25739 y Fq(with)646 b(~)-860 b Fo(')2242 25938 y Fw(0)2768 25739 y Fq(\()p Fo(s)p Fq(\))373 b(:=)h(sgn)221 b([)p 8981 24672 1048 54 v Fo(V)290 b Fq(\()p Fo(s)p Fq(\)])p Fo(')12867 25938 y Fw(0)13392 25739 y Fq(,)437 b(and)f Fo(u)p Fq(\()p Fo(s)p Fq(\))p Fo( )19933 25938 y Fm(r)20438 25739 y Fq(\()p Fo(s)p Fq(\))373 b(=)g Fn(\000)p Fo(')25706 25938 y Fw(0)26232 25739 y Fq(\()p Fo(s)p Fq(\))436 b(holds)g(a.e.)587 b({)436 b(cf.)h(Lemma)873 b(2.2.)587 b(in)436 b([BGW85)q(].)-1575 27344 y(Let)d(us)h(in)-36 b(tro)36 b(duce)432 b(the)h(op)36 b(erator)15903 31941 y Fo(P)16741 32140 y Fw(0)17637 31941 y Fq(:=)19379 29217 y Fi(8)19379 30413 y(<)19379 32804 y(:)20781 30139 y Fq(0)5441 b(in)434 b(the)f(case)h(I)20913 32060 y(\()209 b(~)-859 b Fo(')22271 32259 y Fw(0)22797 32060 y Fo(;)221 b Fn(\001)p Fq(\))p Fo(')25106 32259 y Fw(0)p 20913 32653 4720 54 v 21098 33869 a Fq(\()209 b(~)-859 b Fo(')22456 34068 y Fw(0)22982 33869 y Fo(;)221 b(')24416 34068 y Fw(0)24942 33869 y Fq(\))26872 32958 y(in)434 b(the)f(case)h(I)36 b(I)-1575 36611 y(and)462 b(the)g(complemen)-36 b(tary)463 b(pro)72 b(jection)463 b Fo(Q)19623 36810 y Fw(0)20568 36611 y Fq(:=)418 b(1)315 b Fn(\000)g Fo(P)25510 36810 y Fw(0)26036 36611 y Fq(.)666 b(F)-108 b(rom)462 b(Lemma)g(3.1)i(in)e ([BGW85)q(])h(w)-36 b(e)463 b(infer)g(that)-1575 38216 y(for)434 b Fo(")369 b Fn(2)g Fj(C)p Fn(nf)p Fq(0)p Fn(g)434 b Fq(small)h(enough)e(the)g(follo)-36 b(wing)436 b(norm)d(con)-36 b(v)g(ergen)g(t)433 b(series)h(expansion)g(holds,)13346 42136 y([1)296 b(+)f Fo(Qm)18128 42335 y Fw(0)18654 42136 y Fo(Q)g Fq(+)g Fo(")p Fq(])22256 41588 y Fp(\000)p Fw(1)23882 42136 y Fq(=)25396 41237 y Fo(P)26234 41436 y Fw(0)p 25396 41831 1365 54 v 25773 43047 a Fo(")27188 42136 y Fq(+)28984 40476 y Fp(1)28495 40874 y Fi(X)28568 43664 y Fm(n)p Fw(=0)30413 42136 y Fq(\()p Fn(\000)p Fo(")p Fq(\))33067 41588 y Fm(n)33693 42136 y Fo(T)34636 41586 y Fm(n)p Fw(+1)34455 42506 y Fm(r)26 b(ed)36686 42136 y Fo(;)-1575 46263 y Fq(where)424 b Fo(T)2935 46462 y Fm(r)26 b(ed)4731 46263 y Fq(=)369 b(u)221 b Fn(\000)g Fq(lim)10117 46462 y Fm(")p Fp(!)p Fw(0)12018 46263 y Fq([1)277 b(+)e Fo(Qm)16761 46462 y Fw(0)17287 46263 y Fo(Q)h Fq(+)f Fo(")p Fq(])20850 45780 y Fp(\000)p Fw(1)22108 46263 y Fo(Q)23138 46462 y Fw(0)24088 46263 y Fq(is)424 b(the)g(reduced)f(resolv)-36 b(en)g(t.)575 b(The)424 b(follo)-36 b(wing)427 