Content-Type: multipart/mixed; boundary="-------------0907241053843" This is a multi-part message in MIME format. ---------------0907241053843 Content-Type: text/plain; name="09-120.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="09-120.keywords" Mean-field, Hartree, Rate of convergence ---------------0907241053843 Content-Type: application/postscript; name="knowles_pickl.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="knowles_pickl.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.96.1 Copyright 2007 Radical Eye Software %%Title: knowles_pickl.dvi %%CreationDate: Fri Jul 24 17:37:25 2009 %%Pages: 34 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMSY8 CMB10 CMR10 CMMI10 CMSY7 CMR7 CMSY10 %%+ CMMI8 CMR8 MSBM10 CMEX10 MSAM7 CMR6 MSBM7 CMMI6 CMSY6 CMR9 CMMI9 %%+ MSAM10 CMTI10 CMMIB10 CMBX10 TeX-cmex8 Helvetica %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips knowles_pickl.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2009.07.24:1737 %%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: psfrag.pro 0 0 %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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All Rights Reserved) readonly def /FullName (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 76 /L put readonly def /FontBBox{-15 -250 1216 750}readonly 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 50 /two put dup 95 /dotaccent put readonly def /FontBBox{-301 -250 1164 946}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 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def /version (001.001) def end readonly def /FontName /TeX-cmex8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /P put dup 82 /R put readonly def /FontBBox {-29 -2957 1554 772} readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMB10 %!PS-AdobeFont-1.1: CMB10 1.0 %%CreationDate: 1991 Aug 20 16:34:36 % 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 (CMB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMB10 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 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 78 /N put dup 79 /O 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 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-62 -250 1011 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 13 /fl put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 81 /Q put dup 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 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec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All Rights Reserved) 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 46 /lessorsimilar put dup 54 /lessorequalslant put dup 62 /greaterorequalslant put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % 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 (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 107 /k put dup 111 /o put readonly def /FontBBox{-29 -250 1075 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % 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 (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 46 /period put dup 50 /two put dup 51 /three put dup 64 /at put dup 67 /C put dup 73 /I put dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 119 /w put dup 121 /y put dup 122 /z put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 48 /prime put dup 49 /infinity put dup 121 /dagger 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 14 /delta put dup 78 /N put dup 100 /d put dup 105 /i put dup 107 /k put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: 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 40 /parenleft put dup 41 /parenright put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM7 %!PS-AdobeFont-1.1: MSAM7 2.1 %%CreationDate: 1992 Oct 17 08:30:29 % 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 (MSAM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM7 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{0 -576 1569 1076}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 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracketrightbigg put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 80 /summationtext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 98 /hatwide put dup 99 /hatwider put dup 100 /hatwidest put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 112 /radicalbig put dup 113 /radicalBig put dup 114 /radicalbigg put dup 115 /radicalBigg put dup 116 /radicalbt put dup 117 /radicalvertex put dup 118 /radicaltp put dup 122 /bracehtipdownleft put dup 123 /bracehtipdownright put dup 124 /bracehtipupleft put dup 125 /bracehtipupright put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 78 /N put dup 82 /R put dup 90 /Z put dup 91 /hatwide put dup 92 /hatwider put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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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 9 /Psi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 58 /colon put dup 61 /equal put dup 97 /a put dup 98 /b put dup 99 /c put dup 108 /l put dup 111 /o put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 10 /circlemultiply put dup 17 /equivalence put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 33 /arrowright put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 69 /E put dup 72 /H put dup 76 /L put dup 81 /Q put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 16 /zeta put dup 17 /eta put dup 26 /rho put dup 27 /sigma put dup 30 /phi 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 66 /B put dup 67 /C put dup 71 /G put dup 72 /H put dup 75 /K put dup 76 /L put dup 78 /N put dup 87 /W put dup 88 /X put dup 97 /a put dup 99 /c put dup 100 /d put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 119 /w put dup 120 /x put 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 16 /zeta put dup 17 /eta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 28 /tau put dup 30 /phi put dup 31 /chi 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 69 /E put dup 71 /G put dup 72 /H put dup 75 /K put dup 76 /L put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 84 /T put dup 85 /U put dup 87 /W put dup 88 /X put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 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 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}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 1 /Delta put dup 8 /Phi put dup 9 /Psi put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 34 /quotedblright put dup 35 /numbersign 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 10 /circlemultiply put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 121 /dagger put readonly def /FontBBox{-30 -955 1185 779}readonly 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 44 /comma put dup 45 /hyphen put dup 48 /zero put dup 50 /two put dup 51 /three put dup 52 /four put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 80 /P put dup 84 /T put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c 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 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. 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b(The)27 b(follo)m(wing)i(lemma)f(giv)m(es)h (the)f(relationship)f(b)s(et)m(w)m(een)i(di\013eren)m(t)f(elemen)m(ts)h (of)e(the)h(sequence)14 5252 y Fw(E)86 5219 y Ft(\(1\))181 5252 y Fw(;)15 b(E)293 5219 y Ft(\(2\))388 5252 y Fw(;)g(:)g(:)g(:)i Fx(,)30 b(where,)g(w)m(e)h(recall,)1303 5472 y Fw(E)1375 5435 y Ft(\()p Fv(k)r Ft(\))1524 5472 y Fx(=)50 b(1)21 b Fu(\000)1802 5399 y Fr(\012)1845 5472 y Fw(')1904 5435 y FF(\012)p Fv(k)2012 5472 y Fw(;)15 b(\015)2104 5435 y Ft(\()p Fv(k)r Ft(\))2217 5472 y Fw(')2276 5435 y FF(\012)p Fv(k)2374 5399 y Fr(\013)2432 5472 y Fw(:)1103 b Fx(\(2.1\))p Black 1858 6000 a(4)p Black eop end %%Page: 5 5 TeXDict begin 5 4 bop Black Black Black 14 162 a Fh(Lemma)30 b(2.1.)p Black 43 w Fg(L)-5 b(et)33 b Fw(\015)729 129 y Ft(\()p Fv(k)r Ft(\))852 162 y Fu(2)25 b(L)p Fx(\()p Fu(H)1114 129 y Ft(\()p Fv(k)r Ft(\))1211 162 y Fx(\))33 b Fg(satisfy)1318 377 y Fw(\015)1370 339 y Ft(\()p Fv(k)r Ft(\))1518 377 y Fi(>)51 b Fx(0)15 b Fw(;)201 b Fx(T)-8 b(r)15 b 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y FF(\012)p Ft(\()p Fv(k)r FF(\000)p Ft(1\))2819 2651 y Fw(;)15 b(\015)2911 2614 y Ft(\()p Fv(k)r Ft(\))3024 2651 y Fx(\010)3090 2604 y Ft(\(1\))3090 2679 y Fv(j)3204 2651 y Fu(\012)20 b Fw(')3354 2614 y FF(\012)p Ft(\()p Fv(k)r FF(\000)p Ft(1\))3597 2578 y Fr(\013)171 2903 y Fx(=)50 b(1)21 b Fu(\000)449 2830 y Fr(\012)492 2903 y Fw(')551 2866 y FF(\012)p Ft(\()p Fv(k)r FF(\000)p Ft(1\))804 2903 y Fw(;)15 b(\015)896 2866 y Ft(\()p Fv(k)r FF(\000)p Ft(1\))1099 2903 y Fw(')1158 2866 y FF(\012)p Ft(\()p Fv(k)r FF(\000)p Ft(1\))1401 2830 y Fr(\013)1459 2903 y Fw(:)14 3118 y Fx(This)30 b(yields)1420 3241 y Fw(E)1492 3204 y Ft(\()p Fv(k)r Ft(\))1641 3241 y Fi(6)50 b Fw(E)1834 3204 y Ft(\()p Fv(k)r FF(\000)p Ft(1\))2042 3241 y Fx(+)20 b Fw(E)2205 3204 y Ft(\(1\))2315 3241 y Fw(;)14 3421 y Fx(and)30 b(the)h(claim)g(follo)m(ws.)p 3681 3421 4 62 v 3685 3362 55 4 v 3685 3421 V 3738 3421 4 62 v Black 14 3636 a Fh(Remark)h(2.2.)p Black 43 w Fx(The)f(b)s(ound)f(in)h(\(2.2\))i(is)f(sharp.)43 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b(of)e(the)h(trace)g(class)g (op)s(erator)g Fw(A)2937 1365 y Fx(:)2962 1368 y(=)c Fw(\015)3114 1335 y Ft(\()p Fv(k)r Ft(\))3233 1368 y Fu(\000)21 b Fw(p)3371 1335 y Ft(\()p Fv(k)r Ft(\))3468 1368 y Fx(.)46 b(Since)14 1481 y Fw(p)60 1448 y Ft(\()p Fv(k)r Ft(\))192 1481 y Fx(is)34 b(a)h(rank)f(one)h(pro)5 b(jection,)36 b Fw(A)f Fx(has)f(at)h(most)g(one)f(negativ)m(e)j(eigen)m (v)-5 b(alue,)38 b(sa)m(y)d Fw(\025)3037 1495 y Ft(0)3076 1481 y Fx(.)53 b(Also,)36 b(T)-8 b(r)15 b Fw(A)32 b Fx(=)g(0)14 1594 y(implies)f(that)520 1526 y Fr(P)616 1621 y Fv(n)678 1594 y Fw(\025)731 1608 y Fv(n)803 1594 y Fx(=)25 b(0.)41 b(Th)m(us,)1266 1526 y Fr(P)1362 1621 y Fv(n)1409 1594 y Fu(j)p Fw(\025)1487 1608 y Fv(n)1534 1594 y Fu(j)25 b Fx(=)g(2)p Fu(j)p Fw(\025)1803 1608 y Ft(0)1844 1594 y Fu(j)p Fx(,)30 b(whic)m(h)g(is)h(\(2.4\))r(.)155 1707 y(No)m(w)i(\(2.4\))f(yields)568 1912 y Fw(R)638 1874 y Ft(\()p Fv(k)r Ft(\))786 1912 y Fx(=)50 b(T)-8 b(r)1016 1834 y Fr(\014)1016 1889 y(\014)1046 1912 y Fw(p)1092 1874 y Ft(\()p Fv(k)r Ft(\))1210 1912 y Fu(\000)20 b Fw(\015)1353 1874 y Ft(\()p Fv(k)r Ft(\))1451 1834 y Fr(\014)1451 1889 y(\014)1531 1912 y Fx(=)51 b(2)15 b Fu(k)p Fw(p)1804 1874 y Ft(\()p Fv(k)r Ft(\))1922 1912 y Fu(\000)20 b Fw(\015)2065 1874 y Ft(\()p Fv(k)r Ft(\))2163 1912 y Fu(k)51 b Fi(6)f Fx(2)2440 1794 y Fr(q)p 2531 1794 621 4 v 118 x Fx(T)-8 b(r)2625 1838 y Fr(\000)2667 1912 y Fw(p)2713 1885 y Ft(\()p Fv(k)r Ft(\))2830 1912 y Fu(\000)20 b Fw(\015)2973 1885 y Ft(\()p Fv(k)r Ft(\))3071 1838 y Fr(\001)3112 1861 y Ft(2)3167 1912 y Fw(:)14 2073 y Fx(Then)30 b(\(2.3b\))h(follo)m(ws)h(from)155 2247 y(T)-8 b(r)249 2173 y Fr(\000)290 2247 y Fw(p)336 2209 y Ft(\()p Fv(k)r Ft(\))454 2247 y Fu(\000)20 b Fw(\015)597 2209 y Ft(\()p Fv(k)r Ft(\))694 2173 y Fr(\001)736 2196 y Ft(2)826 2247 y Fx(=)50 b(1)21 b Fu(\000)f Fx(2)15 b(T)-8 b(r)1258 2173 y Fr(\000)1300 2247 y Fw(p)1346 2209 y Ft(\()p Fv(k)r Ft(\))1443 2247 y Fw(\015)1495 2209 y Ft(\()p Fv(k)r Ft(\))1593 2173 y Fr(\001)1655 2247 y 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b(w)m(e)g(drop)e(the)i(irrelev)-5 b(an)m(t)31 b(index)f Fw(k)s Fx(.)41 b(Consider)30 b(\014rst)1174 3025 y Fw(')51 b Fx(=)1406 2897 y Fr(\022)1472 2969 y Fx(1)1472 3081 y(0)1518 2897 y Fr(\023)1615 3025 y Fw(;)197 b(\015)56 b Fx(=)2061 2897 y Fr(\022)2128 2969 y Fx(1)21 b Fu(\000)f Fw(a)84 b Fx(0)2208 3081 y(0)163 b Fw(a)2464 2897 y Fr(\023)2561 3025 y Fw(;)14 3241 y Fx(where)30 b(0)c Fi(6)f Fw(a)g Fi(6)g Fx(1.)41 b(As)30 b(ab)s(o)m(v)m(e)i(w)m(e)f (set)g Fw(p)1463 3238 y Fx(:)1488 3241 y(=)25 b Fu(j)p Fw(')p Fu(ih)p Fw(')p Fu(j)p Fx(.)43 b(One)30 b(\014nds)848 3402 y Fw(E)55 b Fx(=)c(1)20 b Fu(\000)g(h)p Fw(')10 b(;)15 b(\015)22 b(')p Fu(i)51 b Fx(=)f Fw(a)15 b(;)198 b(R)51 b Fx(=)f(T)-8 b(r)p Fu(j)p Fw(p)20 b Fu(\000)g Fw(\015)5 b Fu(j)51 b Fx(=)f(2)p Fw(a)15 b(;)14 3564 y Fx(so)31 b(that)g(\(2.3a\))h(is)f(sharp)e(up)g(to)i(a)g(constan)m(t)h (factor.)155 3677 y(It)c(is)g(not)g(hard)f(to)h(see)h(that)f(if)g Fw(\015)k Fx(and)c Fw(p)f Fx(comm)m(ute)i(then)e(\(2.3b\))i(can)f(b)s 