Content-Type: multipart/mixed; boundary="-------------0809191523627" This is a multi-part message in MIME format. ---------------0809191523627 Content-Type: text/plain; name="08-168.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="08-168.keywords" solvability conditions, non Fredholm operators, elliptic problems ---------------0809191523627 Content-Type: application/postscript; name="fredholm.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="fredholm.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: fredholm.dvi %%Pages: 22 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMBX12 CMR12 CMR8 CMMI12 CMSY8 CMSY10 MSBM10 CMMI8 %%+ CMEX10 MSBM7 CMMI6 CMSY6 CMR6 CMTI12 CMR10 MSAM10 TeX-cmex8 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o fredholm.ps fredholm.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2008.08.13:1833 %%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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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 readonly def /FontBBox{8 -463 1331 1003}readonly 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 48 /zero put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec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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 14 /delta put dup 18 /theta put dup 24 /xi put dup 25 /pi put dup 27 /sigma put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 67 /C put dup 72 /H put dup 73 /I put dup 76 /L 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 86 /V put dup 97 /a 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi 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 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 67 /C put dup 69 /E put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 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 readonly def /FontBBox{-36 -251 1103 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. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 49 /infinity put readonly def /FontBBox{-4 -948 1329 786}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 11 /alpha put dup 14 /delta put dup 27 /sigma put dup 99 /c put dup 100 /d put dup 106 /j put dup 109 /m put dup 110 /n put dup 112 /p put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 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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 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 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 98 /hatwide 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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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 