b(claim)e(is)f(a)-1575 47868 y(generalization) 435 b(of)f(Theorem)g(3.1)h(in)e([BGW85)q(])-1575 50558 y Fd(Lemma)659 b(3.1.)625 b Fl(Supp)-66 b(ose)594 b(that)p 14690 49490 1048 54 v 592 w Fo(V)882 b Fl(satis\014es)593 b(the)g(c)-66 b(onditions)701 b Fq(\(2.4\))593 b Fl(and)g(take)f Fo(\025)p Fq(\()p Fo(")p Fq(\))g Fl(r)-66 b(e)g(al)592 b(analytic)g(ne)-66 b(ar)-1575 52163 y(the)642 b(origin)e(and)h(with)h (the)f(series)h(exp)-66 b(ansion)739 b Fq(\(3.1\))q Fl(.)1128 b(Assume)641 b(that)h Fo(k)35658 51681 y Fw(2)37035 52163 y Fo(=)-805 b Fn(2)696 b Fo(\033)39201 52362 y Fm(p)39730 52163 y Fq(\()p 40236 51096 1181 54 v Fo(H)41416 52362 y Fm(")41906 52163 y Fq(\))p Fl(,)685 b Fq(Im)443 b Fo(k)742 b(>)696 b Fq(0)642 b Fl(and)-1575 53918 y(additional)66 b(ly,)442 b(that)436 b(in)f(the)h(c)-66 b(ase)437 b(II)e Fo(k)414 b Fn(6)p Fq(=)369 b Fn(\000)p Fo(i)20432 53567 y Fq(^)20378 53918 y Fo(\025)o(=)p Fq(\(2\()p Fo(c)24008 53436 y Fw(2)24008 54246 y(1)24766 53918 y Fq(+)231 b Fo(c)26569 53436 y Fw(2)26569 54246 y(2)27095 53918 y Fq(\)\))p Fl(.)587 b(Then)436 b(for)g(al)66 b(l)438 b Fo(")e Fl(smal)66 b(l)437 b(enough)f(the)g(op)-66 b(er)g(ator)-1575 55523 y Fo(T)-813 55722 y Fm(")-323 55523 y Fq(\()p Fo(k)45 b Fq(\))465 b Fl(has)h(the)e(fol)66 b(lowing)465 b(norm-c)-66 b(onver)g(gent)461 b(series)k(exp)-66 b(ansions)19436 59443 y Fo(T)20198 59642 y Fm(")20689 59443 y Fq(\()p Fo(k)45 b Fq(\))368 b(=)24660 57782 y Fp(1)24171 58181 y Fi(X)24242 60970 y Fm(n)p Fw(=)p Fm(p)26311 59443 y Fo(")26920 58894 y Fm(n)27546 59443 y Fo(t)28016 59642 y Fm(n)28642 59443 y Fq(\()p Fo(k)45 b Fq(\))221 b Fo(;)18338 b Fq(\(3.5\))-1575 63611 y Fl(wher)-66 b(e)465 b Fo(p)369 b Fq(=)f(0)465 b Fl(in)f(the)h(c)-66 b(ase)465 b(I)f(and)h Fo(p)369 b Fq(=)f(1)466 b Fl(in)e(the)g(c)-66 b(ase)465 b(II.)f(Mor)-66 b(e)g(over,)462 b(we)k(have)-924 66626 y(\(i\))f(In)f(the)g(c)-66 b(ase)465 b(I)15074 68231 y Fq(\()p Fo(v)48 b(;)221 b(t)17309 68430 y Fw(0)17834 68231 y Fo(u)p Fq(\))369 b(=)g(0)221 b(;)22653 67155 y Fi(\000)23262 68231 y Fq(\()p Fn(\001)p Fq(\))p Fo(v)48 b(;)221 b(t)26372 68430 y Fw(0)26897 68231 y Fo(u)27637 67155 y Fi(\001)28615 68231 y Fq(=)29996 67155 y Fi(\000)30605 68231 y Fo(v)48 b(;)221 b(t)32334 68430 y Fw(0)32859 68231 y Fq(\()p Fn(\001)p Fq(\))p Fo(u)34980 67155 y Fi(\001)35958 68231 y Fq(=)369 b(0)221 b(;)10724 b(\(3.6\))22229 70545 y(\()p Fo(v)48 