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2165 3289 a Fw(N)2273 3140 y Fr(X)2320 3338 y Fv(k)2420 3227 y Fw(k)s(P)2528 3242 y Fv(k)2621 3227 y Fx(=)65 b Fr(b)-65 b Fw(m)15 b(:)651 b Fx(\(3.11\))14 3484 y(Th)m(us,)30 b(b)m(y)g(symmetry)g(of)h(\011,)f(w)m(e)h(get)1301 3663 y Fw(\013)51 b Fx(=)g Fu(h)p Fx(\011)10 b Fw(;)15 b(q)1729 3677 y Ft(1)1783 3663 y Fx(\011)p Fu(i)51 b Fx(=)f Fu(h)p Fx(\011)10 b Fw(;)30 b Fr(b)-66 b Fw(m)16 b Fx(\011)o Fu(i)f Fw(:)1056 b Fx(\(3.12\))14 3842 y(The)30 b(corresp)s(ondence)g Fw(q)877 3856 y Ft(1)941 3842 y Fu(\030)40 b Fr(b)-66 b Fw(m)30 b Fx(of)38 b(\(3.11\))32 b(yields)f(the)g(follo)m(wing)g (useful)f(b)s(ounds.)p Black 14 4009 a Fh(Lemma)g(3.9.)p Black 43 w Fg(F)-7 b(or)34 b(any)f(nonne)-5 b(gative)34 b(function)e Fw(f)j Fx(:)25 b Fu(f)p Fx(0)p Fw(;)15 b(:)g(:)g(:)j(;)d (N)10 b Fu(g)26 b(!)f Fx([0)p Fw(;)15 b Fu(1)p Fx(\))34 b Fg(we)f(have)1245 4114 y Fr(\012)1288 4188 y Fx(\011)10 b Fw(;)1426 4164 y Fr(b)1409 4188 y Fw(f)g(q)1505 4202 y Ft(1)1544 4188 y Fx(\011)1614 4114 y Fr(\013)1708 4188 y Fx(=)1829 4114 y Fr(\012)1872 4188 y Fx(\011)g Fw(;)2010 4164 y Fr(b)1993 4188 y Fw(f)39 b Fr(b)-65 b Fw(m)o Fx(\011)2213 4114 y Fr(\013)2271 4188 y Fw(;)1218 b Fx(\(3.13\))1165 4305 y Fr(\012)1208 4378 y Fx(\011)10 b Fw(;)1346 4354 y Fr(b)1329 4378 y Fw(f)g(q)1425 4392 y Ft(1)1464 4378 y Fw(q)1505 4392 y Ft(2)1544 4378 y Fx(\011)1614 4305 y Fr(\013)1708 4378 y Fi(6)1917 4317 y Fw(N)p 1839 4357 240 4 v 1839 4441 a(N)30 b Fu(\000)20 b Fx(1)2089 4305 y Fr(\012)2131 4378 y Fx(\011)10 b Fw(;)2270 4354 y Fr(b)2252 4378 y Fw(f)40 b Fr(b)-66 b Fw(m)2402 4341 y Ft(2)2441 4378 y Fx(\011)2512 4305 y Fr(\013)2570 4378 y Fw(:)919 b Fx(\(3.14\))p Black 14 4591 a Fh(Pro)s(of.)p Black 46 w Fx(The)29 b(pro)s(of)f(of)37 b(\(3.13\))31 b(is)f(an)f(immediate)h (consequence)g(of)37 b(\(3.11\))r(.)j(In)29 b(order)f(to)i(pro)m(v)m(e) g(\(3.14\))i(w)m(e)14 4703 y(write,)f(using)f(symmetry)g(of)g(\011)g (as)h(w)m(ell)g(as)g(\(3.11\))r(,)97 4872 y Fr(\012)140 4945 y Fx(\011)10 b Fw(;)278 4921 y Fr(b)261 4945 y Fw(f)25 b(q)372 4959 y Ft(1)411 4945 y Fw(q)452 4959 y Ft(2)491 4945 y Fx(\011)562 4872 y Fr(\013)655 4945 y Fx(=)960 4884 y(1)p 786 4925 394 4 v 786 5008 a Fw(N)10 b Fx(\()p Fw(N)31 b Fu(\000)20 b Fx(1\))1204 4859 y Fr(X)1214 5057 y Fv(i)p FF(6)p Ft(=)p Fv(j)1351 4872 y Fr(\012)1394 4945 y Fx(\011)10 b Fw(;)1532 4921 y Fr(b)1515 4945 y Fw(f)24 b(q)1625 4959 y Fv(i)1653 4945 y Fw(q)1694 4959 y Fv(j)1730 4945 y Fx(\011)1801 4872 y Fr(\013)1536 5236 y Fi(6)1841 5174 y Fx(1)p 1668 5215 V 1668 5298 a Fw(N)10 b Fx(\()p Fw(N)30 b Fu(\000)20 b Fx(1\))2086 5149 y Fr(X)2114 5345 y Fv(i;j)2232 5162 y Fr(\012)2275 5236 y Fx(\011)10 b Fw(;)2413 5212 y Fr(b)2396 5236 y Fw(f)25 b(q)2507 5250 y Fv(i)2535 5236 y Fw(q)2576 5250 y Fv(j)2612 5236 y Fx(\011)2682 5162 y Fr(\013)2776 5236 y Fx(=)2985 5174 y Fw(N)p 2907 5215 240 4 v 2907 5298 a(N)30 b Fu(\000)20 b Fx(1)3157 5162 y Fr(\012)3199 5236 y Fx(\011)10 b Fw(;)3338 5212 y Fr(b)3320 5236 y Fw(f)40 b Fr(b)-66 b Fw(m)3470 5198 y Ft(2)3509 5236 y Fx(\011)3580 5162 y Fr(\013)3638 5236 y Fw(;)14 5504 y Fx(whic)m(h)30 b(is)h(the)f(claim.)p 3681 5504 4 62 v 3685 5446 55 4 v 3685 5504 V 3738 5504 4 62 v Black 1835 6000 a(11)p Black eop end %%Page: 12 12 TeXDict begin 12 11 bop Black Black 155 162 a Fx(Next,)32 b(w)m(e)f(in)m(tro)s(duce)f(the)g(shift)h(op)s(eration)f Fw(\034)1749 176 y Fv(n)1796 162 y Fx(,)h Fw(n)24 b Fu(2)h Fs(Z)p Fx(,)30 b(de\014ned)g(on)g(functions)g Fw(f)39 b Fx(through)1425 361 y(\()p Fw(\034)1500 375 y Fv(n)1547 361 y Fw(f)10 b Fx(\)\()p Fw(k)s Fx(\))1808 358 y(:)1833 361 y(=)50 b Fw(f)10 b Fx(\()p Fw(k)24 b Fx(+)19 b Fw(n)p Fx(\))c Fw(:)1179 b Fx(\(3.15\))14 560 y(Its)31 b(usefulness)e(for)h (our)g(purp)s(oses)e(is)j(encapsulated)g(b)m(y)f(the)g(follo)m(wing)i (lemma.)p Black 14 743 a Fh(Lemma)i(3.10.)p Black 46 w Fg(L)-5 b(et)37 b Fw(r)d Fi(>)e Fx(1)37 b Fg(and)g Fw(A)f Fg(b)-5 b(e)37 b(an)f(op)-5 b(er)g(ator)40 b(on)d Fu(H)2100 710 y Ft(\()p Fv(r)r Ft(\))2192 743 y Fg(.)53 b(L)-5 b(et)37 b Fw(Q)2506 757 y Fv(i)2534 743 y Fg(,)g Fw(i)32 b Fx(=)g(1)p Fw(;)15 b Fx(2)p Fg(,)39 b(b)-5 b(e)36 b(two)h(pr)-5 b(oje)g(ctors)39 b(of)14 856 y(the)33 b(form)1542 969 y Fw(Q)1614 983 y Fv(i)1692 969 y Fx(=)50 b(#)1889 983 y Ft(1)1944 969 y Fu(\001)15 b(\001)g(\001)h Fx(#)2141 983 y Fv(r)2194 969 y Fw(;)14 1133 y Fg(wher)-5 b(e)34 b(e)-5 b(ach)33 b Fx(#)g Fg(stands)h(for)f(either)g Fw(p)f Fg(or)i Fw(q)s Fg(.)41 b(Then)1254 1332 y Fw(Q)1326 1346 y Ft(1)1365 1332 y Fw(A)1433 1346 y Ft(1)p Fv(:::)o(r)1582 1308 y Fr(b)1565 1332 y Fw(f)10 b(Q)1692 1346 y Ft(2)1781 1332 y Fx(=)51 b Fw(Q)1975 1346 y Ft(1)2019 1308 y Fr(d)2014 1332 y Fw(\034)2054 1346 y Fv(n)2101 1332 y Fw(f)9 b(A)2223 1346 y Ft(1)p Fv(:::)o(r)2355 1332 y Fw(Q)2427 1346 y Ft(2)2482 1332 y Fw(;)14 1531 y Fg(wher)-5 b(e)34 b Fw(n)25 b Fx(=)g Fw(n)502 1545 y Ft(2)561 1531 y Fu(\000)20 b Fw(n)707 1545 y Ft(1)778 1531 y Fg(and)34 b Fw(n)1010 1545 y Fv(i)1070 1531 y Fg(is)f(the)g(numb)-5 b(er)33 b(of)g(factors)h Fw(q)h Fg(in)d Fw(Q)2310 1545 y Fv(i)2338 1531 y Fg(.)p Black 14 1714 a Fh(Pro)s(of.)p Black 46 w Fx(De\014ne)1234 1890 y Fw(P)1305 1853 y Fv(r)1292 1914 y(k)1394 1887 y Fx(:)1419 1890 y(=)1665 1804 y Fr(X)1540 2013 y Fv(a)p FF(2f)p Ft(0)p Fv(;)p Ft(1)p FF(g)1784 1990 y Fn(N)5 b Fm(\000)p Fn(r)1596 2039 y Fc(P)1671 2109 y Fn(i)1709 2088 y Fv(a)1746 2098 y Fn(i)1773 2088 y Ft(=)p Fv(k)2022 1777 y(N)1995 1804 y Fr(Y)1952 2000 y Fv(i)p Ft(=)p Fv(r)r Ft(+1)2170 1890 y Fw(p)2216 1849 y Ft(1)p FF(\000)p Fv(a)2343 1859 y Fn(i)2216 1918 y Fv(i)2374 1890 y Fw(q)2418 1849 y Fv(a)2455 1859 y Fn(i)2415 1918 y Fv(i)2501 1890 y Fw(:)14 2241 y Fx(Then,)556 2362 y Fw(Q)628 2376 y Fv(i)673 2338 y Fr(b)656 2362 y Fw(f)59 b Fx(=)882 2276 y Fr(X)928 2474 y Fv(k)1028 2362 y Fw(f)10 b Fx(\()p Fw(k)s Fx(\))15 b Fw(Q)1290 2376 y Fv(i)1319 2362 y Fw(P)1377 2377 y Fv(k)1470 2362 y Fx(=)1591 2276 y Fr(X)1638 2474 y Fv(k)1738 2362 y Fw(f)10 b Fx(\()p Fw(k)s Fx(\))15 b Fw(Q)2000 2376 y Fv(i)2028 2362 y Fw(P)2099 2325 y Fv(r)2086 2386 y(k)r FF(\000)p Fv(n)2223 2396 y Fn(i)2304 2362 y Fx(=)2425 2276 y Fr(X)2471 2474 y Fv(k)2571 2362 y Fw(f)10 b Fx(\()p Fw(k)23 b Fx(+)d Fw(n)2877 2376 y Fv(i)2905 2362 y Fx(\))15 b Fw(Q)3027 2376 y Fv(i)3056 2362 y Fw(P)3127 2325 y Fv(r)3114 2386 y(k)3180 2362 y Fw(:)14 2606 y Fx(The)30 b(claim)h(follo)m(ws)h(from)e(the)g(fact)i (that)f Fw(P)1561 2573 y Fv(r)1548 2633 y(k)1629 2606 y Fx(comm)m(utes)g(with)f Fw(A)2331 2620 y Ft(1)p Fv(:::r)2464 2606 y Fx(.)p 3681 2606 4 62 v 3685 2548 55 4 v 3685 2606 V 3738 2606 4 62 v 14 2845 a Fh(3.3.2)93 b(A)30 b(b)s(ound)e(on)53 b Fb(_)-51 b Fa(\013)14 3016 y Fx(Let)31 b(us)f(abbreviate)1536 3129 y Fw(W)1635 3092 y Fv(')1735 3126 y Fx(:)1760 3129 y(=)51 b Fw(w)22 b Fu(\003)f(j)p Fw(')p Fu(j)2144 3092 y Ft(2)2199 3129 y Fw(:)14 3294 y Fx(F)-8 b(rom)34 b(\(A3\))g(and)f(\(A4\))h(w)m(e)g(\014nd)d Fw(W)1290 3261 y Fv(')1370 3294 y Fu(2)e Fw(L)1522 3261 y FF(1)1630 3294 y Fx(\(see)34 b(\(3.20\))h(b)s(elo)m(w\).)49 b(Then)33 b(i)p Fw(@)2730 3308 y Fv(t)2760 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b(\(A2\),)h(w)m(e)f(see)g(that)g Fw(\013)g Fx(is)g(di\013eren)m(tiable)g(in)f Fw(t)h Fx(with)14 4030 y(deriv)-5 b(ativ)m(e)1346 4143 y(_)-44 b Fw(\013)51 b Fx(=)f(i)1582 4069 y Fr(\012)1625 4143 y Fx(\011)10 b Fw(;)1746 4069 y Fr(\002)1784 4143 y Fw(H)28 b Fu(\000)19 b Fw(H)2061 4105 y Fv(')2122 4143 y Fw(;)30 b Fr(b)-66 b Fw(m)2242 4069 y Fr(\003)2280 4143 y Fx(\011)2350 4069 y Fr(\013)2409 4143 y Fw(;)14 4307 y Fx(where)30 b Fw(H)360 4274 y Fv(')435 4304 y Fx(:)461 4307 y(=)557 4239 y Fr(P)653 4334 y Fv(i)681 4307 y Fx(\()p Fw(h)768 4321 y Fv(i)817 4307 y Fx(+)20 b Fw(W)1007 4263 y Fv(')994 4334 y(i)1056 4307 y Fx(\).)41 b(Th)m(us,)1035 4560 y(_)-44 b Fw(\013)51 b Fx(=)f(i)1271 4432 y Fr(\034)1340 4560 y Fx(\011)25 b Fw(;)1491 4432 y Fr(\024)1568 4499 y Fx(1)p 1549 4539 83 4 v 1549 4623 a Fw(N)1657 4474 y Fr(X)1667 4669 y Fv(i)f Fx(0.)60 b(W)-8 b(e)37 b(also)h(assume)e(that)i(there)e(are)h(constan)m(ts)h Fw(\024)3387 3209 y Ft(1)3427 3195 y Fw(;)15 b(\024)3519 3209 y Ft(2)3595 3195 y Fw(>)35 b Fx(0)241 3308 y(suc)m(h)30 b(that)1634 3421 y Fu(\000)p Fx(\001)49 b Fi(6)i Fw(\024)2004 3435 y Ft(1)2059 3421 y Fw(h)20 b Fx(+)g Fw(\024)2274 3435 y Ft(2)2329 3421 y Fw(;)241 3579 y Fx(as)31 b(an)f(inequalit)m(y)i (of)f(forms)e(on)i Fu(H)1460 3546 y Ft(\(1\))1554 3579 y Fx(.)p Black 15 3760 a(\(B2\))p Black 47 w(The)41 b(Hamiltonian)h (\(3.4\))g(is)f(self-adjoin)m(t)h(and)e(b)s(ounded)e(from)i(b)s(elo)m (w.)72 b(W)-8 b(e)42 b(also)f(assume)g(that)241 3873 y Fu(Q)p Fx(\()p Fw(H)426 3887 y Fv(N)494 3873 y Fx(\))25 b Fu(\032)g Fw(X)725 3887 y Fv(N)793 3873 y Fx(,)31 b(where)e Fw(X)1186 3887 y Fv(N)1284 3873 y Fx(is)i(de\014ned)e(as)h(in)g (Assumption)g(\(A1\).)p Black 15 4055 a(\(B3\))p Black 47 w(There)g(is)h(a)f(constan)m(t)i Fw(\024)1090 4069 y Ft(3)1155 4055 y Fu(2)25 b Fx(\(0)p Fw(;)15 b Fx(1\))32 b(suc)m(h)e(that)1387 4240 y(0)51 b Fi(6)f Fx(\(1)21 b Fu(\000)f Fw(\024)1848 4254 y Ft(3)1888 4240 y Fx(\)\()p Fw(h)2010 4254 y Ft(1)2071 4240 y Fx(+)g Fw(h)2214 4254 y 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userdict /pdfmark systemdict /cleartomark get put } if SDict begin [ end } ifelse % % Gnuplot Prolog Version 4.2 (August 2006) % /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /Z {closepath} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow {currentpoint stroke M 0 vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /Rshow {currentpoint stroke M dup stringwidth pop neg vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /Cshow {currentpoint stroke M dup stringwidth pop -2 div vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /UP {dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def} def /DL {Color {setrgbcolor Solid {pop []} if 0 setdash} {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse} def /BL {stroke userlinewidth 2 mul setlinewidth Rounded {1 setlinejoin 1 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dl1 2 dl2 2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 4 dl2] LC8 DL} def /Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def /Dia {stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt} def /Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt} def /Crs {stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke} def /TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt} def /Star {2 copy Pls Crs} def /BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill} def /TriUF {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill} def /TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt} def /TriDF {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill} def /Pent {stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt} def /PentF {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore} def /Circle {stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt} def /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def end 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3063 y(\015)1785 3122 y Fv(p)1840 3086 y Fw(;)2072 3024 y Fx(1)p 2072 3065 46 4 v 2073 3148 a Fw(q)2178 3086 y Fx(=)2309 3024 y(1)p 2309 3065 V 2309 3148 a Fw(p)2385 3086 y Fu(\000)2487 3024 y Fx(1)p 2486 3065 48 4 v 2486 3148 a Fw(d)2558 3086 y(:)931 b Fx(\(4.10\))14 3325 y(Th)m(us)29 b(if)h Fw(p)25 b Fi(>)g Fw(p)540 3339 y Ft(0)609 3325 y Fx(then)30 b Fw(q)e Fi(>)d Fx(2.)41 b(Denote)32 b(b)m(y)e Fw(X)1605 3339 y Ft(12)1710 3325 y Fx(m)m(ultiplication)i(b)m(y)e Fw(\030)t Fx(\()p Fw(x)2550 3339 y Ft(1)2609 3325 y Fu(\000)20 b Fw(x)2752 3339 y Ft(2)2791 3325 y Fx(\).)41 b(F)-8 b(or)31 b(the)f(follo)m(wing)i(it)e(is)14 3437 y(con)m(v)m(enien)m(t)j (to)e(write)f Fu(r)20 b(\001)h Fw(\030)29 b Fx(=)c Fu(r)1190 3404 y Fv(\032)1230 3437 y Fw(\030)1274 3404 y Fv(\032)1314 3437 y Fx(,)31 b(where)f(a)g(summation)h(o)m(v)m(er)g Fw(\032)26 b Fx(=)f(1)p Fw(;)15 b(:)g(:)g(:)i(;)e(d)31 b Fx(is)f(implied.)155 3550 y(Recalling)j(Lemma)d(3.10,)i(w)m(e)f (therefore)g(get)976 3757 y(\(b\))1097 3715 y 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y(\014)66 4924 y(\012)109 4998 y Fw(X)191 4954 y Fv(\032)184 5024 y Ft(12)274 4998 y Fw(p)320 5012 y Ft(2)360 4998 y Fx(\()p Fu(r)471 4960 y Fv(\032)511 4998 y Fw(p)p Fx(\))592 5012 y Ft(1)633 4998 y Fr(d)-132 b Fw(\034)672 5012 y Ft(2)711 4998 y Fw(n)14 b Fx(\011)c