14 /delta put dup 18 /theta put dup 24 /xi put dup 27 /sigma put dup 33 /omega put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 72 /H put dup 76 /L put dup 78 /N put dup 82 /R put dup 83 /S 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 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 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec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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 readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 D10F04E2C2822D3E73F25B81C424627D3D9A158EAB554233A25D3C6849ABA86F 1F25C1667CB57D2E79B7803083CB7CC0616467F68450D9A3FEAB534EB9721003 DBFEEFD050F3AC3492F5C74162A9A531ECEC0F47610B4940E946D21CAA771D30 A6C27ECBA11708CC46C62396BF9D1990D579D0C394899D24FE7A4382EA18E7E1 160E7283AF5BE17254790628E79FCC206F28B5566075B3A5697D5209062544FF D85FD89D6F43D6588B242AB2666B5D2861CD38A8CE676503EDFAE84D12A71E77 8405E468FE391F4F3F50D2C57ED55512036B0DB8E76A7EF413ED08673E56DE2C 16A3B65CD478433C0D2F9FEC4E662D54DAA43CFA6957D2A9AF8979BE06F70B68 ED4C8C493D6DAC4971A3F1D010A7726D084EC1074FECD7D12D72AE16C26194AF 21AF5774D9B860EEE8608D34F150092F09C19959BAA670022B9A9F263CD391E3 74DD1D1B4CD4D75273CAA4E37F68C631723E08FA35AD34C0AFB4621AE6689861 854D16CE1C375FD159A337E221A6FF1CFFB5693A0623E7EBB58C2969F590D081 AD92DD9E5322E26D6A15023664AC73A355998BCC48ADD0E7A4BC79790519606F A1FEF6075033BCD1A542ED2F7EE4943A13D927138CB26A52F33F52249DD24930 BBA9773D5DEB5B8115804C2E65EDBCCB17469C47F2591BB232690DAC5F1780A5 6FE9861DC450426725D35E3E8006C022026C0A383B0A6E8AA30A52055E7E139B DF6ABC491AF90C7A3884582B7407C0DDF37CC49F3CBA0126D07A3639A615400A 01FC5412668335BC7FB0C5C62F533276BC13716EA27CCD3924408650605BEEDE 2A68B5B6105D8766B9DD6A877DE6AEA9C3179677B7C0726022D0F929E7E63574 4692A959C7B4919DEC77FA5012A3CB81439F809D15DA7739FAB5D8E03BD8F283 FB6832C9864D18C4CD499B20534D33C822226FC199D26116A73ABA2B5CAB0B63 42F1B4A3003688088F1F6DA3C61363B4C0C44269FD21F981DA0BDC5D180FFD2C 8BAB61F4330FE5806A35F1235364554FAA1CA61EC79EB01793D586FB1B62F4E9 3FA5AF30C87F9092E25245CBEEC03795B45CAE8D066442B19A229356B074B0FB B6E723B432A0188A1787970CADEB583C652FE7C19CCDF11A3EE606A32F7EA1F6 84B9476BFB90599BA0C48B3CA7052DCD001E429E4BFBF102F45A65474DA6D8AD 5720B1C5D140CE28D343611689E0D9E2C2389D268B14C5F4B130D0FE532FA54C D80A2F3807427511E11471C48FB47798A4F26427201E3198846DD5E743A74E49 1B18EC4A00C86C8CE2E066C42DD0B623C195ADE86F17C7862A01660CA72BD0EA 9A8F7E7FC3C30714CD4DFAE923F5459AB06C8589D2F158BF69CF293AA768C92B 141F4BAEBBB341CFC6F2A333E153469FEA9AC988DFC368786CD3092B78D33734 DFE7AE5AD22CBE0DA85DE277D2DEE2F7B86BCF29A752D197640FC771509CBB4C