b(;)221 b(t)24464 70744 y Fw(1)24990 70545 y Fo(u)p Fq(\))369 b(=)f Fn(\000)p Fq(2)p Fo(ik)267 b(:)17879 b Fq(\(3.7\))24547 74197 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop -924 7638 a Fl(\(ii\))464 b(In)g(the)h(c)-66 b(ase)464 b(II)11577 10864 y Fo(t)12047 11063 y Fp(\000)p Fw(1)13304 10864 y Fo(u)370 b Fq(=)e Fo(t)16264 10316 y Fp(\003)16264 11193 y(\000)p Fw(1)17522 10864 y Fo(v)416 b Fq(=)369 b(0)221 b(;)21771 9788 y Fi(\000)22380 10864 y Fq(\()p Fn(\001)p Fq(\))p Fo(v)48 b(;)221 b(t)25490 11063 y Fp(\000)p Fw(1)26747 10864 y Fq(\()p Fn(\001)p Fq(\))p Fo(u)28868 9788 y Fi(\001)29846 10864 y Fq(=)368 b Fn(\000)35783 9966 y Fq(4)p Fo(ic)37437 9484 y Fw(2)37437 10294 y(2)p 32392 10559 8961 54 v 32392 11991 a Fq(2)p Fo(k)45 b Fq(\()p Fo(c)34829 11534 y Fw(2)34829 12317 y(1)35650 11991 y Fq(+)295 b Fo(c)37517 11534 y Fw(2)37517 12317 y(2)38043 11991 y Fq(\))g(+)f Fo(i)40648 11641 y Fq(^)40594 11991 y Fo(\025)41707 10864 y Fq(;)7227 b(\(3.8\))10786 15087 y(\()p Fo(v)48 b(;)221 b(t)13021 15286 y Fw(0)13546 15087 y Fo(u)p Fq(\))369 b(=)g(0)221 b(;)18365 14011 y Fi(\000)18974 15087 y Fq(\()p Fn(\001)p Fq(\))p Fo(v)48 b(;)221 b(t)22084 15286 y Fw(0)22609 15087 y Fo(u)23349 14011 y Fi(\001)24327 15087 y Fq(=)25708 14011 y Fi(\000)26317 15087 y Fo(v)48 b(;)221 b(t)28046 15286 y Fw(0)28571 15087 y Fq(\()p Fn(\001)p Fq(\))p Fo(u)30692 14011 y Fi(\001)31670 15087 y Fq(=)35893 14188 y(4)p Fo(k)45 b(c)37824 14387 y Fw(1)38350 14188 y Fo(c)38910 14387 y Fw(2)p 33184 14781 V 33184 16214 a Fq(2)p Fo(k)g Fq(\()p Fo(c)35621 15756 y Fw(2)35621 16540 y(1)36442 16214 y Fq(+)294 b Fo(c)38308 15756 y Fw(2)38308 16540 y(2)38834 16214 y Fq(\))h(+)g Fo(i)41440 15863 y Fq(^)41386 16214 y Fo(\025)42498 15087 y Fq(;)6436 b(\(3.9\))17616 19335 y(\()p Fo(v)48 b(;)221 b(t)19851 19534 y Fw(1)20376 19335 y Fo(u)p Fq(\))370 b(=)e Fn(\000)p Fq(2)p Fo(ik)28203 18436 y Fq(2)p Fo(k)45 b(c)30134 17954 y Fw(2)30134 18765 y(2)30955 18436 y Fq(+)295 b Fo(i)32760 18086 y Fq(^)32706 18436 y Fo(\025)p 26352 19030 V 26352 20462 a Fq(2)p Fo(k)45 b Fq(\()p Fo(c)28789 20004 y Fw(2)28789 20788 y(1)29611 20462 y Fq(+)295 b Fo(c)31478 20004 y Fw(2)31478 20788 y(2)32004 20462 y Fq(\))g(+)f Fo(i)34609 20111 y Fq(^)34555 20462 y Fo(\025)35668 19335 y(:)12616 b Fq(\(3.10\))-1575 22773 y Fl(Pr)-66 b(o)g(of.)649 b Fq(W)-108 b(e)409 b(pro)-36 b(v)g(e)409 