Fw(;)18 b Fr(b)-54 b Fw(n)956 4960 y FF(\000)p Ft(1)1051 4998 y Fw(q)1092 5012 y Ft(1)1131 4998 y Fw(q)1172 5012 y Ft(2)1211 4998 y Fx(\011)1281 4924 y Fr(\013)1324 4921 y(\014)1324 4975 y(\014)1405 4998 y Fi(6)1526 4889 y Fr(q)p 1617 4889 1612 4 v 35 x(\012)1660 4998 y Fx(\()p Fu(r)1771 4972 y Fv(\032)1812 4998 y Fw(p)p Fx(\))1893 5012 y Ft(1)1933 4998 y Fr(d)-132 b Fw(\034)1972 5012 y Ft(2)2011 4998 y Fw(n)15 b Fx(\011)10 b Fw(;)15 b(p)2248 5012 y Ft(2)2287 4998 y Fw(X)2369 4954 y Fv(\032)2362 5024 y Ft(12)2437 4998 y Fw(X)2519 4967 y Fv(\033)2512 5024 y Ft(12)2603 4998 y Fw(p)2649 5012 y Ft(2)2688 4998 y Fx(\()p Fu(r)2799 4972 y Fv(\033)2846 4998 y Fw(p)p Fx(\))2927 5012 y Ft(1)2967 4998 y Fr(d)-132 b Fw(\034)3006 5012 y Ft(2)3045 4998 y Fw(n)15 b Fx(\011)3186 4924 y Fr(\013)3244 4921 y(\015)3244 4975 y(\015)3296 4998 y(b)-53 b Fw(n)3349 4960 y FF(\000)p Ft(1)3443 4998 y Fw(q)3484 5012 y Ft(1)3523 4998 y Fw(q)3564 5012 y Ft(2)3603 4998 y Fx(\011)3674 4921 y Fr(\015)3674 4975 y(\015)1405 5196 y Fi(6)1526 5089 y Fr(q)p 1617 5089 495 4 v 30 x(\015)1617 5174 y(\015)1668 5196 y Fu(j)p Fw(')p Fu(j)1777 5170 y Ft(2)1837 5196 y Fu(\003)21 b Fw(\030)1947 5170 y Ft(2)1986 5119 y Fr(\015)1986 5174 y(\015)2037 5232 y FF(1)2127 5196 y Fu(kr)p Fw(')p Fu(k)2367 5119 y Fr(\015)2367 5174 y(\015)2420 5196 y(d)-132 b Fw(\034)2459 5210 y Ft(2)2498 5196 y Fw(n)14 b Fx(\011)2638 5119 y Fr(\015)2638 5174 y(\015)2704 5119 y(\015)2704 5174 y(\015)2756 5196 y(b)-53 b Fw(n)2809 5159 y FF(\000)p Ft(1)2903 5196 y Fw(q)2944 5210 y Ft(1)2983 5196 y Fw(q)3024 5210 y Ft(2)3063 5196 y Fx(\011)3134 5119 y Fr(\015)3134 5174 y(\015)1405 5432 y Fi(.)50 b Fu(k)p Fw(\030)t Fu(k)1660 5446 y Fv(q)1714 5432 y Fu(k)p Fw(')p Fu(k)1863 5452 y Fv(L)1911 5433 y Fp(2)1947 5452 y FF(\\)p Fv(L)2042 5433 y Fm(1)2127 5432 y Fu(k)p Fw(')p Fu(k)2276 5446 y Fv(X)2334 5455 y Fp(1)2374 5289 y Fr(r)p 2465 5289 273 4 v 143 x Fw(\013)20 b Fx(+)2663 5371 y(2)p 2644 5411 83 4 v 2644 5495 a Fw(N)2752 5362 y Fu(p)p 2828 5362 59 4 v 70 x Fw(\013)c(;)p Black 1835 6000 a Fx(21)p Black eop end %%Page: 22 22 TeXDict begin 22 21 bop Black Black 14 162 a Fx(where)34 b(w)m(e)h(used)e(Y)-8 b(oung's)35 b(inequalit)m(y)-8 b(,)37 b(Assumption)c(\(B1\),)k(and)d(Lemma)g(3.9.)54 b(Recalling)36 b(that)e Fw(\014)j Fi(6)32 b Fw(\013)p Fx(,)14 275 y(w)m(e)f(conclude)g(that)g(the)f(\014rst)g(term)g(on)h (the)f(righ)m(t-hand)g(side)h(of)37 b(\(4.11\))c(is)d(b)s(ounded)f(b)m (y)1411 537 y Fw(C)22 b Fu(k)p Fw(')p Fu(k)1647 500 y Ft(2)1647 560 y Fv(X)1705 569 y Fp(1)1741 560 y FF(\\)p Fv(L)1836 541 y Fm(1)1905 409 y Fr(\022)1972 537 y Fw(\014)j Fx(+)2168 476 y(1)p 2149 517 83 4 v 2149 600 a Fw(N)2242 409 y Fr(\023)2324 537 y Fw(:)155 802 y Fx(Next,)32 b(w)m(e)f(estimate) h(the)e(second)h(term)f(on)g(the)h(righ)m(t-hand)f(side)h(of)37 b(\(4.11\))r(.)k(It)31 b(is)f(equal)h(to)249 972 y Fr(\014)249 1027 y(\014)279 976 y(\012)322 1049 y Fw(X)404 1005 y Fv(\032)397 1075 y Ft(12)487 1049 y Fw(p)533 1063 y Ft(1)572 1049 y Fw(p)618 1063 y Ft(2)674 1049 y Fr(d)-132 b Fw(\034)713 1063 y Ft(2)752 1049 y Fw(n)14 b Fx(\011)c Fw(;)15 b Fu(r)1018 1005 y Fv(\032)1018 1075 y Ft(1)1076 1049 y Fr(b)-53 b Fw(n)1129 1012 y FF(\000)p Ft(1)1223 1049 y Fw(q)1264 1063 y Ft(1)1303 1049 y Fw(q)1344 1063 y Ft(2)1383 1049 y Fx(\011)1453 976 y Fr(\013)1496 972 y(\014)1496 1027 y(\014)1577 1049 y Fi(6)1698 940 y Fr(q)p 1789 940 1082 4 v 36 x(\012)1833 1049 y(d)-132 b Fw(\034)1872 1063 y Ft(2)1911 1049 y Fw(n)15 b Fx(\011)10 b Fw(;)15 b(p)2148 1063 y Ft(1)2188 1049 y Fw(p)2234 1063 y Ft(2)2273 1049 y Fw(X)2355 1018 y Ft(2)2348 1075 y(12)2423 1049 y Fw(p)2469 1063 y Ft(1)2508 1049 y Fw(p)2554 1063 y Ft(2)2609 1049 y Fr(d)-132 b Fw(\034)2648 1063 y Ft(2)2687 1049 y Fw(n)15 b Fx(\011)2828 976 y Fr(\013)2886 972 y(\015)2886 1027 y(\015)2936 1049 y Fu(r)3012 1063 y Ft(1)3069 1049 y Fr(b)-53 b Fw(n)3122 1012 y FF(\000)p Ft(1)3231 1049 y Fw(q)3272 1063 y Ft(1)3311 1049 y Fw(q)3352 1063 y Ft(2)3391 1049 y Fx(\011)3462 972 y Fr(\015)3462 1027 y(\015)1577 1248 y Fi(6)1698 1140 y Fr(q)p 1789 1140 495 4 v 31 x(\015)1789 1225 y(\015)1840 1248 y Fu(j)p Fw(')p Fu(j)1949 1222 y Ft(2)2009 1248 y Fu(\003)21 b Fw(\030)2119 1222 y Ft(2)2158 1171 y Fr(\015)2158 1225 y(\015)2209 1284 y FF(1)2299 1248 y Fu(k)q Fr(d)-132 b Fw(\034)2384 1262 y Ft(2)2423 1248 y Fw(n)15 b Fx(\011)p Fu(k)2624 1171 y Fr(\015)2624 1225 y(\015)2675 1248 y Fu(r)2751 1262 y Ft(1)2807 1248 y Fr(b)-53 b Fw(n)2860 1210 y FF(\000)p Ft(1)2969 1248 y Fw(q)3010 1262 y Ft(1)3049 1248 y Fw(q)3090 1262 y Ft(2)3129 1248 y Fx(\011)3200 1171 y Fr(\015)3200 1225 y(\015)1577 1484 y Fi(6)50 b Fu(k)p Fw(\030)t Fu(k)1832 1498 y Fv(q)1886 1484 y Fu(k)p Fw(')p Fu(k)2035 1504 y Fv(L)2083 1485 y Fp(2)2119 1504 y FF(\\)p Fv(L)2214 1485 y Fm(1)2284 1341 y Fr(r)p 2375 1341 273 4 v 143 x Fw(\013)20 b Fx(+)2573 1422 y(2)p 2554 1463 83 4 v 2554 1546 a Fw(N)2662 1407 y Fr(\015)2662 1461 y(\015)2713 1484 y Fu(r)2789 1498 y Ft(1)2845 1484 y Fr(b)-53 b Fw(n)2898 1446 y FF(\000)p Ft(1)3007 1484 y Fw(q)3048 1498 y Ft(1)3087 1484 y Fw(q)3128 1498 y Ft(2)3167 1484 y Fx(\011)3238 1407 y Fr(\015)3238 1461 y(\015)3303 1484 y Fw(:)14 1740 y Fx(W)-8 b(e)31 b(estimate)533 1663 y Fr(\015)533 1718 y(\015)584 1740 y Fu(r)660 1754 y Ft(1)716 1740 y Fr(b)-53 b Fw(n)769 1707 y FF(\000)p Ft(1)878 1740 y Fw(q)919 1754 y Ft(1)958 1740 y Fw(q)999 1754 y Ft(2)1038 1740 y Fx(\011)1109 1663 y Fr(\015)1109 1718 y(\015)1189 1740 y Fx(b)m(y)29 b(in)m(tro)s(ducing)h Fj(1)25 b Fx(=)f Fw(p)2019 1754 y Ft(1)2077 1740 y Fx(+)19 b Fw(q)2208 1754 y Ft(1)2276 1740 y Fx(on)30 b(the)f(left.)42 b(The)29 b(term)g(arising)h(from)f Fw(p)3707 1754 y Ft(1)14 1853 y Fx(is)i(b)s(ounded)d(b)m(y)642 1988 y Fr(\015)642 2043 y(\015)693 2066 y Fw(p)739 2080 y Ft(1)778 2066 y Fu(r)854 2080 y Ft(1)910 2066 y Fr(b)-53 b Fw(n)963 2028 y FF(\000)p Ft(1)1072 2066 y Fw(q)1113 2080 y Ft(1)1152 2066 y Fw(q)1193 2080 y Ft(2)1232 2066 y Fx(\011)1303 1988 y Fr(\015)1303 2043 y(\015)1404 2066 y Fx(=)1525 1988 y Fr(\015)1525 2043 y(\015)1576 2066 y Fw(p)1622 2080 y Ft(1)1661 2066 y Fw(q)1702 2080 y Ft(2)1757 2066 y Fr(d)-132 b Fw(\034)1796 2080 y Ft(1)1835 2066 y Fw(n)1890 2024 y FF(\000)p Ft(1)1999 2066 y Fu(r)2075 2080 y Ft(1)2115 2066 y Fw(q)2156 2080 y Ft(1)2195 2066 y Fx(\011)2266 1988 y Fr(\015)2266 2043 y(\015)1404 2253 y Fi(6)1525 2140 y Fr(q)p 1616 2140 1007 4 v 40 x(\012)1659 2253 y Fu(r)1735 2267 y Ft(1)1774 2253 y Fw(q)1815 2267 y Ft(1)1854 2253 y Fx(\011)10 b Fw(;)15 b(q)2016 2267 y Ft(2)2072 2253 y Fr(d)-132 b Fw(\034)2111 2267 y Ft(1)2150 2253 y Fw(n)2204 2211 y FF(\000)p Ft(2)2314 2253 y Fu(r)2390 2267 y Ft(1)2429 2253 y Fw(q)2470 2267 y Ft(1)2509 2253 y Fx(\011)2580 2180 y Fr(\013)1404 2534 y Fx(=)1525 2340 y Fr(v)1525 2391 y(u)1525 2446 y(u)1525 2500 y(t)p 1621 2340 1498 4 v -94 x(\034)1689 2534 y Fu(r)1765 2548 y Ft(1)1805 2534 y Fw(q)1846 2548 y Ft(1)1885 2534 y Fx(\011)25 b Fw(;)2143 2472 y Fx(1)p 2046 2513 240 4 v 2046 2596 a Fw(N)30 b Fu(\000)20 b Fx(1)2345 2420 y Fv(N)2311 2448 y Fr(X)2319 2643 y Fv(i)p Ft(=2)2457 2534 y Fw(q)2498 2548 y Fv(i)2542 2534 y Fr(d)-132 b Fw(\034)2581 2548 y Ft(1)2620 2534 y Fw(n)2675 2492 y FF(\000)p Ft(2)2784 2534 y Fu(r)2860 2548 y Ft(1)2900 2534 y Fw(q)2941 2548 y Ft(1)2980 2534 y Fx(\011)3050 2406 y Fr(\035)1404 2898 y Fi(6)1525 2705 y Fr(v)1525 2756 y(u)1525 2810 y(u)1525 2865 y(t)p 1621 2705 1341 4 v -95 x(\034)1689 2898 y Fu(r)1765 2912 y Ft(1)1805 2898 y Fw(q)1846 2912 y Ft(1)1885 2898 y Fx(\011)25 b Fw(;)2065 2837 y Fx(1)p 2046 2877 83 4 v 2046 2960 a Fw(N)2188 2784 y Fv(N)2154 2812 y Fr(X)2163 3007 y Fv(i)p Ft(=1)2301 2898 y Fw(q)2342 2912 y Fv(i)2386 2898 y Fr(d)-132 b Fw(\034)2425 2912 y Ft(1)2464 2898 y Fw(n)2518 2856 y FF(\000)p Ft(2)2628 2898 y Fu(r)2704 2912 y Ft(1)2743 2898 y Fw(q)2784 2912 y Ft(1)2823 2898 y Fx(\011)2894 2770 y Fr(\035)1404 3182 y Fx(=)1525 3069 y Fr(q)p 1616 3069 1021 4 v 39 x(\012)1659 3182 y Fu(r)1735 3196 y Ft(1)1774 3182 y Fw(q)1815 3196 y Ft(1)1854 3182 y Fx(\011)10 b Fw(;)18 b Fr(b)-54 b Fw(n)2030 3156 y Ft(2)2086 3182 y Fr(d)-132 b Fw(\034)2125 3196 y Ft(1)2164 3182 y Fw(n)2218 3140 y FF(\000)p Ft(2)2328 3182 y Fu(r)2404 3196 y Ft(1)2443 3182 y Fw(q)2484 3196 y Ft(1)2523 3182 y Fx(\011)2594 3108 y Fr(\013)1404 3341 y Fi(6)50 b Fu(kr)1646 3355 y Ft(1)1686 3341 y Fw(q)1727 3355 y Ft(1)1766 3341 y Fx(\011)p Fu(k)15 b Fw(:)14 3553 y Fx(The)27 b(term)h(arising)g(from) g Fw(q)958 3567 y Ft(1)1024 3553 y Fx(in)g(the)g(ab)s(o)m(v)m(e)h (splitting)f(is)g(dealt)h(with)e(in)g(exactly)j(the)e(same)g(w)m(a)m(y) -8 b(.)41 b(Th)m(us)27 b(w)m(e)14 3666 y(ha)m(v)m(e)32 b(pro)m(v)m(en)e(that)h(the)g(second)f(term)h(on)f(the)h(righ)m(t-hand) f(side)g(of)38 b(\(4.11\))32 b(is)f(b)s(ounded)d(b)m(y)1259 3947 y Fw(C)7 b Fu(k)p Fw(')p Fu(k)1480 3966 y Fv(L)1528 3947 y Fp(2)1564 3966 y FF(\\)p Fv(L)1659 3947 y Fm(1)1728 3804 y Fr(r)p 1819 3804 271 4 v 143 x Fw(\014)25 b Fx(+)2015 3885 y(1)p 1996 3926 83 4 v 1996 4009 a Fw(N)2104 3947 y Fu(kr)2225 3961 y Ft(1)2265 3947 y Fw(q)2306 3961 y Ft(1)2345 3947 y Fx(\011)p Fu(k)15 b Fw(:)155 4192 y Fx(Summarizing,)30 b(w)m(e)h(ha)m(v)m(e)640 4467 y(\(b\))761 4425 y Ft(\()p Fv(p)p Ft(\))906 4467 y Fi(.)51 b Fu(k)p Fw(')p Fu(k)1177 4430 y Ft(2)1177 4490 y Fv(X)1235 4499 y Fp(1)1271 4490 y FF(\\)p Fv(L)1366 4471 y Fm(1)1435 4339 y Fr(\022)1502 4467 y Fw(\014)25 b Fx(+)1698 4406 y(1)p 1679 4446 V 1679 4530 a Fw(N)1772 4339 y Fr(\023)1859 4467 y Fx(+)20 b Fu(k)p Fw(')p Fu(k)2099 4487 y Fv(L)2147 4468 y Fp(2)2183 4487 y FF(\\)p Fv(L)2278 4468 y Fm(1)2347 4325 y Fr(r)p 2438 4325 271 4 v 142 x Fw(\014)25 b Fx(+)2634 4406 y(1)p 2615 4446 83 4 v 2615 4530 a Fw(N)2723 4467 y Fu(kr)2844 4481 y Ft(1)2884 4467 y Fw(q)2925 4481 y Ft(1)2964 4467 y Fx(\011)p Fu(k)15 b Fw(:)14 4850 y Fg(Conclusion)35 b(of)e(the)h(pr)-5 b(o)g(of.)46 b Fx(Putting)31 b(all)h(the)g (estimates)h(of)e(the)h(righ)m(t-hand)f(side)g(of)39 b(\(4.8\))33 b(together,)g(w)m(e)14 4963 y(\014nd)97 5127 y Fr(\012)140 5200 y Fx(\011)10 b Fw(;)15 b Fx(\()p Fj(1)20 b Fu(\000)g Fw(p)507 5214 y Ft(1)547 5200 y Fw(p)593 5214 y Ft(2)632 5200 y Fx(\))p Fw(h)719 5214 y Ft(1)759 5200 y Fx(\()p Fj(1)g Fu(\000)g Fw(p)1005 5214 y Ft(1)1044 5200 y Fw(p)1090 5214 y Ft(2)1129 5200 y Fx(\)\011)1235 5127 y Fr(\013)420 5418 y Fi(.)50 b Fw(E)613 5380 y Ft(\011)693 5418 y Fu(\000)20 b Fw(E)856 5380 y Fv(')926 5418 y Fx(+)1017 5344 y Fr(\000)1059 5418 y Fx(1)h(+)e Fu(k)p Fw(')p Fu(k)1364 5380 y Ft(2)1364 5450 y Fv(X)1427 5427 y Fp(2)1422 5471 y(1)1464 5450 y FF(\\)p Fv(L)1559 5431 y Fm(1)1628 5344 y Fr(\001)1670 5289 y(\022)1736 5418 y Fw(\014)26 b Fx(+)1970 5356 y(1)p 1914 5397 159 4 v 1914 5415 a Fu(p)p 1989 5415 83 4 v 1989 5492 a Fw(N)2082 5289 y Fr(\023)2170 5418 y Fx(+)19 b Fu(k)p Fw(')p Fu(k)2409 5437 y Fv(L)2457 5418 y Fp(2)2493 5437 y FF(\\)p Fv(L)2588 5418 y Fm(1)2658 5275 y Fr(r)p 2749 5275 271 4 v 143 x Fw(\014)25 b Fx(+)2945 5356 y(1)p 2926 5397 83 4 v 2926 5480 a Fw(N)3034 5418 y Fu(kr)3155 5432 y Ft(1)3195 5418 y Fw(q)3236 5432 y Ft(1)3275 5418 y Fx(\011)p Fu(k)15 b Fw(:)83 b Fx(\(4.12\))p Black 1835 6000 a(22)p Black eop end %%Page: 23 23 TeXDict begin 23 22 bop Black Black 14 162 a Fx(Next,)32 b(from)e Fj(1)19 b Fu(\000)h Fw(p)687 176 y Ft(1)726 162 y Fw(p)772 176 y Ft(2)837 162 y Fx(=)25 b Fw(p)979 176 y Ft(1)1018 162 y Fw(q)1059 176 y Ft(2)1118 162 y Fx(+)20 b Fw(q)1250 176 y Ft(1)1319 162 y Fx(w)m(e)31 b(deduce)141 345 y Fu(k)186 261 y Fr(p)p 277 261 92 4 v 84 x Fw(h)329 359 y Ft(1)369 345 y Fw(q)410 359 y Ft(1)449 345 y Fx(\011)p Fu(k)51 b Fx(=)737 267 y Fr(\015)737 322 y(\015)787 261 y(p)p 878 261 V 84 x Fw(h)930 359 y Ft(1)970 345 y Fx(\()p Fj(1)20 b Fu(\000)g Fw(p)1216 359 y Ft(1)1255 345 y Fw(p)1301 359 y Ft(2)1341 345 y Fx(\)\011)g Fu(\000)1558 261 y Fr(p)p 1649 261 V 84 x Fw(h)1701 359 y Ft(1)1740 345 y Fw(p)1786 359 y Ft(1)1826 345 y Fw(q)1867 359 y Ft(2)1906 345 y Fx(\011)1977 267 y Fr(\015)1977 322 y(\015)2077 345 y Fi(6)2199 267 y Fr(\015)2199 322 y(\015)2249 261 y(p)p 2340 261 V 84 x Fw(h)2392 359 y Ft(1)2432 345 y Fx(\()p Fj(1)g Fu(\000)g Fw(p)2678 359 y Ft(1)2717 345 y Fw(p)2763 359 y Ft(2)2802 345 y Fx(\)\011)2908 267 y Fr(\015)2908 322 y(\015)2979 345 y Fx(+)g Fu(k)3115 261 y Fr(p)p 3206 261 V 84 x Fw(h)3258 359 y Ft(1)3298 345 y Fw(p)3344 359 y Ft(1)3383 345 y Fw(q)3424 359 y Ft(2)3463 345 y Fx(\011)p Fu(k)15 b Fw(:)14 527 y Fx(No)m(w,)31 b(recalling)h(that)f