F9F595C91D1062B73547F5F439FEFCEB5AD9160E2221B61BF807E754EEDE39EC 4373D5564D4A491C22AA041E1E47C7BF4029FC28106C8BD040410410BF1D2AEF 450F00C147588F0B17E3F99D22220662EBD05413BF2E0C2F54EC44DE99F20130 C99FDB627C2B06C8FC9EF9096CDAB4F1A12F0B7692E50096DA3D471EAD210610 94D22DC1412AE4ECCAF19BEE8531CEFE83DC786B9586ADFA97C02BD60ADCE14B 8E2D8741B11D52F3CF206D5BF7BF92E1450DFA7DB8D9DEA1FBD7C2EC590FB888 1414575370F54A9908267D6F247B084A06D6BA98E8FE45375D462B4DEC0A2791 E4108B5946A12F6941A33F743C1A624CC89DE1BD19BD0E051F0F76DDB4D80707 D6C2501FBB81E9D7D4BCCA1A4C785D6E0BB534CCD738444395C39FC20BB96E32 6FA101AB8932D74EF495F4D15E56EC594E7E50719191CA3DF52A18418AEB5813 C7254393DDDA88418A746A1A54A44850CA42152FB6F07D2F3961CE7DF6584ECC 4FDAEF7DF25D2FAE98F9B4B1F6AA8E30F05991CADB8BF3851959B3A3FAFB3C30 4C2F0C5E2AC2C748140AA80EC76FE02434D0A8FD7023E643545462287D8A156D 4E192BFB04920C7AA36685B2122DAB40D6F1071EEDD4E49224B214581F0C0317 CF7C27E0DA08DD1A376413498C6B953C11D8C08B5920BF2F7E9B63A5D9AA91C4 A532514413087817ADDFE5324017D85089A9E9C4C07900C05B8DFF0941162314 883EDD8842E17B6FA4CAFB7F834AD765A9EBA8E0F7689C9EE85CFEDF52B3AB00 2A43FC5D49D97A13A27C94989CC4ED846E4850C8E934393FD5531748EC04FD58 DDD44FC377AA1D6A0FED7CB69BD3659FAFE099C6EC4FE70D650432534A83D7ED CB21A413E3FA9AD061508E3482A86923968102 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 20 /lessequal put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec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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 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 67 /C put dup 70 /F put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 79 /O put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def currentdict end currentfile eexec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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. 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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 1 /Delta put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 62 /questiondown put dup 64 /at 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 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 currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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b(+)g Fn(j)p Fp(x)p Fn(j)2503 5323 y Fl(\013)2562 5179 y Fk(p)p 2662 5179 V 90 x Ft(1)g(+)g Fn(j)p Fp(x)p Fn(j)2942 5241 y Fl(\013)2991 5092 y Fk(s)p 3091 5092 653 4 v 42 x(Z)3146 5359 y Fj(R)3194 5340 y Fi(m)3273 5269 y Fn(j)p Fp(g)t Ft(\()p Fp(x;)17 b(z)t Ft(\))p Fn(j)3604 5241 y Fs(2)3643 5269 y Fp(dz)32 b Fn(\024)p Black 1901 5656 a Ft(17)p Black eop end %%Page: 18 18 TeXDict begin 18 17 bop Black Black 599 