b(the)g(lemma)g(\014rst)f(in)h(the)f (case)i(I)36 b(I.)410 b(Let)e(us)h(assume)g(that)f(the)h(equation)g (\(3.4\))h(is)f(solv)-36 b(ed)-1575 24378 y(b)g(y)434 b Fo(')1084 24577 y Fw(0)1979 24378 y Fn(2)368 b Fo(L)4118 23896 y Fw(2)4644 24378 y Fq(\()p Fj(R)p Fq(\).)578 b(By)434 b(using)g(the)f(relation)h([BGW85)q(])14019 27799 y(1)296 b(+)16405 26900 y Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 16405 27493 3455 54 v 17142 28710 a(2)p Fo("k)19992 27799 y(P)550 b Fq(=)22761 25926 y Fi(\024)23462 27799 y Fo(Q)295 b Fq(+)28755 26900 y(2)p Fo("k)p 26227 27493 7037 54 v 26227 28710 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))33397 27799 y Fo(P)34416 25926 y Fi(\025)35117 26223 y Fp(\000)p Fw(1)-1575 31000 y Fq(in)434 b(form)-36 b(ula)434 b(\(3.3\))g(w)-36 b(e)434 b(obtain)7546 34421 y Fo(T)8308 34620 y Fm(")9167 34421 y Fq(=)10547 32548 y Fi(\024)11249 34421 y Fq(1)295 b(+)g Fo(Q)14674 34085 y Fi(f)14531 34421 y Fo(M)15789 34620 y Fm(")16574 34421 y Fq(+)20542 33522 y(2)p Fo("k)p 18014 34115 V 18014 35332 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))25184 34421 y Fo(P)26345 34085 y Fi(f)26203 34421 y Fo(M)27461 34620 y Fm(")27951 32548 y Fi(\025)28652 32845 y Fp(\000)p Fw(1)29910 32548 y Fi(\024)30611 34421 y Fo(Q)295 b Fq(+)35904 33522 y(2)p Fo("k)p 33376 34115 V 33376 35332 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))40545 34421 y Fo(P)41564 32548 y Fi(\025)42487 34421 y Fo(:)5797 b Fq(\(3.11\))-1575 37622 y(Since)433 b Fo(Q)200 b Fi(e)-938 b Fo(m)3989 37821 y Fw(0)4884 37622 y Fq(=)369 b Fo(Qm)8433 37821 y Fw(0)9392 37622 y Fq(the)433 b(follo)-36 b(wing)436 b(norm)d(con)-36 b(v)g(ergen)g(t)433 b(series)h(expansion)g(holds)f([BGW85)q(])9068 39995 y Fi(\000)9677 41071 y Fq(1)296 b(+)f Fo(Q)200 b Fi(e)-938 b Fo(m)14098 41270 y Fw(0)14918 41071 y Fq(+)295 b Fo(\016)16851 39995 y Fi(\001)17460 40293 y Fp(\000)p Fw(1)19086 41071 y Fq(=)20467 39198 y Fi(\024)21301 40173 y Fo(P)22139 40372 y Fw(0)p 21301 40766 1365 54 v 21670 41982 a Fo(\016)23093 41071 y Fq(+)24889 39411 y Fp(1)24400 39809 y Fi(X)24473 42599 y Fm(n)p Fw(=0)26319 41071 y Fq(\()p Fn(\000)p Fo(\016)50 b Fq(\))28990 40523 y Fm(n)29616 41071 y Fo(T)30559 40521 y Fm(n)p Fw(+1)30378 41441 y Fm(r)26 b(ed)32387 39198 y Fi(\025\024)33789 41071 y Fq(1)296 b Fn(\000)36196 40173 y Fo(Qm)38364 40372 y Fw(0)38890 40173 y Fo(P)p 36196 40766 3713 54 v 