Fw(p)25 b Fx(=)g Fu(j)p Fw(')p Fu(ih)p Fw(')p Fu(j)p Fx(,)33 b(w)m(e)e(\014nd)936 719 y Fu(k)981 635 y Fr(p)p 1073 635 V 1073 719 a Fw(h)1125 733 y Ft(1)1164 719 y Fw(p)1210 733 y Ft(1)1250 719 y Fw(q)1291 733 y Ft(2)1330 719 y Fx(\011)p Fu(k)50 b Fi(6)h Fu(k)1663 635 y Fr(p)p 1754 635 V 84 x Fw(h)1806 733 y Ft(1)1846 719 y Fw(p)1892 733 y Ft(1)1931 719 y Fu(kk)p Fw(q)2062 733 y Ft(2)2102 719 y Fx(\011)p Fu(k)f Fi(6)h Fu(k)p Fw(')p Fu(k)2539 733 y Fv(X)2597 742 y Fp(1)2637 637 y Fr(p)p 2728 637 57 4 v 82 x Fw(\014)20 b(:)14 902 y Fx(Therefore,)935 1015 y Fu(k)980 931 y Fr(p)p 1072 931 92 4 v 1072 1015 a Fw(h)1124 1029 y Ft(1)1163 1015 y Fw(q)1204 1029 y Ft(1)1244 1015 y Fx(\011)p Fu(k)1360 977 y Ft(2)1450 1015 y Fi(.)1571 937 y Fr(\015)1571 992 y(\015)1621 931 y(p)p 1712 931 V 84 x Fw(h)1764 1029 y Ft(1)1804 1015 y Fx(\()p Fj(1)g Fu(\000)g Fw(p)2050 1029 y Ft(1)2089 1015 y Fw(p)2135 1029 y Ft(2)2174 1015 y Fx(\)\011)2280 937 y Fr(\015)2280 992 y(\015)2331 964 y Ft(2)2391 1015 y Fx(+)g Fu(k)p Fw(')p Fu(k)2631 977 y Ft(2)2631 1037 y Fv(X)2689 1046 y Fp(1)2729 1015 y Fw(\014)g(:)14 1171 y Fx(Plugging)31 b(in)f(\(4.12\))j(yields)113 1344 y Fr(\015)113 1399 y(\015)163 1337 y(p)p 254 1337 V 84 x Fw(h)306 1435 y Ft(1)346 1421 y Fw(q)387 1435 y Ft(1)426 1421 y Fx(\011)497 1344 y Fr(\015)497 1399 y(\015)547 1370 y Ft(2)637 1421 y Fi(.)50 b Fw(E)830 1384 y Ft(\011)910 1421 y Fu(\000)20 b Fw(E)1073 1384 y Fv(')1143 1421 y Fx(+)1234 1348 y Fr(\000)1276 1421 y Fx(1)h(+)e Fu(k)p Fw(')p Fu(k)1581 1384 y Ft(2)1581 1453 y Fv(X)1644 1431 y Fp(2)1639 1475 y(1)1681 1453 y FF(\\)p Fv(L)1776 1435 y Fm(1)1845 1348 y Fr(\001)1887 1293 y(\022)1953 1421 y Fw(\014)26 b Fx(+)2187 1360 y(1)p 2131 1401 159 4 v 2131 1419 a Fu(p)p 2206 1419 83 4 v 2206 1496 a Fw(N)2299 1293 y Fr(\023)2387 1421 y Fx(+)19 b Fu(k)p Fw(')p Fu(k)2626 1441 y Fv(L)2674 1422 y Fp(2)2710 1441 y FF(\\)p Fv(L)2805 1422 y Fm(1)2875 1279 y Fr(r)p 2966 1279 271 4 v 142 x Fw(\014)25 b Fx(+)3162 1360 y(1)p 3143 1401 83 4 v 3143 1484 a Fw(N)3251 1421 y Fu(kr)3372 1435 y Ft(1)3412 1421 y Fw(q)3453 1435 y Ft(1)3492 1421 y Fx(\011)p Fu(k)15 b Fw(:)14 1654 y Fx(Next,)32 b(w)m(e)e(observ)m(e)h (that)g(Assumption)f(\(B1\))i(implies)1249 1846 y Fu(kr)1370 1860 y Ft(1)1410 1846 y Fw(q)1451 1860 y Ft(1)1490 1846 y Fx(\011)p Fu(k)51 b Fi(.)1778 1769 y Fr(\015)1778 1823 y(\015)1829 1762 y(p)p 1919 1762 92 4 v 1919 1846 a Fw(h)1971 1860 y Ft(1)2011 1846 y Fw(q)2052 1860 y Ft(1)2091 1846 y Fx(\011)2162 1769 y Fr(\015)2162 1823 y(\015)2233 1846 y Fx(+)2324 1764 y Fr(p)p 2415 1764 57 4 v 82 x Fw(\014)20 b(;)14 2028 y Fx(so)31 b(that)g(w)m(e)g(get)79 2197 y Fr(\015)79 2251 y(\015)129 2190 y(p)p 220 2190 92 4 v 84 x Fw(h)272 2288 y Ft(1)312 2274 y Fw(q)353 2288 y Ft(1)392 2274 y Fx(\011)463 2197 y Fr(\015)463 2251 y(\015)513 2223 y Ft(2)603 2274 y Fi(.)50 b Fw(E)796 2237 y Ft(\011)876 2274 y Fu(\000)20 b Fw(E)1039 2237 y Fv(')1110 2274 y Fx(+)1200 2200 y Fr(\000)1242 2274 y Fx(1)h(+)f Fu(k)p Fw(')p Fu(k)1548 2237 y Ft(2)1548 2306 y Fv(X)1611 2283 y Fp(2)1606 2327 y(1)1647 2306 y FF(\\)p Fv(L)1742 2287 y Fm(1)1811 2200 y Fr(\001)1853 2146 y(\022)1920 2274 y Fw(\014)25 b Fx(+)2154 2213 y(1)p 2097 2253 159 4 v 2097 2271 a Fu(p)p 2173 2271 83 4 v 77 x Fw(N)2266 2146 y Fr(\023)2353 2274 y Fx(+)20 b Fu(k)p Fw(')p Fu(k)2593 2294 y Fv(L)2641 2275 y Fp(2)2677 2294 y FF(\\)p Fv(L)2772 2275 y Fm(1)2841 2131 y Fr(r)p 2932 2131 271 4 v 143 x Fw(\014)25 b Fx(+)3128 2213 y(1)p 3109 2253 83 4 v 3109 2336 a Fw(N)3217 2274 y Fu(k)3262 2190 y Fr(p)p 3353 2190 92 4 v 84 x Fw(h)3405 2288 y Ft(1)3445 2274 y Fw(q)3486 2288 y Ft(1)3525 2274 y Fx(\011)p Fu(k)15 b Fw(:)14 2501 y Fx(No)m(w)31 b(w)m(e)g(claim)h(that)733 2634 y Fr(\015)733 2688 y(\015)784 2627 y(p)p 875 2627 V 84 x Fw(h)927 2725 y Ft(1)966 2711 y Fw(q)1007 2725 y Ft(1)1046 2711 y Fx(\011)1117 2634 y Fr(\015)1117 2688 y(\015)1168 2660 y Ft(2)1258 2711 y Fi(.)50 b Fw(E)1451 2674 y Ft(\011)1530 2711 y Fu(\000)20 b Fw(E)1693 2674 y Fv(')1764 2711 y Fx(+)1855 2638 y Fr(\000)1897 2711 y Fx(1)g(+)g Fu(k)p Fw(')p Fu(k)2202 2674 y Ft(2)2202 2743 y Fv(X)2265 2720 y Fp(2)2260 2764 y(1)2301 2743 y FF(\\)p Fv(L)2396 2724 y Fm(1)2466 2638 y Fr(\001)2507 2583 y(\022)2574 2711 y Fw(\014)26 b Fx(+)2808 2650 y(1)p 2751 2690 159 4 v 2751 2708 a Fu(p)p 2827 2708 83 4 v 77 x Fw(N)2920 2583 y Fr(\023)3002 2711 y Fw(:)487 b Fx(\(4.13\))14 2939 y(This)30 b(follo)m(ws)h(from)f(the)h(general)g (estimate)948 3121 y Fw(x)1000 3084 y Ft(2)1090 3121 y Fi(6)50 b Fw(C)7 b Fx(\()p Fw(R)21 b Fx(+)f Fw(ax)p Fx(\))116 b(=)-15 b Fu(\))116 b Fw(x)2065 3084 y Ft(2)2155 3121 y Fi(6)50 b Fx(2)p Fw(C)7 b(R)21 b Fx(+)f Fw(C)2646 3084 y Ft(2)2685 3121 y Fw(a)2733 3084 y Ft(2)2787 3121 y Fw(;)14 3304 y Fx(whic)m(h)30 b(itself)h(follo)m(ws)h(from)e(the)g (elemen)m(tary)i(inequalit)m(y)1171 3519 y Fw(C)7 b Fx(\()p Fw(R)21 b Fx(+)e Fw(ax)p Fx(\))51 b Fi(6)f Fw(C)7 b(R)21 b Fx(+)2028 3458 y(1)p 2028 3498 46 4 v 2028 3582 a(2)2083 3519 y Fw(C)2155 3482 y Ft(2)2194 3519 y Fw(a)2242 3482 y Ft(2)2302 3519 y Fx(+)2403 3458 y(1)p 2403 3498 V 2403 3582 a(2)2458 3519 y Fw(x)2510 3482 y Ft(2)2565 3519 y Fw(:)14 3728 y Fx(The)30 b(claim)h(of)g(the)g(Lemma)f(no)m(w)g(follo) m(ws)i(from)e(\(4.13\))i(b)m(y)f(using)f(Assumption)f(\(B1\).)p 3681 3728 4 62 v 3685 3670 55 4 v 3685 3728 V 3738 3728 4 62 v 14 3964 a Fh(4.3.2)93 b(A)30 b(b)s(ound)e(on)823 3942 y Fb(_)798 3964 y Fa(\014)14 4136 y Fx(W)-8 b(e)34 b(start)g(exactly)g(as)f(in)g(Section)g(3.)49 b(Assumptions)32 b(\(B1\))i({)f(\(B5\))h(imply)f(that)g Fw(\014)38 b Fx(is)33 b(di\013eren)m(tiable)h(in)f Fw(t)14 4249 y Fx(with)d(deriv)-5 b(ativ)m(e)949 4425 y(_)926 4449 y Fw(\014)56 b Fx(=)1174 4387 y(i)p 1164 4428 46 4 v 1164 4511 a(2)1220 4375 y Fr(\012)1263 4449 y Fx(\011)10 b Fw(;)1384 4375 y Fr(\002)1422 4449 y Fx(\()p Fw(N)30 b Fu(\000)20 b Fx(1\))p Fw(W)1817 4463 y Ft(12)1913 4449 y Fu(\000)g Fw(N)10 b(W)2186 4405 y Fv(')2173 4475 y Ft(1)2255 4449 y Fu(\000)20 b Fw(N)10 b(W)2528 4405 y Fv(')2515 4475 y Ft(2)2588 4449 y Fw(;)17 b Fr(b)-53 b Fw(n)2683 4375 y Fr(\003)2721 4449 y Fx(\011)2791 4375 y Fr(\013)1033 4624 y Fx(=)50 b(2\(I\))21 b(+)f(2\(I)s(I\))h(+)f (\(I)s(I)s(I\))f(+)50 b(complex)31 b(conjugate)17 b Fw(;)711 b Fx(\(4.14\))14 4806 y(where)737 5006 y(\(I\))891 5003 y(:)917 5006 y(=)1058 4945 y(i)p 1048 4985 V 1048 5068 a(2)1103 4932 y Fr(\012)1146 5006 y Fx(\011)10 b Fw(;)15 b(p)1313 5020 y Ft(1)1353 5006 y Fw(p)1399 5020 y Ft(2)1438 4932 y Fr(\002)1476 5006 y Fx(\()p Fw(N)30 b Fu(\000)20 b Fx(1\))p Fw(W)1871 5020 y Ft(12)1967 5006 y Fu(\000)g Fw(N)10 b(W)2240 4962 y Fv(')2227 5032 y Ft(1)2309 5006 y Fu(\000)20 b Fw(N)10 b(W)2582 4962 y Fv(')2569 5032 y Ft(2)2642 5006 y Fw(;)17 b Fr(b)-53 b Fw(n)2737 4932 y Fr(\003)2775 5006 y Fw(q)2816 5020 y Ft(1)2855 5006 y Fw(p)2901 5020 y Ft(2)2940 5006 y Fx(\011)3011 4932 y Fr(\013)3069 5006 y Fw(;)702 5224 y Fx(\(I)s(I\))891 5221 y(:)917 5224 y(=)1058 5162 y(i)p 1048 5203 V 1048 5286 a(2)1103 5150 y Fr(\012)1146 5224 y Fx(\011)10 b Fw(;)15 b(q)1308 5238 y Ft(1)1347 5224 y Fw(p)1393 5238 y Ft(2)1433 5150 y Fr(\002)1470 5224 y Fx(\()p Fw(N)31 b Fu(\000)20 b Fx(1\))p Fw(W)1866 5238 y Ft(12)1961 5224 y Fu(\000)g Fw(N)10 b(W)2234 5180 y Fv(')2221 5250 y Ft(1)2304 5224 y Fu(\000)20 b Fw(N)10 b(W)2577 5180 y Fv(')2564 5250 y Ft(2)2637 5224 y Fw(;)17 b Fr(b)-53 b Fw(n)2732 5150 y Fr(\003)2770 5224 y Fw(q)2811 5238 y Ft(1)2850 5224 y Fw(q)2891 5238 y Ft(2)2930 5224 y Fx(\011)3000 5150 y Fr(\013)3058 5224 y Fw(;)667 5442 y Fx(\(I)s(I)s(I\))891 5439 y(:)917 5442 y(=)1058 5380 y(i)p 1048 5421 V 1048 5504 a(2)1103 5368 y Fr(\012)1146 5442 y Fx(\011)10 b Fw(;)15 b(p)1313 5456 y Ft(1)1353 5442 y Fw(p)1399 5456 y Ft(2)1438 5368 y Fr(\002)1476 5442 y Fx(\()p Fw(N)30 b Fu(\000)20 b Fx(1\))p Fw(W)1871 5456 y Ft(12)1967 5442 y Fu(\000)g Fw(N)10 b(W)2240 5397 y Fv(')2227 5468 y Ft(1)2309 5442 y Fu(\000)20 b Fw(N)10 b(W)2582 5397 y Fv(')2569 5468 y Ft(2)2642 5442 y Fw(;)17 b Fr(b)-53 b Fw(n)2737 5368 y Fr(\003)2775 5442 y Fw(q)2816 5456 y Ft(1)2855 5442 y Fw(q)2896 5456 y Ft(2)2935 5442 y Fx(\011)3005 5368 y Fr(\013)3064 5442 y Fw(:)p Black 1835 6000 a Fx(23)p Black eop end %%Page: 24 24 TeXDict begin 24 23 bop Black Black 14 162 a Fg(T)-7 b(erm)33 b Fx(\(I\))q Fg(.)40 b Fx(Using)32 b(\(3.17\))h(w)m(e)d (\014nd)684 382 y(2)729 305 y Fr(\014)729 359 y(\014)760 382 y Fx(\(I\))863 305 y Fr(\014)863 359 y(\014)944 382 y Fx(=)1066 305 y Fr(\014)1066 359 y(\014)1096 308 y(\012)1139 382 y Fx(\011)10 b Fw(;)15 b(p)1306 396 y Ft(1)1345 382 y Fw(p)1391 396 y Ft(2)1430 308 y Fr(\002)1468 382 y Fx(\()p Fw(N)31 b Fu(\000)20 b Fx(1\))p Fw(W)1864 396 y Ft(12)1959 382 y Fu(\000)g Fw(N)10 b(W)2232 338 y Fv(')2219 408 y Ft(1)2302 382 y Fu(\000)20 b Fw(N)10 b(W)2575 338 y Fv(')2562 408 y Ft(2)2634 382 y Fw(;)18 b Fr(b)-54 b Fw(n)2729 308 y Fr(\003)2767 382 y Fw(q)2808 396 y Ft(1)2847 382 y Fw(p)2893 396 y Ft(2)2932 382 y Fx(\011)3003 308 y Fr(\013)3046 305 y(\014)3046 359 y(\014)944 520 y Fx(=)1066 443 y Fr(\014)1066 497 y(\014)1096 446 y(\012)1139 520 y Fx(\011)10 b Fw(;)15 b(p)1306 534 y Ft(1)1345 520 y Fw(p)1391 534 y Ft(2)1430 446 y Fr(\002)1468 520 y Fw(W)1567 476 y Fv(')1554 546 y Ft(1)1627 520 y Fw(;)i Fr(b)-53 b Fw(n)1722 446 y Fr(\003)1760 520 y Fw(q)1801 534 y Ft(1)1840 520 y Fw(p)1886 534 y Ft(2)1925 520 y Fx(\011)1996 446 y Fr(\013)2039 443 y(\014)2039 497 y(\014)944 658 y Fx(=)1066 580 y Fr(\014)1066 635 y(\014)1096 584 y(\012)1139 658 y Fx(\011)10 b Fw(;)15 b(p)1306 672 y Ft(1)1345 658 y Fw(p)1391 672 y Ft(2)1430 658 y Fw(W)1529 614 y Fv(')1516 684 y Ft(1)1579 584 y Fr(\000)1623 658 y(b)-53 b Fw(n)19 b Fu(\000)29 b Fs([)-181 b Fw(\034)1826 672 y FF(\000)p Ft(1)1920 658 y Fw(n)1975 584 y Fr(\001)2017 658 y Fw(q)2058 672 y Ft(1)2097 658 y Fw(p)2143 672 y Ft(2)2182 658 y Fx(\011)2252 584 y Fr(\013)2295 580 y(\014)2295 635 y(\014)2341 658 y Fw(;)14 878 y Fx(where)30 b(w)m(e)h(used)e(Lemma) i(3.10.)42 b(De\014ne)195 1139 y Fw(\026)p Fx(\()p Fw(k)s Fx(\))421 1136 y(:)447 1139 y(=)50 b Fw(N)651 1065 y Fr(\000)692 1139 y Fw(n)p Fx(\()p Fw(k)s Fx(\))21 b Fu(\000)f Fx(\()p Fw(\034)1054 1153 y FF(\000)p Ft(1)1148 1139 y Fw(n)p Fx(\)\()p Fw(k)s Fx(\))1359 1065 y Fr(\001)1451 1139 y Fx(=)1763 1000 y Fu(p)p 1839 1000 83 4 v 77 x Fw(N)p 1583 1118 520 4 v 1583 1136 a Fu(p)p 1658 1136 51 4 v 1658 1213 a Fw(k)k Fx(+)1820 1140 y Fu(p)p 1895 1140 207 4 v 1895 1213 a Fw(k)g Fu(\000)c Fx(1)2163 1139 y Fi(6)50 b Fw(n)2339 1101 y FF(\000)p Ft(1)2433 1139 y Fx(\()p Fw(k)s Fx(\))15 b Fw(;)198 b(k)28 b Fx(=)d(1)p Fw(;)15 b(:)g(:)g(:)i(;)e(N)26 b(:)181 b Fx(\(4.15\))14 1405 y(Th)m(us,)1197 1581 y Fr(\014)1197 1635 y(\014)1228 1658 y Fx(\(I\))1331 1581 y Fr(\014)1331 1635 y(\014)1412 1658 y Fx(=)1562 1597 y(1)p 1543 1637 83 4 v 1543 1721 a Fw(N)1636 1581 y Fr(\014)1636 1635 y(\014)1666 1585 y(\012)1709 1658 y Fx(\011)10 b Fw(;)15 b(p)1876 1672 y Ft(1)1916 1658 y Fw(p)1962 1672 y Ft(2)2001 1658 y Fw(W)2100 1614 y Fv(')2087 1684 y Ft(1)2169 1658 y Fr(b)-55 b Fw(\026)15 b(q)2276 1672 y Ft(1)2315 1658 y Fw(p)2361 1672 y Ft(2)2400 1658 y Fx(\011)2471 1585 y Fr(\013)2514 1581 y(\014)2514 1635 y(\014)1412 1874 y Fi(6)1562 1812 y Fx(1)p 1543 1853 V 1543 1936 a Fw(N)1636 1874 y Fu(k)p Fw(W)1780 1836 y Fv(')1830 1874 y Fu(k)1875 1888 y FF(1)1950 1764 y Fr(q)p 2041 1764 468 4 v 36 x(\012)2084 1874 y Fx(\011)10 b Fw(;)20 b Fr(b)-56 b Fw(\026)2260 1848 y Ft(2)2315 1874 y Fw(q)2356 1888 y Ft(1)2395 1874 y Fx(\011)2466 1800 y Fr(\013)1412 2090 y Fi(6)1562 2028 y Fx(1)p 1543 2069 83 4 v 1543 2152 a Fw(N)1636 2090 y Fu(k)p Fw(W)1780 2052 y Fv(')1830 2090 y Fu(k)1875 2104 y FF(1)1950 1980 y Fr(q)p 2041 1980 522 4 v 36 x(\012)2084 2090 y Fx(\011)10 b Fw(;)18 b Fr(b)-54 b Fw(n)2260 2063 y FF(\000)p Ft(2)2370 2090 y Fw(q)2411 2104 y Ft(1)2450 2090 y Fx(\011)2520 2016 y Fr(\013)1412 2305 y Fi(.)1562 2244 y Fx(1)p 1543 2284 83 4 v 1543 2368 a Fw(N)1636 2305 y Fu(k)p Fw(')p Fu(k)1785 2268 y Ft(2)1785 2333 y Fv(L)1833 2314 y Fp(2)1869 2333 y FF(\\)p Fv(L)1964 2314 y Fm(1)2049 2305 y Fw(;)14 2551 y Fx(b)m(y)32 b(\(3.13\))r(.)14 2787 y Fg(T)-7 b(erm)33 b Fx(\(I)s(I\))p Fg(.)40 b Fx(Using)31 b(Lemma)f(3.10)i(w)m(e)f(\014nd) 695 3007 y(2)p Fu(j)p Fx(\(I)s(I\))q Fu(j)51 b Fx(=)1102 2930 y Fr(\014)1102 2984 y(\014)1132 2933 y(\012)1175 3007 y Fx(\011)10 b Fw(;)15 b(q)1337 3021 y Ft(1)1376 3007 y Fw(p)1422 3021 y Ft(2)1462 2933 y Fr(\002)1500 3007 y Fx(\()p