496 a Fn(\024)785 429 y Ft(1)p 714 473 191 4 v 714 493 a Fn(p)p 797 493 108 4 v 83 x Ft(2)p Fp(\031)915 315 y Fk(s)p 1014 315 702 4 v 1014 361 a(Z)1114 387 y Fs(+)p Fo(1)1070 586 y(\0001)1260 496 y Fp(dx)1494 429 y(x)1549 400 y Fs(2)p 1376 473 330 4 v 1376 565 a Ft(1)22 b(+)g Fn(j)p Fp(x)p Fn(j)1656 536 y Fl(\013)1715 321 y Fk(s)p 1815 321 1383 4 v 40 x(Z)1915 387 y Fo(1)1870 586 y(\0001)2017 496 y Fp(dx)p Ft(\(1)g(+)g Fn(j)p Fp(x)p Fn(j)2441 467 y Fl(\013)2490 496 y Ft(\))2545 361 y Fk(Z)2600 586 y Fj(R)2648 567 y Fi(m)2727 496 y Fn(j)p Fp(g)t Ft(\()p Fp(x;)17 b(z)t Ft(\))p 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1297 y Fl(p)144 1394 y Fo(\000)199 1334 y Fn(p)p 282 1334 121 4 v 60 x Fo(\000)p Fl(e)370 1404 y Fi(j)433 1301 y Fl(d)q Fa(b)-40 b Fl(v)503 1311 y Fi(j)536 1301 y Fs(\()p Fl(s)p Fs(\))p 433 1328 191 4 v 494 1386 a Fl(ds)634 1351 y Fp(ds)p 97 1446 634 4 v 269 1537 a(p)318 1508 y Fs(2)379 1537 y Ft(+)22 b Fp(e)522 1552 y Fl(j)740 1469 y Fp(\037)801 1496 y Fs(\012)852 1466 y Fh(\000)852 1520 y Fi(\016)909 1469 y Fp(')973 1427 y Fs(1)973 1493 y Fl(j)1012 1469 y Ft(\()p Fp(y)t Ft(\))1140 1354 y Fk(\014)1140 1414 y(\014)1140 1474 y(\014)1200 1469 y Fn(\024)1511 1401 y Fp(C)p 1315 1446 469 4 v 1315 1537 a Fn(j)p Fp(p)g Fn(\000)1513 1472 y(p)p 1596 1472 160 4 v 65 x(\000)p Fp(e)1718 1552 y Fl(j)1756 1537 y Fn(j)1793 1469 y Fp(\037)1854 1496 y Fs(\012)1905 1466 y Fh(\000)1905 1520 y Fi(\016)1962 1469 y Fn(j)p Fp(')2054 1427 y Fs(1)2054 1493 y Fl(j)2093 1469 y Ft(\()p Fp(y)t Ft(\))p Fn(j)k(\024)2582 1401 y Fp(C)p 2390 1446 460 4 v 2390 1537 a Ft(2)2439 1472 y Fn(p)p 2522 1472 160 4 v 65 x(\000)p Fp(e)2644 1552 y Fl(j)2703 1537 y Fn(\000)d Fp(\016)2860 1469 y(\037)2921 1496 y Fs(\012)2972 1466 y Fh(\000)2972 1520 y Fi(\016)3028 1469 y Fn(j)p Fp(')3120 1427 y Fs(1)3120 1493 y Fl(j)3159 1469 y Ft(\()p Fp(y)t Ft(\))p Fn(j)k(2)h Fp(L)3502 1427 y Fs(2)3541 1469 y Ft(\()p Fm(R)3651 1427 y Fs(1+)p Fl(m)3808 1469 y Ft(\))0 1744 y(Near)33 b(the)g(p)s(ositiv)m(e)h(singularit)m(y)g (w)m(e)f(use)h(the)f(iden)m(tit)m(y)1185 2014 y Fk(b)-55 b Fp(v)1232 2029 y Fl(j)1269 2014 y Ft(\()p Fp(p)p Ft(\))27 b(=)1525 1878 y Fk(Z)1624 1904 y Fl(p)1580 2044 y Fn(p)p 1663 2044 121 4 v 60 x Fo(\000)p Fl(e)1751 2114 y Fi(j)1814 1946 y Fp(d)p Fk(b)-55 b Fp(v)1912 1961 y Fl(j)1948 1946 y Ft(\()p Fp(s)p Ft(\))p 1814 1991 257 4 v 1894 2082 a Fp(ds)2080 2014 y(ds)22 b Ft(+)g Fk(b)-55 b Fp(v)2344 2029 y Fl(j)2380 2014 y Ft(\()2418 1933 y Fk(p)p 2518 1933 160 4 v 81 x Fn(\000)p Fp(e)2640 2029 y Fl(j)2677 2014 y Ft(\))0 2317 y(to)32 b(study)i(the)f(conditions)h(of)e(the)h (square)g(in)m(tegrabilit)m(y)i(of)d(the)h(term)1202 2544 y