36613 41982 a Fq(1)g(+)f Fo(\016)40042 39198 y Fi(\025)40964 41071 y Fo(:)7320 b Fq(\(3.12\))-1575 44597 y(T)-108 b(aking)470 b(in)-36 b(to)469 b(accoun)-36 b(t)469 b(that)f Fo(P)14001 44796 y Fw(0)14847 44597 y Fn(\000)319 b Fo(P)17037 44796 y Fw(0)17564 44597 y Fo(Qm)19732 44796 y Fw(0)20257 44597 y Fo(P)611 b Fq(=)429 b Fn(\000)p Fo(P)25018 44796 y Fw(0)25544 44597 y Fo(m)26682 44796 y Fw(0)27677 44597 y Fq(and)468 b(p)36 b(erforming)469 b(a)h(simple)f(manipulation,)478 b(w)-36 b(e)-1575 46202 y(can)434 b(set)f Fo(\016)419 b Fq(=)369 b Fn(\000)p Fq(2)p Fo(i"k)45 b(=)p Fq(\()p Fo(v)j(;)221 b(u)p Fq(\))434 b(and)f(use)g(relation)h(\(3.12\))g(in)g (form)-36 b(ula)434 b(\(3.11\))h(to)e(obtain)4724 49623 y Fo(T)5486 49822 y Fm(")6345 49623 y Fq(=)7357 47750 y Fi(\024)8058 49623 y Fq(1)295 b(+)10310 47750 y Fi(\022)11421 48724 y Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 11421 49318 3012 54 v 11714 50534 a(2)p Fo(i"k)14564 49623 y(P)15402 49822 y Fw(0)15929 49623 y Fo(m)17067 49822 y Fw(0)17887 49623 y Fq(+)295 b Fo(D)20274 49822 y Fm(")20764 47750 y Fi(\023\022)23146 48724 y Fq(2)p Fo(i"k)p 22852 49318 V 22852 50534 a Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))26291 49623 y(+)295 b Fo(Q)28771 49287 y Fi(f)28628 49623 y Fo(M)30025 49075 y Fw(\(1\))29886 49951 y Fm(")31578 49623 y Fq(+)35546 48724 y(2)p Fo("k)p 33018 49318 7037 54 v 33018 50534 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))40188 49623 y Fo(P)41349 49287 y Fi(f)41207 49623 y Fo(M)42465 49822 y Fm(")42955 47750 y Fi(\023\025)44634 48048 y Fp(\000)p Fw(1)7652 53254 y Fn(\002)8980 51381 y Fi(\024)9814 52355 y Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 9814 52948 3012 54 v 10108 54165 a(2)p Fo(i"k)12958 53254 y(P)13796 53453 y Fw(0)14322 53254 y Fo(m)15460 53453 y Fw(0)16281 53254 y Fq(+)295 b Fo(D)18668 53453 y Fm(")19157 51381 y Fi(\025\024)20559 53254 y Fo(Q)h Fq(+)25853 52355 y(2)p Fo("k)p 23324 52948 7037 54 v 23324 54165 a Fq(2)p Fo("k)341 b Fq(+)294 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))30494 53254 y Fo(P)31513 51381 y Fi(\025)32436 53254 y Fo(;)-1575 56381 y Fq(where)3964 59498 y Fo(D)5044 59697 y Fm(")5534 59498 y Fq(\()p Fo(k)45 b Fq(\))368 b(:=)12039 58600 y(2)p Fo("k)p 9510 59193 V 9510 60410 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))16680 59498 y Fo(P)17518 59697 y Fw(0)18044 59498 y