Fw(N)30 b Fu(\000)20 b Fx(1\))p Fw(W)1895 3021 y Ft(12)1991 3007 y Fu(\000)f Fw(N)10 b(W)2263 2963 y Fv(')2250 3033 y Ft(2)2323 3007 y Fw(;)18 b Fr(b)-54 b Fw(n)2418 2933 y Fr(\003)2456 3007 y Fw(q)2497 3021 y Ft(1)2536 3007 y Fw(q)2577 3021 y Ft(2)2616 3007 y Fx(\011)2687 2933 y Fr(\013)2730 2930 y(\014)2730 2984 y(\014)3514 3007 y Fx(\(4.16\))981 3206 y(=)1102 3074 y Fr(\014)1102 3129 y(\014)1102 3183 y(\014)1102 3238 y(\014)1132 3078 y(\034)1201 3206 y Fx(\011)24 b Fw(;)31 b(q)1393 3220 y Ft(1)1432 3206 y Fw(p)1478 3220 y Ft(2)1517 3078 y Fr(\022)1594 3144 y Fw(N)f Fu(\000)20 b Fx(1)p 1594 3185 240 4 v 1672 3268 a Fw(N)1844 3206 y(W)1930 3220 y Ft(12)2024 3206 y Fu(\000)g Fw(W)2214 3162 y Fv(')2201 3232 y Ft(2)2264 3078 y Fr(\023)2351 3206 y(b)-56 b Fw(\026)15 b(q)2457 3220 y Ft(1)2496 3206 y Fw(q)2537 3220 y Ft(2)2576 3206 y Fx(\011)2647 3078 y Fr(\035)2715 3074 y(\014)2715 3129 y(\014)2715 3183 y(\014)2715 3238 y(\014)3514 3206 y Fx(\(4.17\))981 3405 y Fi(6)1102 3327 y Fr(\014)1102 3382 y(\014)1132 3331 y(\012)1175 3405 y Fx(\011)10 b Fw(;)15 b(q)1337 3419 y Ft(1)1376 3405 y Fw(p)1422 3419 y Ft(2)1462 3405 y Fw(W)1548 3419 y Ft(12)1642 3405 y Fr(b)-56 b Fw(\026)15 b(q)1748 3419 y Ft(1)1787 3405 y Fw(q)1828 3419 y Ft(2)1867 3405 y Fx(\011)1938 3331 y Fr(\013)1981 3327 y(\014)1981 3382 y(\014)1102 3472 y(|)p 1143 3472 373 11 v 373 w({z)p 1598 3472 V 373 w(})1465 3562 y Ft(=)1520 3560 y(:)1559 3562 y(\(a\))2026 3405 y Fx(+)2112 3327 y Fr(\014)2112 3382 y(\014)2143 3331 y(\012)2186 3405 y Fx(\011)10 b Fw(;)15 b(q)2348 3419 y Ft(1)2387 3405 y Fw(p)2433 3419 y Ft(2)2472 3405 y Fw(W)2571 3360 y Fv(')2558 3431 y Ft(2)2640 3405 y Fr(b)-55 b Fw(\026)15 b(q)2747 3419 y Ft(1)2786 3405 y Fw(q)2827 3419 y Ft(2)2866 3405 y Fx(\011)2936 3331 y Fr(\013)2979 3327 y(\014)2979 3382 y(\014)2112 3472 y(|)p 2153 3472 367 11 v 367 w({z)p 2602 3472 V 367 w(})2467 3562 y Ft(=)2522 3560 y(:)2561 3562 y(\(b\))3040 3405 y Fw(:)449 b Fx(\(4.18\))14 3766 y(One)30 b(immediately)i(\014nds)812 3986 y(\(b\))50 b Fi(6)h Fu(k)p Fw(W)1249 3948 y Fv(')1299 3986 y Fu(k)1344 4000 y FF(1)1434 3986 y Fu(k)p Fw(q)1520 4000 y Ft(1)1559 3986 y Fx(\011)p Fu(k)1675 3903 y Fr(p)p 1767 3903 517 4 v 1767 3986 a Fu(h)p Fx(\011)10 b Fw(;)20 b Fr(b)-56 b Fw(\026)1978 3960 y Ft(2)2017 3986 y Fw(q)2058 4000 y Ft(1)2097 3986 y Fw(q)2138 4000 y Ft(2)2177 3986 y Fx(\011)p Fu(i)51 b Fi(.)f Fu(k)p Fw(')p Fu(k)2604 3948 y Ft(2)2604 4014 y Fv(L)2652 3995 y Fp(2)2688 4014 y FF(\\)p Fv(L)2783 3995 y Fm(1)2852 3986 y Fw(\014)21 b(:)14 4206 y Fx(In)30 b(\(a\))h(w)m(e)g(split)936 4334 y Fw(w)53 b Fx(=)e Fw(w)1243 4297 y Ft(\()p Fv(p)p Ft(\))1358 4334 y Fx(+)20 b Fw(w)1516 4297 y Ft(\()p FF(1)p Ft(\))1661 4334 y Fw(;)197 b(w)1950 4297 y Ft(\()p Fv(p)p Ft(\))2071 4334 y Fu(2)25 b Fw(L)2219 4297 y Fv(p)2273 4334 y Fw(;)41 b(w)2406 4297 y Ft(\()p FF(1)p Ft(\))2561 4334 y Fu(2)25 b Fw(L)2709 4297 y FF(1)2799 4334 y Fw(;)14 4519 y Fx(with)30 b(a)h(resulting)f(splitting)i(\(a\))26 b Fi(6)f Fx(\(a\))1384 4477 y Ft(\()p Fv(p)p Ft(\))1499 4519 y Fx(+)20 b(\(a\))1706 4477 y Ft(\()p FF(1)p Ft(\))1836 4519 y Fx(.)40 b(The)30 b(easy)h(part)f(is)1208 4749 y(\(a\))1324 4707 y Ft(\()p FF(1)p Ft(\))1504 4749 y Fi(6)50 b Fu(k)p Fw(w)1737 4711 y Ft(\()p FF(1)p Ft(\))1868 4749 y Fu(k)1913 4763 y FF(1)2003 4749 y Fu(k)p Fw(q)2089 4763 y Ft(1)2129 4749 y Fx(\011)p Fu(k)2245 4711 y Ft(2)2335 4749 y Fi(.)g Fw(\014)20 b(:)14 4990 y Fx(In)31 b(order)f(to)j(deal)e(with)g(\(a\))996 4948 y Ft(\()p Fv(p)p Ft(\))1122 4990 y Fx(w)m(e)h(write)f Fw(w)1557 4957 y Ft(\()p Fv(p)p Ft(\))1679 4990 y Fx(=)c Fu(r)20 b(\001)h Fw(\030)36 b Fx(as)31 b(the)h(div)m(ergence)g(of)g(a)f (v)m(ector)i(\014eld)e Fw(\030)t Fx(,)h(exactly)14 5103 y(as)d(in)g(the)g(pro)s(of)f(of)i(Lemma)f(4.6;)i(see)e(\(4.9\))i(and)d (the)h(remarks)g(after)h(it.)40 b(W)-8 b(e)30 b(in)m(tegrate)i(b)m(y)d (parts)f(to)i(\014nd)599 5332 y(\(a\))715 5290 y Ft(\()p Fv(p)p Ft(\))860 5332 y Fx(=)981 5255 y Fr(\014)981 5310 y(\014)1011 5259 y(\012)1054 5332 y Fx(\011)10 b Fw(;)15 b(q)1216 5346 y Ft(1)1255 5332 y Fw(p)1301 5346 y Ft(2)1341 5332 y Fx(\()p Fu(r)1452 5288 y Fv(\032)1452 5358 y Ft(1)1492 5332 y Fw(X)1574 5295 y Fv(\032)1615 5332 y Fx(\))1650 5346 y Ft(12)1745 5332 y Fr(b)-56 b Fw(\026)15 b(q)1851 5346 y Ft(1)1890 5332 y Fw(q)1931 5346 y Ft(2)1970 5332 y Fx(\011)2041 5259 y Fr(\013)2084 5255 y(\014)2084 5310 y(\014)860 5470 y Fi(6)981 5393 y Fr(\014)981 5447 y(\014)1011 5397 y(\012)1054 5470 y Fu(r)1130 5426 y Fv(\032)1130 5496 y Ft(1)1170 5470 y Fw(q)1211 5484 y Ft(1)1250 5470 y Fw(p)1296 5484 y Ft(2)1335 5470 y Fx(\011)10 b Fw(;)15 b(X)1538 5426 y Fv(\032)1531 5496 y Ft(12)1627 5470 y Fr(b)-56 b Fw(\026)15 b(q)1733 5484 y Ft(1)1772 5470 y Fw(q)1813 5484 y Ft(2)1852 5470 y Fx(\011)1923 5397 y Fr(\013)1965 5393 y(\014)1965 5447 y(\014)2016 5470 y Fx(+)2107 5393 y Fr(\014)2107 5447 y(\014)2137 5397 y(\012)2180 5470 y Fw(q)2221 5484 y Ft(1)2260 5470 y Fw(p)2306 5484 y Ft(2)2345 5470 y Fx(\011)10 b Fw(;)15 b(X)2548 5426 y Fv(\032)2541 5496 y Ft(12)2617 5470 y Fu(r)2693 5426 y Fv(\032)2693 5496 y Ft(1)2752 5470 y Fr(b)-55 b Fw(\026)15 b(q)2859 5484 y Ft(1)2898 5470 y Fw(q)2939 5484 y Ft(2)2978 5470 y Fx(\011)3048 5397 y Fr(\013)3091 5393 y(\014)3091 5447 y(\014)3137 5470 y Fw(:)352 b Fx(\(4.19\))p Black 1835 6000 a(24)p Black eop end %%Page: 25 25 TeXDict begin 25 24 bop Black Black 14 162 a Fx(The)30 b(\014rst)g(term)g(of)38 b(\(4.19\))32 b(is)f(equal)g(to)349 309 y Fr(\014)349 363 y(\014)379 312 y(\012)422 386 y Fw(X)504 342 y Fv(\032)497 412 y Ft(12)572 386 y Fw(p)618 400 y Ft(2)658 386 y Fu(r)734 342 y Fv(\032)734 412 y Ft(1)774 386 y Fw(q)815 400 y Ft(1)854 386 y Fx(\011)9 b Fw(;)20 b Fr(b)-56 b Fw(\026)16 b(q)1086 400 y Ft(1)1125 386 y Fw(q)1166 400 y Ft(2)1205 386 y Fx(\011)1276 312 y Fr(\013)1318 309 y(\014)1318 363 y(\014)1399 386 y Fi(6)1520 277 y Fr(q)p 1611 277 1147 4 v 35 x(\012)1654 386 y Fu(r)1730 342 y Fv(\032)1730 412 y Ft(1)1770 386 y Fw(q)1811 400 y Ft(1)1850 386 y Fx(\011)10 b Fw(;)15 b(p)2017 400 y Ft(2)2057 386 y Fw(X)2139 342 y Fv(\032)2132 412 y Ft(12)2207 386 y Fw(X)2289 355 y Fv(\033)2282 412 y Ft(12)2357 386 y Fw(p)2403 400 y Ft(2)2442 386 y Fu(r)2518 355 y Fv(\033)2518 412 y Ft(1)2565 386 y Fw(q)2606 400 y Ft(1)2645 386 y Fx(\011)2715 312 y Fr(\013)2773 277 y(q)p 2864 277 548 4 v 35 x(\012)2907 386 y Fx(\011)10 b Fw(;)20 b Fr(b)-56 b Fw(\026)3083 360 y Ft(2)3138 386 y Fw(q)3179 400 y Ft(1)3218 386 y Fw(q)3259 400 y Ft(2)3298 386 y Fx(\011)3369 312 y Fr(\013)1399 587 y Fi(.)1520 504 y Fr(p)p 1611 504 485 4 v 83 x Fu(k)p Fw(\030)1700 560 y Ft(2)1760 587 y Fu(\003)21 b(j)p Fw(')p Fu(j)1935 560 y Ft(2)1975 587 y Fu(k)2020 601 y FF(1)2111 587 y Fu(kr)2232 601 y Ft(1)2271 587 y Fw(q)2312 601 y Ft(1)2351 587 y Fx(\011)p Fu(k)2482 477 y Fr(q)p 2574 477 602 4 v 2574 513 a(\012)2617 587 y Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)2793 560 y FF(\000)p Ft(2)2902 587 y Fw(q)2943 601 y Ft(1)2982 587 y Fw(q)3023 601 y Ft(2)3062 587 y Fx(\011)3133 513 y Fr(\013)1399 818 y Fi(6)1520 736 y Fr(p)p 1611 736 485 4 v 82 x Fu(k)p Fw(\030)1700 792 y Ft(2)1760 818 y Fu(\003)21 b(j)p Fw(')p Fu(j)1935 792 y Ft(2)1975 818 y Fu(k)2020 832 y FF(1)2111 818 y Fu(kr)2232 832 y Ft(1)2271 818 y Fw(q)2312 832 y Ft(1)2351 818 y Fx(\011)p Fu(k)2482 678 y Fr(r)p 2574 678 632 4 v 2662 757 a Fw(N)p 2584 798 240 4 v 2584 881 a(N)30 b Fu(\000)20 b Fx(1)2833 745 y Fr(\012)2876 818 y Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)3052 792 y Ft(2)3091 818 y Fx(\011)3162 745 y Fr(\013)1399 1015 y Fi(.)50 b Fu(k)p Fw(\030)t Fu(k)1654 1029 y Fv(q)1709 1015 y Fu(k)p Fw(')p Fu(k)1858 1035 y Fv(L)1906 1016 y Fp(2)1941 1035 y FF(\\)p Fv(L)2036 1016 y Fm(1)2121 1015 y Fu(kr)2242 1029 y Ft(1)2282 1015 y Fw(q)2323 1029 y Ft(1)2362 1015 y Fx(\011)p Fu(k)2493 933 y Fr(p)p 2584 933 57 4 v 82 x Fw(\014)1399 1162 y Fi(.)g Fu(kr)1641 1176 y Ft(1)1681 1162 y Fw(q)1722 1176 y Ft(1)1761 1162 y Fx(\011)p Fu(k)1877 1125 y Ft(2)1932 1162 y Fu(k)p Fw(')p Fu(k)2081 1182 y Fv(L)2129 1163 y Fp(2)2165 1182 y FF(\\)p Fv(L)2260 1163 y Fm(1)2349 1162 y Fx(+)20 b Fw(\014)h Fu(k)p Fw(')p Fu(k)2661 1182 y Fv(L)2709 1163 y Fp(2)2745 1182 y FF(\\)p Fv(L)2840 1163 y Fm(1)2924 1162 y Fw(;)14 1351 y Fx(where)26 b(in)h(the)g(second) g(step)g(w)m(e)g(used)f(\(4.15\))r(,)i(in)e(the)h(third)f(Lemma)h(3.9,) i(and)d(in)h(the)g(last)g(\(4.3\))r(,)h(Y)-8 b(oung's)14 1464 y(inequalit)m(y)g(,)33 b(and)c(\(4.10\))s(.)40 b(The)30 b(second)h(term)f(of)38 b(\(4.19\))32 b(is)f(equal)g(to)97 1601 y Fr(\014)97 1655 y(\014)127 1604 y(\012)170 1678 y Fw(q)211 1692 y Ft(1)250 1678 y Fw(p)296 1692 y Ft(2)336 1678 y Fx(\011)9 b Fw(;)15 b(X)538 1634 y Fv(\032)531 1704 y Ft(12)607 1678 y Fx(\()p Fw(p)688 1692 y Ft(1)748 1678 y Fx(+)20 b Fw(q)880 1692 y Ft(1)919 1678 y Fx(\))p Fu(r)1030 1634 y Fv(\032)1030 1704 y Ft(1)1090 1678 y Fr(b)-56 b Fw(\026)15 b(q)1196 1692 y Ft(1)1235 1678 y Fw(q)1276 1692 y Ft(2)1315 1678 y Fx(\011)1386 1604 y Fr(\013)1429 1601 y(\014)1429 1655 y(\014)884 1816 y Fi(6)1006 1739 y Fr(\014)1006 1793 y(\014)1036 1742 y(\012)1079 1816 y Fw(q)1120 1830 y Ft(1)1159 1816 y Fw(p)1205 1830 y Ft(2)1244 1816 y Fx(\011)10 b Fw(;)15 b(X)1447 1772 y Fv(\032)1440 1842 y Ft(12)1515 1816 y Fw(p)1561 1830 y Ft(1)1617 1816 y Fr(d)-132 b Fw(\034)1656 1830 y Ft(1)1695 1816 y Fw(\026)15 b Fu(r)1841 1772 y Fv(\032)1841 1842 y Ft(1)1881 1816 y Fw(q)1922 1830 y Ft(1)1961 1816 y Fw(q)2002 1830 y Ft(2)2041 1816 y Fx(\011)2112 1742 y Fr(\013)2154 1739 y(\014)2154 1793 y(\014)2205 1816 y Fx(+)2296 1739 y Fr(\014)2296 1793 y(\014)2326 1742 y(\012)2369 1816 y Fw(q)2410 1830 y Ft(1)2449 1816 y Fw(p)2495 1830 y Ft(2)2534 1816 y Fx(\011)10 b Fw(;)15 b(X)2737 1772 y Fv(\032)2730 1842 y Ft(12)2806 1816 y Fw(q)2847 1830 y Ft(1)2905 1816 y Fr(b)-55 b Fw(\026)15 b Fu(r)3047 1772 y Fv(\032)3047 1842 y Ft(1)3087 1816 y Fw(q)3128 1830 y Ft(1)3167 1816 y Fw(q)3208 1830 y Ft(2)3247 1816 y Fx(\011)3317 1742 y Fr(\013)3360 1739 y(\014)3360 1793 y(\014)3406 1816 y Fw(;)83 b Fx(\(4.20\))14 2005 y(where)35 b(w)m(e)h(used)e(Lemma)i(3.10.)57 b(W)-8 b(e)36 b(estimate)i(the)d(\014rst)g(term)g(of)43 b(\(4.20\))r(.)56 b(The)34 b(second)i(term)f(is)g(dealt)14 2118 y(with)30 b(in)g(exactly)i(the)f(same)g(w)m(a)m(y)-8 b(.)42 b(W)-8 b(e)31 b(\014nd)141 2263 y Fr(\014)141 2317 y(\014)171 2267 y(\012)214 2340 y Fw(p)260 2354 y Ft(1)300 2340 y Fw(X)382 2296 y Fv(\032)375 2366 y Ft(12)450 2340 y Fw(q)491 2354 y Ft(1)530 2340 y Fw(p)576 2354 y Ft(2)615 2340 y Fx(\011)10 b Fw(;)16 b Fr(d)-132 b Fw(\034)776 2354 y Ft(1)815 2340 y Fw(\026)15 b Fu(r)961 2296 y Fv(\032)961 2366 y Ft(1)1001 2340 y Fw(q)1042 2354 y Ft(1)1081 2340 y Fw(q)1122 2354 y Ft(2)1161 2340 y Fx(\011)1232 2267 y Fr(\013)1275 2263 y(\014)1275 2317 y(\014)1356 2340 y Fi(6)1477 2231 y Fr(q)p 1568 2231 759 4 v 36 x(\012)1611 2340 y Fx(\011)10 b Fw(;)15 b(q)1773 2354 y Ft(1)1812 2340 y Fw(p)1858 2354 y Ft(2)1897 2340 y Fw(X)1979 2309 y Ft(2)1972 2366 y(12)2047 2340 y Fw(p)2093 2354 y Ft(2)2132 2340 y Fw(q)2173 2354 y Ft(1)2212 2340 y Fx(\011)2283 2267 y Fr(\013)2341 2227 y(q)p 2432 2227 1032 4 v 40 x(\012)2475 2340 y Fu(r)2551 2354 y Ft(1)2590 2340 y Fw(q)2631 2354 y Ft(1)2670 2340 y Fx(\011)10 b Fw(;)15 b(q)2832 2354 y Ft(2)2888 2340 y Fr(d)-132 b Fw(\034)2927 2354 y Ft(1)2966 2340 y Fw(\026)3021 2298 y Ft(2)3075 2340 y Fw(q)3116 2354 y Ft(2)3155 2340 y Fu(r)3231 2354 y Ft(1)3270 2340 y Fw(q)3311 2354 y Ft(1)3350 2340 y Fx(\011)3421 2267 y Fr(\013)1356 2541 y Fi(6)1477 2458 y Fr(p)p 1568 2458 485 4 v 83 x Fu(k)p Fw(\030)1657 2514 y Ft(2)1717 2541 y Fu(\003)20 b(j)p Fw(')p Fu(j)1891 2514 y Ft(2)1932 2541 y Fu(k)1977 2555 y FF(1)2067 2541 y Fu(k)p Fw(q)2153 2555 y Ft(1)2193 2541 y Fx(\011)p Fu(k)2324 2431 y Fr(q)p 2415 2431 913 4 v 36 x(\012)2458 2541 y Fu(r)2534 2555 y Ft(1)2573 2541 y Fw(q)2614 2555 y Ft(1)2653 2541 y Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)2829 2514 y FF(\000)p Ft(2)2938 2541 y Fw(q)2979 2555 y Ft(2)3018 2541 y Fu(r)3094 2555 y Ft(1)3134 2541 y Fw(q)3175 2555 y Ft(1)3214 2541 y Fx(\011)3284 2467 y Fr(\013)1356 2825 y Fi(.)25 b Fu(k)p Fw(\030)t Fu(k)1586 2839 y Fv(q)1640 2825 y Fu(k)p Fw(')p Fu(k)1789 2845 y Fv(L)1837 2826 y Fp(2)1873 2845 y FF(\\)p Fv(L)1968 2826 y Fm(1)2052 2755 y Fu(p)p 2128 2755 59 4 v 70 x Fw(\013)2201 2632 y Fr(v)2201 2683 y(u)2201 2737 y(u)2201 2792 y(t)p 2297 2632 1323 4 v 2404 2764 a Fx(1)p 