Fk(b)-56 b Fp(v)1248 2559 y Fl(j)1285 2544 y Ft(\()1323 2479 y Fn(p)p 1406 2479 V 65 x(\000)p Fp(e)1528 2559 y Fl(j)1565 2544 y Ft(\))22 b(+)1723 2464 y Fk(R)1790 2490 y Fl(p)1770 2527 y Fn(p)p 1853 2527 121 4 v 60 x Fo(\000)p Fl(e)1941 2597 y Fi(j)2004 2494 y Fl(d)q Fa(b)-40 b Fl(v)2074 2504 y Fi(j)2107 2494 y Fs(\()p Fl(s)p Fs(\))p 2004 2521 191 4 v 2065 2579 a Fl(ds)2205 2544 y Fp(ds)p 1201 2639 1101 4 v 1606 2730 a(p)1655 2701 y Fs(2)1717 2730 y Ft(+)22 b Fp(e)1860 2745 y Fl(j)2311 2662 y Fp(\037)2372 2689 y Fs(\012)2423 2659 y Fg(+)2423 2713 y Fi(\016)2478 2662 y Fp(')2542 2621 y Fs(1)2542 2686 y Fl(j)2582 2662 y Ft(\()p Fp(y)t Ft(\))p Black 941 w(\(3.16\))p Black 0 2935 a(Analogously)32 b(to)g(the)g(situation)g(at)f(the)h(negativ)m (e)h(singularit)m(y)g(w)m(e)g(pro)m(v)m(e)f(the)g(square)h(in)m (tegrabilit)m(y)g(of)0 3055 y(the)g(second)h(term)f(in)g(\(3.16\))f (using)h(the)g(b)s(ound)g(on)f(the)h(deriv)-5 b(ativ)m(e)34 b(in)m(v)m(olv)m(ed)h(in)e(it.)44 b(Hence)830 3292 y Fk(\014)830 3351 y(\014)830 3411 y(\014)874 3208 y(R)940 3235 y Fl(p)921 3272 y Fn(p)p 1004 3272 121 4 v 59 x Fo(\000)p Fl(e)1092 3341 y Fi(j)1155 3238 y Fl(d)q Fa(b)-40 b Fl(v)1225 3248 y Fi(j)1258 3238 y Fs(\()p Fl(s)p Fs(\))p 1155 3266 191 4 v 1215 3323 a Fl(ds)1355 3289 y Fp(ds)p 874 3383 579 4 v 1018 3474 a(p)1067 3446 y Fs(2)1128 3474 y Ft(+)22 b Fp(e)1271 3489 y Fl(j)1462 3406 y Fp(\037)1523 3433 y Fs(\012)1574 3404 y Fg(+)1574 3457 y Fi(\016)1629 3406 y Fp(')1693 3365 y Fs(1)1693 3431 y Fl(j)1732 3406 y Ft(\()p Fp(y)t Ft(\))1860 3292 y Fk(\014)1860 3351 y(\014)1860 3411 y(\014)1920 3406 y Fn(\024)2230 3339 y Fp(C)p 2035 3383 467 4 v 2035 3474 a Fn(j)p Fp(p)g Ft(+)2232 3409 y Fn(p)p 2315 3409 160 4 v 65 x(\000)p Fp(e)2437 3489 y Fl(j)2474 3474 y Fn(j)2512 3406 y Fp(\037)2573 3433 y Fs(\012)2624 3404 y Fg(+)2624 3457 y Fi(\016)2679 3406 y Fn(j)p Fp(')2771 3365 y Fs(1)2771 3431 y Fl(j)2810 3406 y Ft(\()p Fp(y)t Ft(\))p Fn(j)k(\024)1165 3748 y(\024)1472 3681 y Fp(C)p 1280 3725 460 4 v 1280 3816 a Ft(2)1329 3751 y Fn(p)p 1412 3751 160 4 v 65 x(\000)p Fp(e)1534 3831 y Fl(j)1593 3816 y Fn(\000)d Fp(\016)1750 3748 y(\037)1811 3775 y Fs(\012)1862 3746 y Fg(+)1862 3799 y Fi(\016)1917 3748 y Fn(j)p Fp(')2009 3707 y Fs(1)2009 3773 y Fl(j)2048 3748 y Ft(\()p Fp(y)t Ft(\))p Fn(j)j(2)i Fp(L)2390 3707 y Fs(2)2430 3748 y Ft(\()p Fm(R)2540 3707 y Fs(1+)p Fl(m)2697 3748 y Ft(\))0 3984 y(Th)m(us)52 b(it)f(remains)h(to)e(deriv)m(e)j(the) e(conditions)g(under)h(whic)m(h)g(the)f(\014rst)h(term)f(in)g(\(3.15\)) f(and)h(the)0 4104 y(\014rst)46 b(term)g(in)f(\(3.16\))g(are)g(square)h (in)m(tegrable.)83 b(Estimating)46 b(the)g(square)h(of)d(the)i Fp(L)3288 