Fo(Qm)20212 59697 y Fw(0)20738 59498 y Fo(P)476 b Fq(+)23848 57838 y Fp(1)23359 58236 y Fi(X)23431 61026 y Fm(n)p Fw(=0)25499 57625 y Fi(\022)26903 58600 y Fq(2)p Fo(i"k)p 26609 59193 3012 54 v 26609 60410 a Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))29753 57625 y Fi(\023)30731 57923 y Fm(n)31357 59498 y Fo(T)32300 58949 y Fm(n)p Fw(+1)32119 59868 y Fm(r)26 b(ed)34129 57625 y Fi(\024)34830 59498 y Fq(1)296 b Fn(\000)39560 58600 y Fo(Qm)41728 58799 y Fw(0)42254 58600 y Fo(P)p 37237 59193 8360 54 v 37237 60410 a Fq(1)f Fn(\000)h Fq(2)p Fo(i"k)45 b(=)p Fq(\()p Fo(v)j(;)221 b(u)p Fq(\))45729 57625 y Fi(\025)-1575 64276 y Fq(and)1280 63940 y Fi(f)1137 64276 y Fo(M)2534 63728 y Fw(\()p Fm(j)51 b Fw(\))2395 64604 y Fm(")3753 64276 y Fq(\()p Fo(k)45 b Fq(\))679 b(=)8346 62616 y Fp(1)7857 63014 y Fi(X)7949 65814 y Fm(n)p Fw(=)p Fm(j)9997 64276 y Fo(")10606 63728 y Fm(n)11432 64276 y Fi(e)-938 b Fo(m)12370 64475 y Fm(n)12996 64276 y Fq(\()p Fo(k)45 b Fq(\))616 b(with)g Fo(j)755 b Fq(=)679 b(1)p Fo(;)221 b Fq(2)p Fo(;)g(:)g(:)g(:)684 b Fq(.)1126 b(After)617 b(some)f(computation)g(w)-36 b(e)617 b(arriv)-36 b(e)617 b(at)f(the)-1575 67152 y(follo)-36 b(wing)436 b(form)-36 b(ula)434 b(for)g(the)f(op)36 b(erator)434 b Fo(T)18914 67351 y Fm(")19404 67152 y Fq(,)6742 70279 y Fo(T)7504 70478 y Fm(")8363 70279 y Fq(=)9744 69203 y Fi(\002)10297 70279 y Fq(1)296 b(+)f Fo(P)13388 70478 y Fw(0)14181 69943 y Fi(e)13914 70279 y Fo(B)362 b Fq(+)295 b Fo(E)17534 70478 y Fm(")18024 69203 y Fi(\003)18577 69500 y Fp(\000)p Fw(1)19835 68406 y Fi(\024)20669 69380 y Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 20669 69973 3012 54 v 20962 71190 a(2)p Fo(i"k)23813 70279 y(P)24651 70478 y Fw(0)25177 70279 y Fo(m)26315 70478 y Fw(0)27135 70279 y Fq(+)295 b Fo(D)29522 70478 y Fm(")30012 68406 y Fi(\025\024)31414 70279 y Fo(Q)h Fq(+)36708 69380 y(2)p Fo("k)p 34179 69973 7037 54 v 34179 71190 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))41349 70279 y Fo(P)42368 68406 y Fi(\025)43290 70279 y Fo(;)4994 b Fq(\(3.13\))24547 74197 y(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop -1575 7638 a Fq(where)13028 9308 y Fi(e)12761 9644 y Fo(B)67 b Fq(\()p Fo(k)45 b Fq(\))369 b(=)f Fo(m)18436 9843 y Fw(0)19257 9644 y Fq(+)20697 8745 y(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 20697 9338 3012 54 v 21295 10555 a(2)p Fo(ik)23841 9644 