2307 2804 240 4 v 2307 2888 a Fw(N)30 b Fu(\000)20 b Fx(1)2606 2712 y Fv(N)2572 2739 y Fr(X)2581 2934 y Fv(i)p Ft(=2)2718 2752 y Fr(\012)2761 2825 y Fu(r)2837 2839 y Ft(1)2877 2825 y Fw(q)2918 2839 y Ft(1)2957 2825 y Fx(\011)9 b Fw(;)18 b Fr(b)-54 b Fw(n)3132 2799 y FF(\000)p Ft(2)3242 2825 y Fw(q)3283 2839 y Fv(i)3311 2825 y Fu(r)3387 2839 y Ft(1)3426 2825 y Fw(q)3467 2839 y Ft(1)3506 2825 y Fx(\011)3577 2752 y Fr(\013)1356 3189 y Fi(.)50 b Fu(k)p Fw(')p Fu(k)1626 3209 y Fv(L)1674 3190 y Fp(2)1710 3209 y FF(\\)p Fv(L)1805 3190 y Fm(1)1874 3107 y Fr(p)p 1965 3107 57 4 v 82 x Fw(\014)2021 2996 y Fr(v)2021 3047 y(u)2021 3101 y(u)2021 3156 y(t)p 2117 2996 1323 4 v 2224 3128 a Fx(1)p 2127 3168 240 4 v 2127 3252 a Fw(N)30 b Fu(\000)20 b Fx(1)2426 3076 y Fv(N)2392 3103 y Fr(X)2400 3298 y Fv(i)p Ft(=1)2538 3116 y Fr(\012)2581 3189 y Fu(r)2657 3203 y Ft(1)2696 3189 y Fw(q)2737 3203 y Ft(1)2776 3189 y Fx(\011)10 b Fw(;)18 b Fr(b)-54 b Fw(n)2952 3163 y FF(\000)p Ft(2)3062 3189 y Fw(q)3103 3203 y Fv(i)3130 3189 y Fu(r)3206 3203 y Ft(1)3246 3189 y Fw(q)3287 3203 y Ft(1)3326 3189 y Fx(\011)3396 3116 y Fr(\013)1356 3501 y Fx(=)50 b Fu(k)p Fw(')p Fu(k)1626 3520 y Fv(L)1674 3502 y Fp(2)1710 3520 y FF(\\)p Fv(L)1805 3502 y Fm(1)1874 3419 y Fr(p)p 1965 3419 57 4 v 82 x Fw(\014)2021 3360 y Fr(r)p 2112 3360 1201 4 v 2200 3439 a Fw(N)p 2122 3480 240 4 v 2122 3563 a(N)30 b Fu(\000)20 b Fx(1)2372 3427 y Fr(\012)2414 3501 y Fu(r)2490 3515 y Ft(1)2530 3501 y Fw(q)2571 3515 y Ft(1)2610 3501 y Fx(\011)9 b Fw(;)18 b Fr(b)-54 b Fw(n)2785 3474 y FF(\000)p Ft(2)2897 3501 y Fr(b)h Fw(n)2950 3474 y Ft(2)3004 3501 y Fu(r)3080 3515 y Ft(1)3119 3501 y Fw(q)3160 3515 y Ft(1)3199 3501 y Fx(\011)3270 3427 y Fr(\013)1356 3697 y Fi(.)50 b Fu(k)p Fw(')p Fu(k)1626 3717 y Fv(L)1674 3698 y Fp(2)1710 3717 y FF(\\)p Fv(L)1805 3698 y Fm(1)1874 3615 y Fr(p)p 1965 3615 57 4 v 82 x Fw(\014)20 b Fu(kr)2157 3711 y Ft(1)2197 3697 y Fw(q)2238 3711 y Ft(1)2277 3697 y Fx(\011)p Fu(k)1356 3845 y Fi(6)50 b Fw(\014)20 b Fu(k)p Fw(')p Fu(k)1697 3864 y Fv(L)1745 3845 y Fp(2)1781 3864 y FF(\\)p Fv(L)1876 3845 y Fm(1)29 b Fx(+)20 b Fu(kr)2178 3859 y Ft(1)2217 3845 y Fw(q)2258 3859 y Ft(1)2297 3845 y Fx(\011)p Fu(k)2413 3807 y Ft(2)2468 3845 y Fu(k)p Fw(')p Fu(k)2617 3864 y Fv(L)2665 3845 y Fp(2)2701 3864 y FF(\\)p Fv(L)2796 3845 y Fm(1)j Fw(:)14 4034 y Fx(In)30 b(summary)-8 b(,)30 b(w)m(e)h(ha)m(v)m(e)g(pro)m(v)m(en)g(that)980 4145 y Fr(\014)980 4200 y(\014)1011 4222 y Fx(\(I)s(I\))1150 4145 y Fr(\014)1150 4200 y(\014)1230 4222 y Fi(.)51 b Fw(\014)20 b Fu(k)p Fw(')p Fu(k)1572 4242 y Fv(L)1620 4223 y Fp(2)1656 4242 y FF(\\)p Fv(L)1751 4223 y Fm(1)1840 4222 y Fx(+)g Fu(kr)2052 4236 y Ft(1)2092 4222 y Fw(q)2133 4236 y Ft(1)2172 4222 y Fx(\011)p Fu(k)2288 4185 y Ft(2)2343 4222 y Fu(k)p Fw(')p Fu(k)2492 4242 y Fv(L)2540 4223 y Fp(2)2576 4242 y FF(\\)p Fv(L)2671 4223 y Fm(1)2755 4222 y Fw(:)14 4530 y Fg(T)-7 b(erm)33 b Fx(\(I)s(I)s(I\))p Fg(.)40 b Fx(Using)30 b(Lemma)h(3.10)h(w)m(e)f(\014nd)104 4719 y(2)p Fu(j)p Fx(\(I)s(I)s(I\))p Fu(j)51 b Fx(=)f(\()p Fw(N)31 b Fu(\000)20 b Fx(1\))856 4641 y Fr(\014)856 4696 y(\014)887 4645 y(\012)930 4719 y Fx(\011)10 b Fw(;)15 b(p)1097 4733 y Ft(1)1136 4719 y Fw(p)1182 4733 y Ft(2)1221 4645 y Fr(\002)1259 4719 y Fw(W)1345 4733 y Ft(12)1430 4719 y Fw(;)i Fr(b)-53 b Fw(n)1525 4645 y Fr(\003)1563 4719 y Fw(q)1604 4733 y Ft(1)1643 4719 y Fw(q)1684 4733 y Ft(2)1723 4719 y Fx(\011)1794 4645 y Fr(\013)1837 4641 y(\014)1837 4696 y(\014)1917 4719 y Fx(=)51 b(\()p Fw(N)30 b Fu(\000)20 b Fx(1\))2348 4641 y Fr(\014)2348 4696 y(\014)2379 4645 y(\012)2422 4719 y Fx(\011)10 b Fw(;)15 b(p)2589 4733 y Ft(1)2628 4719 y Fw(p)2674 4733 y Ft(2)2714 4719 y Fw(W)2800 4733 y Ft(12)2874 4645 y Fr(\000)2918 4719 y(b)-53 b Fw(n)20 b Fu(\000)28 b Fs([)-181 b Fw(\034)3121 4733 y FF(\000)p Ft(2)3216 4719 y Fw(n)3270 4645 y Fr(\001)3312 4719 y Fw(q)3353 4733 y Ft(1)3392 4719 y Fw(q)3433 4733 y Ft(2)3472 4719 y Fx(\011)3543 4645 y Fr(\013)3585 4641 y(\014)3585 4696 y(\014)3631 4719 y Fw(:)14 4908 y Fx(De\014ning)197 5155 y Fw(\027)6 b Fx(\()p Fw(k)s Fx(\))419 5152 y(:)445 5155 y(=)50 b Fw(N)649 5082 y Fr(\000)690 5155 y Fw(n)p Fx(\()p Fw(k)s Fx(\))21 b Fu(\000)f Fx(\()p Fw(\034)1052 5169 y FF(\000)p Ft(2)1146 5155 y Fw(n)p Fx(\)\()p Fw(k)s Fx(\))1357 5082 y Fr(\001)1449 5155 y Fx(=)1761 5017 y Fu(p)p 1837 5017 83 4 v 77 x Fw(N)p 1580 5134 520 4 v 1580 5153 a Fu(p)p 1656 5153 51 4 v 77 x Fw(k)k Fx(+)1818 5156 y Fu(p)p 1893 5156 207 4 v 1893 5230 a Fw(k)g Fu(\000)c Fx(2)2161 5155 y Fi(6)50 b Fw(n)2337 5118 y FF(\000)p Ft(1)2431 5155 y Fx(\()p Fw(k)s Fx(\))15 b Fw(;)198 b(k)28 b Fx(=)d(2)p Fw(;)15 b(:)g(:)g(:)i(;)e(N)26 b(;)183 b Fx(\(4.21\))14 5391 y(w)m(e)31 b(ha)m(v)m(e)1199 5504 y(2)1244 5427 y Fr(\014)1244 5481 y(\014)1275 5504 y Fx(\(I)s(I)s(I\))1449 5427 y Fr(\014)1449 5481 y(\014)1530 5504 y Fi(6)1651 5427 y Fr(\014)1651 5481 y(\014)1681 5430 y(\012)1724 5504 y Fx(\011)10 b Fw(;)15 b(p)1891 5518 y Ft(1)1931 5504 y Fw(p)1977 5518 y Ft(2)2016 5504 y Fw(W)2102 5518 y Ft(12)2194 5504 y Fr(b)-53 b Fw(\027)21 b(q)2299 5518 y Ft(1)2338 5504 y Fw(q)2379 5518 y Ft(2)2418 5504 y Fx(\011)2488 5430 y Fr(\013)2531 5427 y(\014)2531 5481 y(\014)p Black 1835 6000 a Fx(25)p Black eop end %%Page: 26 26 TeXDict begin 26 25 bop Black Black 14 162 a Fx(As)31 b(usual)e(w)m(e)i(start)g(b)m(y)f(splitting)936 366 y Fw(w)53 b Fx(=)e Fw(w)1243 329 y Ft(\()p Fv(p)p Ft(\))1358 366 y Fx(+)20 b Fw(w)1516 329 y Ft(\()p FF(1)p Ft(\))1661 366 y Fw(;)197 b(w)1950 329 y Ft(\()p Fv(p)p Ft(\))2071 366 y Fu(2)25 b Fw(L)2219 329 y Fv(p)2273 366 y Fw(;)41 b(w)2406 329 y Ft(\()p FF(1)p Ft(\))2561 366 y Fu(2)25 b Fw(L)2709 329 y FF(1)2799 366 y Fw(;)14 570 y Fx(with)30 b(the)h(induced)e(splitting)i(\(I)s(I)s(I\))25 b(=)g(\(I)s(I)s(I\))1545 528 y Ft(\()p Fv(p)p Ft(\))1660 570 y Fx(+)20 b(\(I)s(I)s(I\))1925 528 y Ft(\()p FF(1)p Ft(\))2055 570 y Fx(.)40 b(Th)m(us,)30 b(using)g(Lemma)g(3.10,)i(w)m(e)f(\014nd)743 790 y(2)788 712 y Fr(\014)788 767 y(\014)818 790 y Fx(\(I)s(I)s(I\))993 748 y Ft(\()p FF(1)p Ft(\))1122 712 y Fr(\014)1122 767 y(\014)1203 790 y Fx(=)1324 712 y Fr(\014)1324 767 y(\014)1355 716 y(\012)1398 790 y Fx(\011)10 b Fw(;)15 b(p)1565 804 y Ft(1)1604 790 y Fw(p)1650 804 y Ft(2)1689 790 y Fw(W)1788 742 y Ft(\()p FF(1)p Ft(\))1775 816 y(12)1934 790 y Fr(b)-53 b Fw(n)1987 752 y Ft(1)p Fv(=)p Ft(2)2114 790 y Fr(b)g Fw(n)2167 752 y FF(\000)p Ft(1)p Fv(=)p Ft(2)2349 790 y Fr(b)g Fw(\027)21 b(q)2454 804 y Ft(1)2493 790 y Fw(q)2534 804 y Ft(2)2573 790 y Fx(\011)2643 716 y Fr(\013)2686 712 y(\014)2686 767 y(\014)1203 954 y Fx(=)1324 877 y Fr(\014)1324 932 y(\014)1355 881 y(\012)1398 954 y Fx(\011)10 b Fw(;)15 b(p)1565 968 y Ft(1)1604 954 y Fw(p)1650 968 y Ft(2)1706 954 y Fr(d)-133 b Fw(\034)1744 968 y Ft(2)1783 954 y Fw(n)1838 912 y Ft(1)p Fv(=)p Ft(2)1963 954 y Fw(W)2062 906 y Ft(\()p FF(1)p Ft(\))2049 980 y(12)2208 954 y Fr(b)-53 b Fw(n)2261 917 y FF(\000)p Ft(1)p Fv(=)p Ft(2)2444 954 y Fr(b)f Fw(\027)21 b(q)2548 968 y Ft(1)2587 954 y Fw(q)2628 968 y Ft(2)2667 954 y Fx(\011)2738 881 y Fr(\013)2781 877 y(\014)2781 932 y(\014)1203 1138 y Fi(6)50 b Fu(k)p Fw(w)1436 1101 y Ft(\()p FF(1)p Ft(\))1567 1138 y Fu(k)1612 1152 y FF(1)1687 1029 y Fr(q)p 1778 1029 427 4 v 35 x(\012)1821 1138 y Fx(\011)10 b Fw(;)16 b Fr(d)-132 b Fw(\034)1982 1152 y Ft(2)2021 1138 y Fw(n)15 b Fx(\011)2162 1064 y Fr(\013)2220 1029 y(q)p 2311 1029 708 4 v 35 x(\012)2354 1138 y Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)2530 1112 y FF(\000)p Ft(1)2642 1138 y Fr(b)f Fw(\027)2690 1112 y Ft(2)2744 1138 y Fw(q)2785 1152 y Ft(1)2824 1138 y Fw(q)2865 1152 y Ft(2)2904 1138 y Fx(\011)2975 1064 y Fr(\013)1203 1410 y Fi(.)1299 1229 y Fr(s)p 1390 1229 362 4 v 181 x Fw(\014)25 b Fx(+)1557 1267 y Fr(r)p 1648 1267 103 4 v 1677 1348 a Fx(2)p 1658 1389 83 4 v 1658 1472 a Fw(N)1766 1300 y Fr(q)p 1857 1300 602 4 v 36 x(\012)1900 1410 y Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)2076 1383 y FF(\000)p Ft(3)2185 1410 y Fw(q)2226 1424 y Ft(1)2265 1410 y Fw(q)2306 1424 y Ft(2)2345 1410 y Fx(\011)2416 1336 y Fr(\013)1203 1719 y Fi(6)1324 1539 y Fr(s)p 1415 1539 362 4 v 180 x Fw(\014)26 b Fx(+)1583 1576 y Fr(r)p 1674 1576 103 4 v 1702 1658 a Fx(2)p 1684 1698 83 4 v 1684 1782 a Fw(N)1792 1578 y Fr(r)p 1882 1578 316 4 v 1971 1658 a Fw(N)p 1892 1698 240 4 v 1892 1782 a(N)31 b Fu(\000)19 b Fx(1)2142 1719 y Fw(\014)1203 1961 y Fi(.)25 b Fw(\014)h Fx(+)1533 1900 y(1)p 1476 1940 159 4 v 1476 1958 a Fu(p)p 1552 1958 83 4 v 77 x Fw(N)1660 1961 y(;)14 2208 y Fx(where)k(in)g(the)h(\014fth)e(step)i(w)m(e)f(used)g(Lemma)g (3.9.)155 2321 y(In)i(order)g(to)i(estimate)g(\(I)s(I)s(I\))1165 2279 y Ft(\()p Fv(p)p Ft(\))1292 2321 y Fx(w)m(e)f(in)m(tro)s(duce)g(a) g(splitting)g(of)g 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3053 y Fp(0)1668 3030 y Fi(6)50 b Fw(a)1837 2993 y Ft(1)p FF(\000)p Fv(p=p)2034 3002 y Fp(0)2087 3030 y Fu(k)p Fw(w)2199 2993 y Ft(\()p Fv(p)p Ft(\))2295 3030 y Fu(k)2340 2993 y Fv(p=p)2447 3002 y Fp(0)2340 3053 y Fv(p)2500 3030 y Fw(;)944 b Fx(\(4.23a\))1270 3186 y Fu(k)p Fw(w)1382 3148 y Ft(\()p Fv(p;)p Ft(2\))1532 3186 y Fu(k)1577 3200 y Ft(2)1668 3186 y Fi(6)50 b Fw(a)1837 3148 y Ft(1)p FF(\000)p Fv(p=)p Ft(2)2052 3186 y Fu(k)p Fw(w)2164 3148 y Ft(\()p Fv(p)p Ft(\))2260 3186 y Fu(k)2305 3148 y Fv(p=)p Ft(2)2305 3208 y Fv(p)2431 3186 y Fw(:)1008 b Fx(\(4.23b\))14 3390 y(The)30 b(pro)s(of)g(of)37 b(\(4.23\))c(is)d (elemen)m(tary;)i(for)f(instance)g(\(4.23a\))i(follo)m(ws)e(from)97 3660 y Fu(k)p Fw(w)209 3623 y Ft(\()p Fv(p;)p Ft(1\))360 3660 y Fu(k)405 3623 y Fv(p)441 3632 y Fp(0)405 3683 y Fv(p)441 3692 y Fp(0)530 3660 y Fx(=)651 3537 y Fr(Z)757 3660 y Fx(d)p Fw(x)885 3583 y Fr(\014)885 3638 y(\014)915 3660 y Fw(w)982 3623 y Ft(\()p Fv(p)p Ft(\))1077 3583 y Fr(\014)1077 3638 y(\014)1108 3609 y Fv(p)1162 3583 y Fr(\014)1162 3638 y(\014)1193 3660 y Fw(w)1260 3623 y Ft(\()p Fv(p)p Ft(\))1355 3583 y Fr(\014)1355 3638 y(\014)1385 3609 y Fv(p)1421 3618 y Fp(0)1455 3609 y FF(\000)p Fv(p)1565 3660 y Fj(1)1619 3686 y FF(fj)p Fv(w)1727 3666 y Fp(\()p Fn(p)p Fp(\))1810 3686 y FF(j)p Fv(>a)p FF(g)1471 3896 y Fi(6)50 b Fw(a)1640 3858 y Fv(p)1676 3867 y Fp(0)1710 3858 y FF(\000)p Fv(p)1820 3772 y Fr(Z)1926 3896 y Fx(d)p Fw(x)2053 3818 y Fr(\014)2053 3873 y(\014)2084 3896 y Fw(w)2151 3858 y Ft(\()p Fv(p)p Ft(\))2246 3818 y Fr(\014)2246 3873 y(\014)2276 3845 y Fv(p)2331 3896 y Fj(1)2385 3921 y FF(fj)p Fv(w)2493 3902 y Fp(\()p Fn(p)p Fp(\))2576 3921 y FF(j)p Fv(>a)p FF(g)2778 3896 y Fi(6)g Fw(a)2947 3858 y Fv(p)2983 3867 y Fp(0)3017 3858 y FF(\000)p Fv(p)3127 3772 y Fr(Z)3233 3896 y Fx(d)p Fw(x)3361 3818 y Fr(\014)3361 3873 y(\014)3391 3896 y Fw(w)3458 3858 y Ft(\()p Fv(p)p Ft(\))3553 3818 y Fr(\014)3553 3873 y(\014)3583 3845 y Fv(p)3638 3896 y Fw(:)155 4165 y Fx(Let)31 b(us)f(start)h(with)f(\(I)s(I)s(I\))1034 4123 y Ft(\()p Fv(p;)p Ft(1\))1184 4165 y Fx(.)40 b(As)31 b(in)f(\(4.9\))q(,)h(w)m(e)g (use)f(the)h(represen)m(tation)1573 4369 y Fw(w)1640 4331 y Ft(\()p Fv(p;)p Ft(1\))1841 4369 y Fx(=)50 b Fu(r)20 b(\001)g Fw(\030)f(:)14 4572 y Fx(Then)30 b(\(4.10\))i(and)e(\(4.23a\)) j(imply)d(that)1269 4776 y Fu(k)p Fw(\030)t Fu(k)1403 4790 y Ft(2)1493 4776 y Fi(.)51 b Fu(k)p Fw(w)1727 4739 y Ft(\()p Fv(p;)p Ft(1\))1877 4776 y Fu(k)1922 4790 y Fv(p)1958 4799 y Fp(0)2047 4776 y Fi(.)f Fw(a)2216 4739 y Ft(1)p FF(\000)p Fv(p=p)2413 4748 y Fp(0)2467 4776 y Fw(:)1022 b Fx(\(4.24\))14 4980 y(In)m(tegrating)32 b(b)m(y)e(parts,)h(w)m(e)g(\014nd)488 5195 y(2)533 5117 y Fr(\014)533 5172 y(\014)564 5195 y Fx(\(I)s(I)s(I\))738 5153 y Ft(\()p Fv(p;)p Ft(1\))887 5117 y Fr(\014)887 5172 y(\014)968 5195 y Fx(=)1089 5117 y Fr(\014)1089 5172 y(\014)1120 5121 y(\012)1163 5195 y Fx(\011)10 b Fw(;)15 b(p)1330 5209 y Ft(1)1369 5195 y Fw(p)1415 5209 y Ft(2)1454 5195 y Fw(W)1553 5147 y Ft(\()p Fv(p;)p Ft(1\))1540 5221 y(12)1720 5195 y Fr(b)-54 b Fw(\027)21 b(q)1824 5209 y Ft(1)1863 5195 y Fw(q)1904 5209 y Ft(2)1943 5195 y Fx(\011)2014 5121 y Fr(\013)2057 5117 y(\014)2057 5172 y(\014)968 5332 y Fx(=)1089 5255 y Fr(\014)1089 5310 y(\014)1120 5259 y(\012)1163 5332 y Fx(\011)10 b Fw(;)15 b(p)1330 5346 y Ft(1)1369 5332 y Fw(p)1415 5346 y Ft(2)1454 5332 y Fx(\()p Fu(r)1565 5288 y Fv(\032)1565 5358 y Ft(1)1606 5332 y Fw(X)1688 5288 y Fv(\032)1681 5358 y Ft(12)1756 5332 y Fx(\))j Fr(b)-54 b Fw(\027)21 b(q)1913 5346 y Ft(1)1952 5332 y Fw(q)1993 5346 