4068 y Fs(2)3328 4104 y Ft(\()p Fm(R)3438 4068 y Fs(1+)p Fl(m)3595 4104 y Ft(\))f(norm)0 4281 y(of)121 4212 y Fk(b)-55 b Fp(v)168 4227 y Fl(j)205 4212 y Ft(\()p Fn(\000)320 4146 y(p)p 403 4146 V 66 x(\000)p Fp(e)525 4227 y Fl(j)562 4212 y Ft(\))p 121 4258 480 4 v 216 4349 a Fp(p)265 4321 y Fs(2)326 4349 y Ft(+)22 b Fp(e)469 4364 y Fl(j)610 4281 y Fp(\037)671 4308 y Fs(\012)722 4278 y Fh(\000)722 4332 y Fi(\016)779 4281 y Fp(')843 4240 y Fs(1)843 4306 y Fl(j)882 4281 y Ft(\()p Fp(y)t Ft(\))f(+)1140 4212 y Fk(b)-56 b Fp(v)1186 4227 y Fl(j)1223 4212 y Ft(\()1261 4146 y Fn(p)p 1344 4146 160 4 v 66 x(\000)p Fp(e)1466 4227 y Fl(j)1503 4212 y Ft(\))p 1139 4258 402 4 v 1195 4349 a Fp(p)1244 4321 y Fs(2)1305 4349 y Ft(+)22 b Fp(e)1448 4364 y Fl(j)1551 4281 y Fp(\037)1612 4308 y Fs(\012)1663 4278 y Fg(+)1663 4332 y Fi(\016)1718 4281 y Fp(')1782 4240 y Fs(1)1782 4306 y Fl(j)1821 4281 y Ft(\()p Fp(y)t Ft(\))32 b(w)m(e)h(easily)h(arriv)m(e)g(at)766 4527 y Fk(Z)865 4553 y Fo(\000)920 4493 y Fn(p)p 1003 4493 121 4 v 60 x Fo(\000)p Fl(e)1091 4563 y Fi(j)1123 4553 y Fs(+)p Fl(\016)821 4752 y Fo(\000)876 4692 y Fn(p)p 959 4692 V 60 x Fo(\000)p Fl(e)1047 4762 y Fi(j)1079 4752 y Fo(\000)p Fl(\016)1233 4662 y Fp(dp)1343 4593 y Fn(j)p Fk(b)-55 b Fp(v)1418 4608 y Fl(j)1454 4593 y Ft(\()p Fn(\000)1569 4528 y(p)p 1652 4528 160 4 v 65 x(\000)p Fp(e)1774 4608 y Fl(j)1811 4593 y Ft(\))p Fn(j)1877 4557 y Fs(2)p 1343 4639 575 4 v 1427 4742 a Ft(\()p Fp(p)1514 4714 y Fs(2)1575 4742 y Ft(+)22 b Fp(e)1718 4757 y Fl(j)1755 4742 y Ft(\))1793 4694 y Fs(2)1948 4662 y Ft(+)2046 4527 y Fk(Z)2146 4493 y Fn(p)p 2229 4493 121 4 v 60 x Fo(\000)p Fl(e)2317 4563 y Fi(j)2349 4553 y Fs(+)p Fl(\016)2102 4692 y Fn(p)p 2185 4692 V 60 x Fo(\000)p Fl(e)2273 4762 y Fi(j)2305 4752 y Fo(\000)p Fl(\016)2459 4662 y Fp(dp)2569 4593 y Fn(j)p Fk(b)-55 b Fp(v)2644 4608 y Fl(j)2680 4593 y Ft(\()2718 4528 y Fn(p)p 2801 4528 160 4 v 65 x(\000)p Fp(e)2923 4608 y Fl(j)2960 4593 y Ft(\))p Fn(j)3026 4557 y Fs(2)p 2569 4639 497 4 v 2614 4742 a Ft(\()p Fp(p)2701 4714 y Fs(2)2762 4742 y Ft(+)22 b Fp(e)2905 4757 y Fl(j)2942 4742 y Ft(\))2980 4694 y Fs(2)3107 4662 y Fp(;)0 4965 y Ft(whic)m(h)34 b(can)f(b)s(e)g(b)s(ounded)g(b)s(elo)m(w)g(b)m(y)1008 5179 y Fn(j)p Fk(b)-55 b Fp(v)1083 5194 y Fl(j)1120 5179 y Ft(\()p Fn(\000)1235 5113 y(p)p 1318 5113 160 4 v 66 x(\000)p Fp(e)1440 5194 y Fl(j)1477 5179 y Ft(\))p Fn(j)1543 5143 y Fs(2)p 1008 5225 575 4 v 1008 5316 a Ft(\(2)1095 5251 y Fn(p)p 1178 5251 160 4 v 65 x(\000)p Fp(e)1300 5331 y Fl(j)1360 5316 y Ft(+)22 b Fp(\016)t Ft(\))1543 5287 y Fs(2)1609 5112 y Fk(Z)1709 5138 y Fl(\016)1664 5338 y Fo(\000)p Fl(\016)1784 5180 y Fp(ds)p 1784 