y(m)24979 9843 y Fw(0)25504 9644 y Fo(Q)200 b Fi(e)-938 b Fo(m)27672 9843 y Fw(1)28198 9644 y Fq(\()p Fo(k)45 b Fq(\))295 b Fn(\000)g Fo(m)32692 9843 y Fw(0)33218 9644 y Fo(P)380 b Fi(e)-937 b Fo(m)35375 9843 y Fw(0)35900 9644 y Fq(\()p Fo(k)45 b Fq(\))-1575 12238 y(and)-196 15411 y Fo(E)767 15610 y Fm(")1257 15411 y Fq(\()p Fo(k)g Fq(\))368 b(=)4503 14512 y(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 4503 15105 V 4796 16322 a(2)p Fo(i"k)7647 15411 y(P)8485 15610 y Fw(0)9011 15411 y Fo(m)10149 15610 y Fw(0)10674 15411 y Fo(Q)11847 15075 y Fi(f)11704 15411 y Fo(M)13101 14862 y Fw(\(2\))12962 15739 y Fm(")14359 15411 y Fq(\()p Fo(k)45 b Fq(\))295 b(+)20355 14512 y(2)p Fo("k)p 17827 15105 7037 54 v 17827 16322 a Fq(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))24996 15411 y Fo(P)25834 15610 y Fw(0)26361 15411 y Fo(m)27499 15610 y Fw(0)28024 15411 y Fo(P)381 b Fi(e)-938 b Fo(m)30181 15610 y Fw(0)30707 15411 y Fq(\()p Fo(k)45 b Fq(\))294 b Fn(\000)35987 14512 y Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 34196 15105 V 34196 16322 a(2)p Fo("k)340 b Fq(+)295 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))41365 15411 y Fo(P)42203 15610 y Fw(0)42730 15411 y Fo(m)43868 15610 y Fw(0)44393 15411 y Fo(P)45555 15075 y Fi(f)45412 15411 y Fo(M)46809 14862 y Fw(\(1\))46670 15739 y Fm(")48067 15411 y Fq(\()p Fo(k)45 b Fq(\)+)4665 19023 y(+)295 b Fo(D)7052 19222 y Fm(")7542 19023 y Fq(\()p Fo(k)45 b Fq(\))9275 17150 y Fi(\022)10679 18124 y Fq(2)p Fo(i"k)p 10385 18717 3012 54 v 10385 19934 a Fq(\()p Fo(v)j(;)221 b(u)p Fq(\))13824 19023 y(+)295 b Fo(Q)16304 18687 y Fi(f)16161 19023 y Fo(M)17558 18474 y Fw(\(1\))17419 19351 y Fm(")18816 19023 y Fq(\()p Fo(k)45 b Fq(\))295 b(+)24812 18124 y(2)p Fo("k)p 22283 18717 7037 54 v 22283 19934 a Fq(2)p Fo("k)341 b Fq(+)294 b Fo(i)p Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))29453 19023 y Fo(P)30615 18687 y Fi(f)30472 19023 y Fo(M)31730 19222 y Fm(")32220 19023 y Fq(\()p Fo(k)45 b Fq(\))33953 17150 y Fi(\023)35152 19023 y Fo(:)-1575 22857 y Fq(The)603 b(op)36 b(erator)6943 22521 y Fi(e)6676 22857 y Fo(B)67 b Fq(\()p Fo(k)45 b Fq(\))603 b(do)36 b(es)603 b(not)g(dep)36 b(end)601 b(on)i Fo(")g Fq(while)g Fo(D)28170 23056 y Fm(")28660 22857 y Fq(\()p Fo(k)45 b Fq(\))603 b(and)f Fo(E)34657 23056 y Fm(")35147 22857 y Fq(\()p Fo(k)45 b Fq(\))602 b(ha)-36 b(v)g(e)603 