y Ft(2)2032 5332 y Fx(\011)2103 5259 y Fr(\013)2146 5255 y(\014)2146 5310 y(\014)968 5470 y Fi(6)1089 5393 y Fr(\014)1089 5447 y(\014)1120 5397 y(\012)1163 5470 y Fu(r)1239 5426 y Fv(\032)1239 5496 y Ft(1)1279 5470 y Fw(p)1325 5484 y Ft(1)1364 5470 y Fw(p)1410 5484 y Ft(2)1449 5470 y Fx(\011)10 b Fw(;)15 b(X)1652 5426 y Fv(\032)1645 5496 y Ft(12)1738 5470 y Fr(b)-54 b Fw(\027)21 b(q)1842 5484 y Ft(1)1881 5470 y Fw(q)1922 5484 y Ft(2)1961 5470 y Fx(\011)2032 5397 y Fr(\013)2075 5393 y(\014)2075 5447 y(\014)2125 5470 y Fx(+)2216 5393 y Fr(\014)2216 5447 y(\014)2247 5397 y(\012)2290 5470 y Fw(p)2336 5484 y Ft(1)2375 5470 y Fw(p)2421 5484 y Ft(2)2460 5470 y Fx(\011)10 b Fw(;)15 b(X)2663 5426 y Fv(\032)2656 5496 y Ft(12)2731 5470 y Fu(r)2807 5426 y Fv(\032)2807 5496 y Ft(1)2865 5470 y Fr(b)-54 b Fw(\027)21 b(q)2969 5484 y Ft(1)3008 5470 y Fw(q)3049 5484 y Ft(2)3088 5470 y Fx(\011)3159 5397 y Fr(\013)3202 5393 y(\014)3202 5447 y(\014)3247 5470 y Fw(:)242 b Fx(\(4.25\))p Black 1835 6000 a(26)p Black eop end %%Page: 27 27 TeXDict begin 27 26 bop Black Black 14 162 a Fx(Using)31 b Fu(kr)p Fw(p)p Fu(k)25 b Fx(=)g Fu(kr)p Fw(')p Fu(k)32 b Fx(and)e(Lemma)g(3.9)i(w)m(e)e(\014nd)f(that)i(the)g(\014rst)e(term)i (of)37 b(\(4.25\))c(is)d(b)s(ounded)f(b)m(y)315 294 y Fr(q)p 406 294 1158 4 v 36 x(\012)449 403 y Fu(r)525 359 y Fv(\032)525 429 y Ft(1)565 403 y Fw(p)611 417 y Ft(1)650 403 y Fx(\011)10 b Fw(;)15 b(p)817 417 y Ft(2)857 403 y Fw(X)939 359 y Fv(\032)932 429 y Ft(12)1007 403 y Fw(X)1089 372 y Fv(\033)1082 429 y Ft(12)1157 403 y Fw(p)1203 417 y Ft(2)1242 403 y Fu(r)1318 372 y Fv(\033)1318 429 y Ft(1)1365 403 y Fw(p)1411 417 y Ft(1)1450 403 y Fx(\011)1521 330 y Fr(\013)1579 294 y(q)p 1670 294 528 4 v 36 x(\012)1712 403 y Fx(\011)10 b Fw(;)18 b Fr(b)-54 b Fw(\027)1884 377 y Ft(2)1924 403 y Fw(q)1965 417 y Ft(1)2004 403 y Fw(q)2045 417 y Ft(2)2084 403 y Fx(\011)2155 330 y Fr(\013)2248 403 y Fi(.)50 b Fu(kr)p Fw(p)p Fu(k)15 b(k)p Fw(')p Fu(k)2745 417 y FF(1)2822 403 y Fu(k)p Fw(\030)t Fu(k)2956 417 y Ft(2)3011 333 y Fu(p)p 3087 333 59 4 v 70 x Fw(\013)2248 577 y Fi(6)50 b Fu(kr)p Fw(')p Fu(k)15 b(k)p Fw(')p Fu(k)2758 591 y FF(1)2851 577 y Fw(a)2899 539 y Ft(1)p FF(\000)p Fv(p=p)3096 548 y Fp(0)3149 494 y Fr(p)p 3240 494 57 4 v 83 x Fw(\014)2248 731 y Fi(6)50 b Fu(kr)p Fw(')p Fu(k)15 b(k)p Fw(')p Fu(k)2758 745 y FF(1)2836 657 y Fr(\000)2877 731 y Fw(\014)26 b Fx(+)20 b Fw(a)3093 693 y Ft(2)p FF(\000)p Ft(2)p Fv(p=p)3325 702 y Fp(0)3363 657 y Fr(\001)3420 731 y Fw(;)14 937 y Fx(where)33 b(in)g(the)g(second)g(step)g(w)m(e)h(used)e(the)i (estimate)h(\(4.24\))r(.)49 b(Next,)35 b(using)e(Lemma)g(3.10,)j(w)m(e) d(\014nd)f(that)14 1050 y(the)f(second)f(term)h(of)37 b(\(4.25\))c(is)d(equal)h(to)97 1204 y Fr(\014)97 1259 y(\014)127 1208 y(\012)170 1281 y Fw(p)216 1295 y Ft(1)256 1281 y Fw(p)302 1295 y Ft(2)341 1281 y Fx(\011)10 b Fw(;)15 b(X)544 1237 y Fv(\032)537 1307 y Ft(12)612 1281 y Fx(\()p Fw(p)693 1295 y Ft(1)753 1281 y Fx(+)20 b Fw(q)885 1295 y Ft(1)924 1281 y Fx(\))p Fu(r)1035 1237 y Fv(\032)1035 1307 y Ft(1)1093 1281 y Fr(b)-54 b Fw(\027)21 b(q)1197 1295 y Ft(1)1236 1281 y Fw(q)1277 1295 y Ft(2)1316 1281 y Fx(\011)1387 1208 y Fr(\013)1430 1204 y(\014)1430 1259 y(\014)1115 1419 y Fi(6)1236 1342 y Fr(\014)1236 1396 y(\014)1266 1346 y(\012)1309 1419 y Fw(p)1355 1433 y Ft(1)1394 1419 y Fw(p)1440 1433 y Ft(2)1479 1419 y Fx(\011)10 b Fw(;)15 b(X)1682 1375 y Fv(\032)1675 1445 y Ft(12)1751 1419 y Fw(p)1797 1433 y Ft(1)1870 1419 y Fr(c)-110 b Fw(\034)1891 1433 y Ft(1)1930 1419 y Fw(\027)21 b Fu(r)2072 1375 y Fv(\032)2072 1445 y Ft(1)2112 1419 y Fw(q)2153 1433 y Ft(1)2192 1419 y Fw(q)2233 1433 y Ft(2)2272 1419 y Fx(\011)2343 1346 y Fr(\013)2386 1342 y(\014)2386 1396 y(\014)2436 1419 y Fx(+)2527 1342 y Fr(\014)2527 1396 y(\014)2557 1346 y(\012)2600 1419 y Fw(p)2646 1433 y Ft(1)2686 1419 y Fw(p)2732 1433 y Ft(2)2771 1419 y Fx(\011)10 b Fw(;)15 b(X)2974 1375 y Fv(\032)2967 1445 y Ft(12)3042 1419 y Fw(q)3083 1433 y Ft(1)3140 1419 y Fr(b)-54 b Fw(\027)21 b Fu(r)3279 1375 y Fv(\032)3279 1445 y Ft(1)3319 1419 y Fw(q)3360 1433 y Ft(1)3399 1419 y Fw(q)3440 1433 y Ft(2)3479 1419 y Fx(\011)3550 1346 y Fr(\013)3593 1342 y(\014)3593 1396 y(\014)3638 1419 y Fw(:)14 1625 y Fx(W)-8 b(e)32 b(estimate)g(the)e(\014rst)g(term)g(\(the)h(second)g(is)f(dealt) i(with)e(in)g(exactly)i(the)e(same)h(w)m(a)m(y\):)244 1793 y Fr(\014)244 1848 y(\014)275 1797 y(\012)317 1870 y Fw(p)363 1884 y Ft(1)403 1870 y Fw(p)449 1884 y Ft(2)488 1870 y Fx(\011)10 b Fw(;)15 b(X)691 1826 y Fv(\032)684 1896 y Ft(12)759 1870 y Fw(p)805 1884 y Ft(1)879 1870 y Fr(c)-111 b Fw(\034)899 1884 y Ft(1)939 1870 y Fw(\027)20 b Fu(r)1080 1826 y Fv(\032)1080 1896 y Ft(1)1120 1870 y Fw(q)1161 1884 y Ft(1)1200 1870 y Fw(q)1241 1884 y Ft(2)1281 1870 y Fx(\011)1351 1797 y Fr(\013)1394 1793 y(\014)1394 1848 y(\014)1475 1870 y Fi(6)1596 1761 y Fr(q)p 1687 1761 769 4 v 36 x(\012)1730 1870 y Fx(\011)10 b Fw(;)15 b(p)1897 1884 y Ft(1)1936 1870 y Fw(p)1982 1884 y Ft(2)2022 1870 y Fw(X)2104 1839 y Ft(2)2097 1896 y(12)2172 1870 y Fw(p)2218 1884 y Ft(1)2257 1870 y Fw(p)2303 1884 y Ft(2)2342 1870 y Fx(\011)2413 1797 y Fr(\013)2471 1757 y(q)p 2562 1757 933 4 v 40 x(\012)2605 1870 y Fu(r)2681 1884 y Ft(1)2720 1870 y Fw(q)2761 1884 y Ft(1)2800 1870 y Fx(\011)10 b Fw(;)34 b Fr(c)-110 b Fw(\034)2961 1884 y Ft(1)3000 1870 y Fw(\027)3051 1828 y Ft(2)3105 1870 y Fw(q)3146 1884 y Ft(2)3185 1870 y Fu(r)3261 1884 y Ft(1)3301 1870 y Fw(q)3342 1884 y Ft(1)3381 1870 y Fx(\011)3451 1797 y Fr(\013)1475 2155 y Fi(6)1596 2044 y Fr(q)p 1687 2044 412 4 v 111 x Fu(k)p Fw(p)1778 2169 y Ft(2)1818 2155 y Fw(X)1900 2124 y Ft(2)1893 2181 y(12)1968 2155 y Fw(p)2014 2169 y Ft(2)2053 2155 y Fu(k)2098 1961 y Fr(v)2098 2012 y(u)2098 2067 y(u)2098 2121 y(t)p 2194 1961 1323 4 v 2301 2093 a Fx(1)p 2204 2134 240 4 v 2204 2217 a Fw(N)30 b Fu(\000)20 b Fx(1)2503 2041 y Fv(N)2469 2068 y Fr(X)2477 2264 y Fv(i)p Ft(=2)2615 2081 y Fr(\012)2658 2155 y Fu(r)2734 2169 y Ft(1)2774 2155 y Fw(q)2815 2169 y Ft(1)2854 2155 y Fx(\011)9 b Fw(;)18 b Fr(b)-54 b Fw(n)3029 2129 y FF(\000)p Ft(2)3139 2155 y Fw(q)3180 2169 y Fv(i)3208 2155 y Fu(r)3284 2169 y Ft(1)3323 2155 y Fw(q)3364 2169 y Ft(1)3403 2155 y Fx(\011)3473 2081 y Fr(\013)1475 2519 y Fi(6)50 b Fu(k)p Fw(\030)t Fu(k)1730 2533 y Ft(2)1786 2519 y Fu(k)p Fw(')p Fu(k)1935 2533 y FF(1)2011 2325 y Fr(v)2011 2376 y(u)2011 2431 y(u)2011 2485 y(t)p 2107 2325 1323 4 v 2214 2457 a Fx(1)p 2117 2498 240 4 v 2117 2581 a Fw(N)30 b Fu(\000)20 b Fx(1)2415 2405 y Fv(N)2381 2433 y Fr(X)2390 2628 y Fv(i)p Ft(=1)2528 2445 y Fr(\012)2571 2519 y Fu(r)2647 2533 y Ft(1)2686 2519 y Fw(q)2727 2533 y Ft(1)2766 2519 y Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)2942 2493 y FF(\000)p Ft(2)3051 2519 y Fw(q)3092 2533 y Fv(i)3120 2519 y Fu(r)3196 2533 y Ft(1)3235 2519 y Fw(q)3276 2533 y Ft(1)3315 2519 y Fx(\011)3386 2445 y Fr(\013)1475 2830 y Fi(.)50 b Fw(a)1644 2793 y Ft(1)p FF(\000)p Fv(p=p)1841 2802 y Fp(0)1879 2830 y Fu(k)p Fw(')p Fu(k)2028 2844 y FF(1)2105 2690 y Fr(r)p 2195 2690 943 4 v 2284 2769 a Fw(N)p 2205 2809 240 4 v 2205 2893 a(N)31 b Fu(\000)19 b Fx(1)2470 2757 y Fr(\012)2513 2830 y Fu(r)2589 2844 y Ft(1)2628 2830 y Fw(q)2669 2844 y Ft(1)2708 2830 y Fx(\011)10 b Fw(;)15 b Fu(r)2905 2844 y Ft(1)2945 2830 y Fw(q)2986 2844 y Ft(1)3025 2830 y Fx(\011)3095 2757 y Fr(\013)1475 3025 y Fi(6)50 b Fu(k)p Fw(')p Fu(k)1745 3039 y FF(1)1821 2951 y Fr(\000)1863 3025 y Fw(a)1911 2987 y Ft(2)p FF(\000)p Ft(2)p Fv(p=p)2143 2996 y Fp(0)2202 3025 y Fx(+)20 b Fu(kr)2414 3039 y Ft(1)2453 3025 y Fw(q)2494 3039 y Ft(1)2533 3025 y Fx(\011)p Fu(k)2649 2987 y Ft(2)2689 2951 y Fr(\001)2746 3025 y Fw(:)14 3231 y Fx(Summarizing,)671 3378 y Fr(\014)671 3432 y(\014)702 3455 y Fx(\(I)s(I)s(I\))876 3413 y Ft(\()p Fv(p;)p Ft(1\))1025 3378 y Fr(\014)1025 3432 y(\014)1106 3455 y Fi(.)50 b Fu(k)p Fw(')p Fu(k)1376 3469 y FF(1)1453 3354 y Fr(\020)1507 3455 y Fw(\014)5 b Fu(k)p Fw(')p Fu(k)1712 3469 y Fv(X)1770 3478 y Fp(1)1830 3455 y Fx(+)20 b Fu(kr)2042 3469 y Ft(1)2082 3455 y Fw(q)2123 3469 y Ft(1)2162 3455 y Fx(\011)p Fu(k)2278 3417 y Ft(2)2338 3455 y Fx(+)g Fw(a)2477 3417 y Ft(2)p FF(\000)p Ft(2)p Fv(p=p)2709 3426 y Fp(0)2747 3455 y Fu(k)p Fw(')p Fu(k)2896 3469 y Fv(X)2954 3478 y Fp(1)2994 3354 y Fr(\021)3064 3455 y Fw(:)155 3679 y Fx(Finally)-8 b(,)32 b(w)m(e)f(estimate)171 3904 y(\(I)s(I)s(I\))345 3862 y Ft(\()p Fv(p;)p Ft(2\))545 3904 y Fx(=)666 3827 y Fr(\014)666 3881 y(\014)696 3830 y(\012)739 3904 y Fx(\011)10 b Fw(;)15 b(p)906 3918 y Ft(1)946 3904 y Fw(p)992 3918 y Ft(2)1031 3904 y Fw(W)1130 3856 y Ft(\()p Fv(p;)p Ft(2\))1117 3930 y(12)1296 3904 y Fr(b)-53 b Fw(\027)21 b(q)1401 3918 y Ft(1)1440 3904 y Fw(q)1481 3918 y Ft(2)1520 3904 y Fx(\011)1590 3830 y Fr(\013)1633 3827 y(\014)1633 3881 y(\014)1714 3904 y Fx(=)1835 3827 y Fr(\014)1835 3881 y(\014)1866 3830 y(\012)1909 3904 y Fx(\011)10 b Fw(;)15 b(p)2076 3918 y Ft(1)2115 3904 y Fw(p)2161 3918 y Ft(2)2200 3904 y Fw(W)2299 3856 y Ft(\()p Fv(p;)p Ft(2\))2286 3930 y(12)2466 3904 y Fr(b)-54 b Fw(\027)21 b Fx(\()2574 3867 y Fr(d)2564 3904 y Fw(\037)2621 3878 y Ft(\(1\))2736 3904 y Fx(+)2837 3867 y Fr(d)2827 3904 y Fw(\037)2884 3878 y Ft(\(2\))2978 3904 y Fx(\))p Fw(q)3054 3918 y Ft(1)3093 3904 y Fw(q)3134 3918 y Ft(2)3173 3904 y Fx(\011)3244 3830 y Fr(\013)3287 3827 y(\014)3287 3881 y(\014)3332 3904 y Fw(;)157 b Fx(\(4.26\))14 4110 y(where)927 4225 y(1)51 b(=)f Fw(\037)1201 4188 y Ft(\(1\))1316 4225 y Fx(+)20 b Fw(\037)1464 4188 y Ft(\(2\))1573 4225 y Fw(;)197 b(\037)1852 4188 y Ft(\(1\))1946 4225 y Fw(;)15 b(\037)2043 4188 y Ft(\(2\))2189 4225 y Fu(2)50 b(f)p Fx(0)p Fw(;)15 b Fx(1)p Fu(g)2520 4188 y FF(f)p Ft(0)p Fv(;:::)q(;N)7 b FF(g)2808 4225 y Fw(;)14 4394 y Fx(is)23 b(some)f(partition)i(of)e (the)h(unit)m(y)f(to)h(b)s(e)f(c)m(hosen)h(later.)39 b(The)22 b(need)g(for)g(this)h(partitioning)g(will)g(so)s(on)f(b)s (ecome)14 4518 y(clear.)41 b(In)28 b(order)g(to)i(b)s(ound)c(the)j (term)g(with)f Fw(\037)1635 4485 y Ft(\(1\))1729 4518 y Fx(,)h(w)m(e)g(note)h(that)f(the)g(op)s(erator)g(norm)e(of)i Fw(p)3214 4532 y Ft(1)3253 4518 y Fw(p)3299 4532 y Ft(2)3338 4518 y Fw(W)3437 4470 y Ft(\()p Fv(p;)p Ft(2\))3424 4544 y(12)3586 4518 y Fw(q)3627 4532 y Ft(1)3666 4518 y Fw(q)3707 4532 y Ft(2)14 4631 y Fx(on)e(the)g(full)g(space)g Fw(L)747 4598 y Ft(2)786 4631 y Fx(\()p Fs(R)887 4598 y Fv(dN)991 4631 y Fx(\))g(is)g(m)m(uc)m(h)g(larger)g(than)g(on)g(its)g(symmetric)g (subspace.)39 b(Th)m(us,)27 b(as)g(a)g(\014rst)f(step,)14 4760 y(w)m(e)31 b(symmetrize)g(the)g(op)s(erator)f Fw(p)1200 4774 y Ft(1)1239 4760 y Fw(p)1285 4774 y Ft(2)1325 4760 y Fw(W)1424 4712 y Ft(\()p Fv(p;)p Ft(2\))1411 4786 y(12)1573 4760 y Fw(q)1614 4774 y Ft(1)1653 4760 y Fw(q)1694 4774 y Ft(2)1763 4760 y Fx(in)g(co)s(ordinate)h(2.)41 b(W)-8 b(e)32 b(get)f(the)g(b)s(ound)14 4978 y Fr(\014)14 5033 y(\014)44 4982 y(\012)87 5056 y Fx(\011)10 b Fw(;)15 b(p)254 5070 y Ft(1)294 5056 y Fw(p)340 5070 y Ft(2)379 5056 y Fw(W)478 5008 y Ft(\()p Fv(p;)p Ft(2\))465 5082 y(12)645 5056 y Fr(b)-54 b Fw(\027)718 5019 y Fr(d)708 5056 y Fw(\037)765 5029 y Ft(\(1\))874 5056 y Fw(q)915 5070 y Ft(1)954 5056 y Fw(q)995 5070 y Ft(2)1034 5056 y Fx(\011)1105 4982 y Fr(\013)1148 4978 y(\014)1148 5033 y(\014)1229 5056 y Fx(=)1457 4994 y(1)p 1360 5035 V 1360 5118 a Fw(N)30 b Fu(\000)20 b Fx(1)1609 4924 y Fr(\014)1609 4978 y(\014)1609 5033 y(\014)1609 5087 y(\014)1640 4927 y(\034)1708 5056 y Fx(\011)25 b Fw(;)1894 4942 y Fv(N)1859 4969 y Fr(X)1868 5165 y Fv(i)p 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Fw(q)2832 5415 y Ft(1)2871 5401 y Fw(q)2912 5415 y Fv(i)2964 5364 y Fr(d)2955 5401 y Fw(\037)3012 5375 y Ft(\(1\))3121 5401 y Fw(q)3162 5415 y Ft(1)3201 5401 y Fw(q)3242 5415 y Fv(j)3278 5401 y Fw(W)3377 5353 y Ft(\()p Fv(p)p FF(\000)p Ft(2\))3364 5428 y(1)p Fv(j)3561 5401 y Fw(p)3607 5415 y Fv(j)3643 5401 y Fw(p)3689 5415 y Ft(1)3729 5401 y Fx(\011)3799 5328 y Fr(\013)3857 5401 y Fw(:)p Black 1835 6000 a Fx(27)p Black eop end %%Page: 28 28 TeXDict begin 28 27 bop Black Black 14 162 a Fx(Using)1332 198 y Fr(\015)1332 252 y(\015)1385 275 y(b)-54 b Fw(\027)21 b(q)1489 289 y Ft(1)1528 275 y Fx(\011)1599 198 y Fr(\015)1599 252 y(\015)1700 275 y Fi(6)50 b Fu(k)r Fr(b)-53 b Fw(n)1921 238 y FF(\000)p Ft(1)2015 275 y Fw(q)2056 289 y Ft(1)2095 275 y Fx(\011)p Fu(k)51 b Fi(6)f Fx(1)14 438 y(w)m(e)31 b(\014nd)898 489 y Fr(\014)898 