5225 97 4 v 1790 5316 a(s)1836 5287 y Fs(2)1912 5248 y Ft(+)2059 5179 y Fn(j)p Fk(b)-55 b Fp(v)2134 5194 y Fl(j)2170 5179 y Ft(\()2208 5113 y Fn(p)p 2291 5113 160 4 v 66 x(\000)p Fp(e)2413 5194 y Fl(j)2450 5179 y Ft(\))p Fn(j)2516 5143 y Fs(2)p 2020 5225 574 4 v 2020 5316 a Ft(\(2)2107 5251 y Fn(p)p 2190 5251 160 4 v 65 x(\000)p Fp(e)2312 5331 y Fl(j)2371 5316 y Ft(+)22 b Fp(\016)t Ft(\))2554 5287 y Fs(2)2620 5112 y Fk(Z)2720 5138 y Fl(\016)2676 5338 y Fo(\000)p Fl(\016)2795 5180 y Fp(ds)p 2795 5225 97 4 v 2801 5316 a(s)2847 5287 y Fs(2)p Black 1901 5656 a Ft(18)p Black eop end %%Page: 19 19 TeXDict begin 19 18 bop Black Black 0 407 a Ft(This)29 b(b)s(ound)e(implies)i(that)e(the)h(necessary)i(and)d(su\016cien)m(t)j (conditions)e(for)f(the)h(existence)h(of)e Fp(u)3563 422 y Fo(\000)p Fl(;j)3674 407 y Ft(\()p Fp(x;)17 b(y)t Ft(\))0 527 y Fn(2)28 b Fp(L)160 491 y Fs(2)200 527 y Ft(\()p Fm(R)310 491 y Fs(1+)p Fl(m)467 527 y Ft(\))k(solving)h(the)g (equation)h(\(3.11\))e(are)1243 725 y Fk(b)-56 b Fp(v)1289 740 y Fl(j)1326 725 y Ft(\()1364 645 y Fk(p)p 1463 645 160 4 v 1463 725 a Fn(\000)p Fp(e)1585 740 y Fl(j)1623 725 y Ft(\))27 b(=)h(0)p Fp(;)114 b Fk(b)-55 b Fp(v)2029 740 y Fl(j)2066 725 y Ft(\()p Fn(\000)2181 645 y Fk(p)p 2281 645 V 80 x Fn(\000)p Fp(e)2403 740 y Fl(j)2440 725 y Ft(\))27 b(=)h(0)0 924 y(whic)m(h)34 b(b)m(y)g(means)f(of)f(the)h (de\014nition)h(of)e(the)h(functions)h Fp(v)2173 939 y Fl(j)2209 924 y Ft(\()p Fp(x)p Ft(\))f(is)g(equiv)-5 b(alen)m(t)34 b(to)491 1220 y(\()p Fp(g)t Ft(\()p Fp(x;)17 b(y)t Ft(\))p Fp(;)859 1152 y(e)904 1106 y Fo(\006)p Fl(i)983 1046 y Fn(p)p 1066 1046 121 4 v 60 x Fo(\000)p Fl(e)1154 1116 y Fi(j)1186 1106 y Fl(x)p 859 1197 372 4 v 949 1217 a Fn(p)p 1032 1217 108 4 v 82 x Ft(2)p Fp(\031)1240 1220 y(')1304 1178 y Fl(k)1304 1244 y(j)1347 1220 y Ft(\()p Fp(y)t Ft(\)\))1513 1236 y Fl(L)1561 1217 y Fg(2)1594 1236 y Fs(\()p Fj(R)1669 1217 y Fg(1+)p Fi(m)1805 1236 y Fs(\))1864 1220 y Ft(=)28 b(0)p Fp(;)114 b Ft(1)27 b Fn(\024)i Fp(k)h Fn(\024)f Fp(m)2612 1235 y Fl(j)2648 1220 y Fp(;)115 b Ft(1)27 b Fn(\024)h Fp(j)34 b Fn(\024)28 b Fp(N)33 b Fn(\000)22 b Ft(1)146 1553 y Fc(\003)146 1761 y Ft(After)31 b(establishing)h(the)f(solv)-5 b(abilit)m(y)32 b(conditions)g(for)e(the)h(equation)g(\(3.11\))f(when)h(the)g (situation)g(is)0 1881 y(one)39 b(dimensional)g(in)g(the)g(\014rst)g(v) -5 b(ariable)38 b(w)m(e)i(turn)e(our)h(atten)m(tion)f(to)g(the)h(cases) h(of)e(dimensions)i(t)m(w)m(o)0 2001 y(and)33 b(higher.)146 2209 y Fr(Lemma)57 b(3.7)49 b Ff(L)-5 b(et)49 b(the)g(assumptions)g(of) f(the)i(The)-5 b(or)g(em)48 b(2)h(hold.)87 b(Then)48 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