b(with)g(resp)36 b(ect)603 b(to)g(the)-1575 24462 y(parameter)433 b(the)h(follo)-36 b(wing)435 b(norm)e(con)-36 b(v)g(ergen)g(t)434 b(series)g(expansions)12413 28173 y Fo(D)13493 28372 y Fm(")13982 28173 y Fq(\()p Fo(k)45 b Fq(\))369 b(=)17953 26512 y Fp(1)17465 26911 y Fi(X)17537 29700 y Fm(n)p Fw(=0)19605 28173 y Fo(")20214 27624 y Fm(n)20840 28173 y Fo(d)21516 28372 y Fm(n)22142 28173 y Fq(\()p Fo(k)45 b Fq(\))368 b Fo(;)1523 b(E)27090 28372 y Fm(")27579 28173 y Fq(\()p Fo(k)45 b Fq(\))369 b(=)31551 26512 y Fp(1)31062 26911 y Fi(X)31134 29700 y Fm(n)p Fw(=1)33202 28173 y Fo(")33811 27624 y Fm(n)34437 28173 y Fo(e)35040 28372 y Fm(n)35666 28173 y Fq(\()p Fo(k)45 b Fq(\))221 b Fo(:)10664 b Fq(\(3.14\))-1575 32033 y(Let)433 b(us)h(notice)f(that)12347 33439 y(\()209 b(~)-859 b Fo(')13705 33638 y Fw(0)14230 33439 y Fo(;)15080 33103 y Fi(e)14812 33439 y Fo(B)68 b(')16720 33638 y Fw(0)17246 33439 y Fq(\))p 12347 34032 5406 54 v 12874 35249 a(\()209 b(~)-859 b Fo(')14232 35448 y Fw(0)14758 35249 y Fo(;)221 b(')16192 35448 y Fw(0)16719 35249 y Fq(\))18254 34337 y(=)368 b Fn(\000)p Fq(1)296 b Fn(\000)23744 33439 y Fq(\()p Fo(v)48 b(;)221 b(u)p Fq(\))p 23074 34032 4351 54 v 23074 35249 a(\()209 b(~)-859 b Fo(')24432 35448 y Fw(0)24958 35249 y Fo(;)221 b(')26392 35448 y Fw(0)26918 35249 y Fq(\))27557 34337 y(\()p Fo(c)28623 33789 y Fw(2)28623 34666 y(1)29444 34337 y Fq(+)295 b Fo(c)31311 33789 y Fw(2)31311 34666 y(2)32131 34337 y Fq(+)g Fo(i)33936 33987 y Fq(^)33882 34337 y Fo(\025=)p Fq(\(2)p Fo(k)45 b Fq(\)\))-1575 37637 y(and)408 b Fo(P)1767 37836 y Fw(0)2560 37301 y Fi(e)2293 37637 y Fo(B)67 b(P)4186 37836 y Fw(0)5081 37637 y Fq(=)369 b(\()209 b(~)-859 b Fo(')7820 37836 y Fw(0)8345 37637 y Fo(;)9195 37301 y Fi(e)8927 37637 y Fo(B)68 b(')10835 37836 y Fw(0)11361 37637 y Fq(\))p Fo(=)p Fq(\()209 b(~)-859 b Fo(')13875 37836 y Fw(0)14401 37637 y Fo(;)221 b(')15835 37836 y Fw(0)16361 37637 y Fq(\))p Fo(P)17705 37836 y Fw(0)18231 37637 y Fq(.)570 b(In)408 b(a)g(similar)h(w)-36 b(a)g(y)409 b(as)f(in)g([BGW85)q(])g(w) -36 b(e)408 b(can)g(explicitly)i(ev)-72 b(aluate)-1575 39375 y(for)434 b Fo(k)414 b Fn(6)p Fq(=)369 b Fn(\000)p Fo(i)4414 39024 y Fq(^)4360 39375 y Fo(\025=)p Fq(\(2\()p Fo(c)7991 38893 y Fw(2)7991 39703 y(1)8812 39375 y Fq(+)294 b Fo(c)10678 38893 y Fw(2)10678 39703 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