544 y(\014)929 493 y(\012)971 567 y Fx(\011)10 b Fw(;)15 b(p)1138 581 y Ft(1)1178 567 y Fw(p)1224 581 y Ft(2)1263 567 y Fw(W)1362 519 y Ft(\()p Fv(p;)p Ft(2\))1349 593 y(12)1529 567 y Fr(b)-54 b Fw(\027)1602 530 y Fr(d)1592 567 y Fw(\037)1649 540 y Ft(\(1\))1758 567 y Fw(q)1799 581 y Ft(1)1838 567 y Fw(q)1879 581 y Ft(2)1918 567 y Fx(\011)1989 493 y Fr(\013)2032 489 y(\014)2032 544 y(\014)2113 567 y Fi(6)2341 505 y Fx(1)p 2244 546 240 4 v 2244 629 a Fw(N)30 b Fu(\000)20 b Fx(1)2493 489 y Fu(p)p 2569 489 253 4 v 78 x Fw(A)h Fx(+)e Fw(B)h(;)652 b Fx(\(4.27\))14 758 y(where)809 955 y Fw(A)928 952 y Fx(:)953 955 y(=)1168 868 y Fr(X)1074 1066 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1409 881 y Fr(\012)1452 955 y Fx(\011)10 b Fw(;)15 b(p)1619 969 y Ft(1)1658 955 y Fw(p)1704 969 y Fv(i)1732 955 y Fw(W)1831 907 y Ft(\()p Fv(p;)p Ft(2\))1818 982 y(1)p Fv(i)1980 955 y Fw(q)2021 969 y Ft(1)2060 955 y Fw(q)2101 969 y Fv(i)2154 918 y Fr(d)2144 955 y Fw(\037)2201 928 y Ft(\(1\))2310 955 y Fw(q)2351 969 y Fv(j)2387 955 y Fw(W)2486 907 y Ft(\()p Fv(p;)p Ft(2\))2473 982 y(1)p Fv(j)2635 955 y Fw(p)2681 969 y Fv(j)2718 955 y Fw(p)2764 969 y Ft(1)2803 955 y Fx(\011)2873 881 y Fr(\013)2932 955 y Fw(;)804 1289 y(B)928 1286 y Fx(:)953 1289 y(=)1108 1176 y Fv(N)1074 1203 y Fr(X)1083 1398 y Fv(i)p Ft(=2)1221 1216 y Fr(\012)1264 1289 y Fx(\011)10 b Fw(;)15 b(p)1431 1303 y Ft(1)1470 1289 y Fw(p)1516 1303 y Fv(i)1544 1289 y Fw(W)1643 1241 y Ft(\()p Fv(p;)p Ft(2\))1630 1316 y(1)p Fv(i)1792 1289 y Fw(q)1833 1303 y Ft(1)1872 1289 y Fw(q)1913 1303 y Fv(i)1966 1252 y Fr(d)1956 1289 y Fw(\037)2013 1263 y Ft(\(1\))2122 1289 y Fw(W)2221 1241 y Ft(\()p Fv(p;)p Ft(2\))2208 1316 y(1)p Fv(i)2370 1289 y Fw(p)2416 1303 y Fv(i)2444 1289 y Fw(p)2490 1303 y Ft(1)2529 1289 y Fx(\011)2600 1216 y Fr(\013)2658 1289 y Fw(:)155 1562 y Fx(The)30 b(easy)h(part)f(is)1098 1840 y Fw(B)55 b Fi(6)1378 1727 y Fv(N)1343 1754 y Fr(X)1352 1949 y Fv(i)p Ft(=2)1490 1767 y Fr(\012)1533 1840 y Fx(\011)10 b Fw(;)15 b(p)1700 1854 y Ft(1)1739 1840 y Fw(p)1785 1854 y Fv(i)1813 1767 y Fr(\000)1855 1840 y Fw(W)1954 1792 y Ft(\()p Fv(p;)p Ft(2\))1941 1867 y(1)p Fv(i)2103 1767 y Fr(\001)2144 1789 y Ft(2)2184 1840 y Fw(p)2230 1854 y Fv(i)2258 1840 y Fw(p)2304 1854 y Ft(1)2343 1840 y Fx(\011)2414 1767 y Fr(\013)1222 2160 y Fi(6)1378 2046 y Fv(N)1343 2073 y Fr(X)1352 2269 y Fv(i)p Ft(=2)1490 2082 y Fr(\015)1490 2137 y(\015)1540 2086 y(\000)1582 2160 y Fw(w)1649 2122 y Ft(\()p Fv(p;)p Ft(2\))1799 2086 y Fr(\001)1841 2109 y Ft(2)1900 2160 y Fu(\003)21 b(j)p Fw(')p Fu(j)2075 2122 y Ft(2)2115 2082 y Fr(\015)2115 2137 y(\015)2166 2196 y FF(1)2241 2160 y Fu(h)p Fx(\011)10 b Fw(;)15 b(p)2443 2174 y Ft(1)2482 2160 y Fw(p)2528 2174 y Fv(i)2556 2160 y Fx(\011)p Fu(i)1222 2398 y Fi(6)50 b Fx(\()p Fw(N)31 b Fu(\000)20 b Fx(1\))p Fu(k)p Fw(')p Fu(k)1802 2361 y Ft(2)1802 2421 y FF(1)1879 2398 y Fu(k)p Fw(w)1991 2361 y Ft(\()p Fv(p;)p Ft(2\))2141 2398 y Fu(k)2186 2361 y Ft(2)2186 2421 y(2)1222 2546 y Fi(.)50 b Fw(N)26 b(a)1490 2508 y Ft(2)p FF(\000)p Fv(p)1635 2546 y Fu(k)p Fw(')p Fu(k)1784 2508 y Ft(2)1784 2568 y FF(1)1875 2546 y Fw(:)14 2742 y Fx(Let)31 b(us)f(therefore)h(concen)m(trate)h(on)669 2939 y Fw(A)51 b Fx(=)1003 2853 y Fr(X)909 3050 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1244 2865 y Fr(\012)1287 2939 y Fx(\011)10 b Fw(;)15 b(p)1454 2953 y Ft(1)1493 2939 y Fw(p)1539 2953 y Fv(i)1567 2939 y Fw(W)1666 2891 y Ft(\()p Fv(p;)p Ft(2\))1653 2966 y(1)p Fv(i)1815 2939 y Fw(q)1856 2953 y Ft(1)1895 2939 y Fw(q)1936 2953 y Fv(i)1989 2902 y Fr(d)1979 2939 y Fw(\037)2036 2913 y Ft(\(1\))2155 2902 y Fr(d)2145 2939 y Fw(\037)2202 2913 y Ft(\(1\))2312 2939 y Fw(q)2353 2953 y Fv(j)2389 2939 y Fw(W)2488 2891 y Ft(\()p Fv(p;)p Ft(2\))2475 2966 y(1)p Fv(j)2637 2939 y Fw(p)2683 2953 y Fv(j)2719 2939 y Fw(p)2765 2953 y Ft(1)2804 2939 y Fx(\011)2875 2865 y Fr(\013)788 3215 y Fx(=)1003 3128 y Fr(X)909 3326 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1244 3141 y Fr(\012)1287 3215 y Fx(\011)10 b Fw(;)15 b(p)1454 3229 y Ft(1)1493 3215 y Fw(p)1539 3229 y Fv(i)1567 3215 y Fw(q)1608 3229 y Fv(j)1668 3180 y Fs(\\)1659 3215 y 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Fv(j)t Fq(6)p Fv(N)869 3798 y Fr(\014)869 3853 y(\014)899 3802 y(\012)942 3875 y Fx(\011)10 b Fw(;)15 b(p)1109 3889 y Ft(1)1148 3875 y Fw(p)1194 3889 y Fv(i)1222 3875 y Fw(q)1263 3889 y Fv(j)1324 3841 y Fs(\\)1315 3875 y Fw(\034)1355 3889 y Ft(2)1394 3875 y Fw(\037)1451 3849 y Ft(\(1\))1560 3875 y Fw(W)1659 3827 y Ft(\()p Fv(p;)p Ft(2\))1646 3902 y(1)p Fv(i)1808 3875 y Fw(W)1907 3827 y Ft(\()p Fv(p;)p Ft(2\))1894 3902 y(1)p Fv(j)2080 3841 y Fs(\\)2071 3875 y Fw(\034)2111 3889 y Ft(2)2150 3875 y Fw(\037)2207 3849 y Ft(\(1\))2317 3875 y Fw(q)2358 3889 y Fv(i)2385 3875 y Fw(p)2431 3889 y Fv(j)2468 3875 y Fw(p)2514 3889 y Ft(1)2553 3875 y Fx(\011)2624 3802 y Fr(\013)2666 3798 y(\014)2666 3853 y(\014)413 4171 y Fx(=)628 4085 y Fr(X)534 4282 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)869 4094 y Fr(\014)869 4148 y(\014)899 4097 y(\012)942 4171 y Fx(\011)10 b Fw(;)15 b(p)1109 4185 y Ft(1)1148 4171 y Fw(p)1194 4185 y Fv(i)1222 4171 y Fw(q)1263 4185 y Fv(j)1324 4137 y Fs(\\)1315 4171 y Fw(\034)1355 4185 y Ft(2)1394 4171 y Fw(\037)1451 4145 y Ft(\(1\))1560 4049 y Fr(q)p 1651 4049 248 4 v 122 x Fw(W)1750 4123 y Ft(\()p Fv(p;)p Ft(2\))1737 4198 y(1)p Fv(i)1899 4056 y Fr(q)p 1990 4056 V 115 x Fw(W)2089 4123 y Ft(\()p Fv(p;)p Ft(2\))2076 4198 y(1)p Fv(j)2238 4049 y Fr(q)p 2329 4049 V 122 x Fw(W)2428 4123 y Ft(\()p Fv(p;)p Ft(2\))2415 4198 y(1)p Fv(i)2577 4056 y Fr(q)p 2668 4056 V 115 x Fw(W)2767 4123 y Ft(\()p Fv(p;)p Ft(2\))2754 4198 y(1)p Fv(j)2940 4137 y Fs(\\)2931 4171 y Fw(\034)2971 4185 y Ft(2)3010 4171 y Fw(\037)3067 4145 y Ft(\(1\))3176 4171 y Fw(q)3217 4185 y Fv(i)3245 4171 y Fw(p)3291 4185 y Fv(j)3327 4171 y Fw(p)3373 4185 y Ft(1)3412 4171 y Fx(\011)3483 4097 y Fr(\013)3526 4094 y(\014)3526 4148 y(\014)413 4447 y Fi(6)628 4360 y Fr(X)534 4558 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)869 4373 y Fr(\012)912 4447 y Fx(\011)10 b Fw(;)1042 4413 y Fs(\\)1033 4447 y Fw(\034)1073 4461 y Ft(2)1112 4447 y Fw(\037)1169 4420 y Ft(\(1\))1278 4447 y Fw(q)1319 4461 y Fv(j)1356 4447 y Fw(p)1402 4461 y Ft(1)1441 4447 y Fw(p)1487 4461 y Fv(i)1515 4369 y Fr(\014)1515 4424 y(\014)1545 4447 y Fw(W)1644 4399 y Ft(\()p Fv(p;)p Ft(2\))1631 4474 y(1)p Fv(i)1793 4369 y Fr(\014)1793 4424 y(\014)1823 4369 y(\014)1823 4424 y(\014)1853 4447 y Fw(W)1952 4399 y Ft(\()p Fv(p;)p Ft(2\))1939 4474 y(1)p Fv(j)2101 4369 y Fr(\014)2101 4424 y(\014)2132 4447 y Fw(p)2178 4461 y Ft(1)2217 4447 y Fw(p)2263 4461 y Fv(i)2291 4447 y Fw(q)2332 4461 y Fv(j)2392 4413 y Fs(\\)2383 4447 y Fw(\034)2423 4461 y Ft(2)2462 4447 y Fw(\037)2519 4420 y Ft(\(1\))2629 4447 y Fx(\011)2699 4373 y Fr(\013)2757 4447 y Fw(;)14 4745 y Fx(b)m(y)30 b(Cauc)m(h)m(y-Sc)m(h)m(w)m(arz)i(and)e(symmetry)g (of)h(\011.)40 b(Here)1874 4679 y Fu(p)p 1950 4679 26 4 v 66 x(\001)30 b Fx(is)h(an)m(y)f(complex)i(square)e(ro)s(ot.)155 4858 y(In)g(order)g(to)h(estimate)h(this)e(w)m(e)h(claim)h(that,)f(for) f Fw(i)c Fu(6)p Fx(=)f Fw(j)5 b Fx(,)912 4968 y Fr(\015)912 5022 y(\015)912 5077 y(\015)962 5072 y Fw(p)1008 5086 y Ft(1)1048 5072 y Fw(p)1094 5086 y Fv(i)1121 4995 y Fr(\014)1121 5050 y(\014)1152 5072 y Fw(W)1251 5024 y Ft(\()p Fv(p;)p Ft(2\))1238 5100 y(1)p Fv(i)1400 4995 y Fr(\014)1400 5050 y(\014)1430 4995 y(\014)1430 5050 y(\014)1460 5072 y Fw(W)1559 5024 y Ft(\()p Fv(p;)p Ft(2\))1546 5100 y(1)p Fv(j)1708 4995 y Fr(\014)1708 5050 y(\014)1739 5072 y Fw(p)1785 5086 y Ft(1)1824 5072 y Fw(p)1870 5086 y Fv(i)1898 4968 y Fr(\015)1898 5022 y(\015)1898 5077 y(\015)1999 5072 y Fi(6)2120 4995 y Fr(\015)2120 5050 y(\015)2170 4995 y(\014)2170 5050 y(\014)2201 5072 y Fw(w)2268 5035 y Ft(\()p Fv(p;)p Ft(2\))2418 4995 y Fr(\014)2418 5050 y(\014)2468 5072 y Fu(\003)21 b(j)p Fw(')p Fu(j)2643 5035 y Ft(2)2683 4995 y Fr(\015)2683 5050 y(\015)2734 5021 y Ft(2)2734 5108 y FF(1)2824 5072 y Fw(:)665 b Fx(\(4.28\))14 5292 y(Indeed,)30 b(b)m(y)h(\(3.17\))s(,)f(w)m(e)h(ha)m(v)m(e)159 5504 y Fw(p)205 5518 y Ft(1)244 5504 y Fw(p)290 5518 y Fv(i)318 5427 y Fr(\014)318 5481 y(\014)348 5504 y Fw(W)447 5456 y Ft(\()p Fv(p;)p Ft(2\))434 5531 y(1)p Fv(i)596 5427 y Fr(\014)596 5481 y(\014)627 5427 y(\014)627 5481 y(\014)657 5504 y Fw(W)756 5456 y Ft(\()p Fv(p;)p Ft(2\))743 5531 y(1)p Fv(j)905 5427 y Fr(\014)905 5481 y(\014)935 5504 y Fw(p)981 5518 y Ft(1)1020 5504 y Fw(p)1066 5518 y Fv(i)1145 5504 y Fx(=)50 b Fw(p)1312 5518 y Ft(1)1351 5504 y Fw(p)1397 5518 y Fv(i)1425 5427 y Fr(\014)1425 5481 y(\014)1455 5504 y Fw(W)1554 5456 y Ft(\()p Fv(p;)p Ft(2\))1541 5531 y(1)p Fv(i)1703 5427 y Fr(\014)1703 5481 y(\014)1734 5504 y Fw(p)1780 5518 y Fv(i)1807 5427 y Fr(\014)1807 5481 y(\014)1838 5504 y Fw(W)1937 5456 y Ft(\()p Fv(p;)p Ft(2\))1924 5531 y(1)p Fv(j)2086 5427 y Fr(\014)2086 5481 y(\014)2116 5504 y Fw(p)2162 5518 y Ft(1)2252 5504 y Fx(=)g Fw(p)2419 5518 y Ft(1)2458 5504 y Fw(p)2504 5518 y Fv(i)2532 5430 y Fr(\000)2574 5427 y(\014)2574 5481 y(\014)2604 5504 y Fw(w)2671 5466 y Ft(\()p Fv(p;)p Ft(2\))2821 5427 y Fr(\014)2821 5481 y(\014)2871 5504 y Fu(\003)21 b(j)p Fw(')p Fu(j)3046 5466 y Ft(2)3086 5430 y Fr(\001)3128 5540 y Ft(1)3168 5427 y Fr(\014)3168 5481 y(\014)3198 5504 y Fw(W)3297 5456 y Ft(\()p Fv(p;)p Ft(2\))3284 5531 y(1)p Fv(j)3446 5427 y Fr(\014)3446 5481 y(\014)3476 5504 y Fw(p)3522 5518 y Ft(1)3576 5504 y Fw(:)p Black 1835 6000 a Fx(28)p Black eop end %%Page: 29 29 TeXDict begin 29 28 bop Black Black 14 169 a Fx(The)30 b(op)s(erator)h Fw(p)614 183 y Ft(1)653 95 y Fr(\000)695 91 y(\014)695 146 y(\014)725 169 y Fw(w)792 136 y Ft(\()p Fv(p;)p Ft(2\))942 91 y Fr(\014)942 146 y(\014)992 169 y Fu(\003)21 b(j)p Fw(')p Fu(j)1167 136 y Ft(2)1207 95 y Fr(\001)1249 205 y Ft(1)1289 91 y Fr(\014)1289 146 y(\014)1319 169 y Fw(W)1418 121 y Ft(\()p Fv(p;)p Ft(2\))1405 196 y(1)p Fv(j)1567 91 y Fr(\014)1567 146 y(\014)1597 169 y Fw(p)1643 183 y Ft(1)1713 169 y Fx(is)30 b(equal)h(to)g Fw(f)2200 183 y Fv(j)2251 169 y Fw(p)2297 183 y Ft(1)2336 169 y Fx(,)g(where)611 436 y Fw(f)10 b Fx(\()p Fw(x)753 450 y Fv(j)789 436 y Fx(\))51 b(=)996 312 y Fr(Z)1102 436 y Fx(d)p Fw(x)1205 450 y Ft(1)p 1269 357 222 4 v 1269 436 a Fw(')p Fx(\()p Fw(x)1415 450 y Ft(1)1455 436 y Fx(\))1491 362 y Fr(\000)1532 358 y(\014)1532 413 y(\014)1563 436 y Fw(w)1630 398 y Ft(\()p Fv(p;)p Ft(2\))1779 358 y Fr(\014)1779 413 y(\014)1830 436 y Fu(\003)21 b(j)p Fw(')p Fu(j)2005 398 y Ft(2)2045 362 y Fr(\001)2087 436 y Fx(\()p Fw(x)2174 450 y Ft(1)2213 436 y Fx(\))2248 358 y Fr(\014)2248 413 y(\014)2279 436 y Fw(w)2346 398 y Ft(\()p Fv(p;)p Ft(2\))2496 436 y Fx(\()p Fw(x)2583 450 y Ft(1)2643 436 y Fu(\000)f Fw(x)2786 450 y Fv(j)2822 436 y Fx(\))2857 358 y Fr(\014)2857 413 y(\014)2888 436 y Fw(')p Fx(\()p Fw(x)3034 450 y Ft(1)3074 436 y Fx(\))15 b Fw(:)14 680 y Fx(Th)m(us,)1320 797 y Fu(k)p Fw(f)10 b Fu(k)1465 811 y FF(1)1590 797 y Fi(6)1712 720 y Fr(\015)1712 774 y(\015)1762 720 y(\014)1762 774 y(\014)1792 797 y Fw(w)1859 759 y Ft(\()p Fv(p;)p Ft(2\))2009 720 y Fr(\014)2009 774 y(\014)2060 797 y Fu(\003)21 b(j)p Fw(')p Fu(j)2235 759 y Ft(2)2275 720 y Fr(\015)2275 774 y(\015)2326 746 y Ft(2)2326 833 y FF(1)2415 797 y Fw(;)14 968 y Fx(from)30 b(whic)m(h)g(\(4.28\))j(follo)m(ws)e(immediately)-8 b(.)155 1082 y(Using)32 b(\(4.28\))r(,)f(w)m(e)g(get)943 1317 y Fu(j)p Fw(A)1036 1331 y Ft(1)1076 1317 y Fu(j)51 b Fi(6)1367 1231 y Fr(X)1273 1429 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1607 1240 y Fr(\015)1607 1295 y(\015)1658 1240 y(\014)1658 1295 y(\014)1688 1317 y Fw(w)1755 1280 y Ft(\()p Fv(p;)p Ft(2\))1905 1240 y Fr(\014)1905 1295 y(\014)1956 1317 y Fu(\003)20 b(j)p Fw(')p Fu(j)2130 1280 y Ft(2)2171 1240 y Fr(\015)2171 1295 y(\015)2221 1266 y Ft(2)2221 1353 y FF(1)2296 1240 y Fr(\015)2296 1295 y(\015)2356 1283 y Fs(\\)2347 1317 y Fw(\034)2387 1331 y Ft(2)2426 1317 y Fw(\037)2483 1291 y Ft(\(1\))2577 1317 y Fw(q)2618 1331 y Ft(1)2657 1317 y Fx(\011)2728 1240 y Fr(\015)2728 1295 y(\015)2778 1266 y Ft(2)1152 1593 y Fi(6)50 b Fw(N)1356 1555 y Ft(2)1395 1593 y Fu(k)p Fw(w)1507 1555 y Ft(\()p Fv(p)p Ft(\))1603 1593 y Fu(k)1648 1555 y Ft(2)1648 1615 y Fv(p)1703 1593 y Fu(k)p Fw(')p Fu(k)1852 1555 y Ft(4)1852 1621 y Fv(L)1900 1602 y Fp(2)1936 1621 y FF(\\)p Fv(L)2031 1602 y Fm(1)2115 1519 y Fr(\012)2158 1593 y Fx(\011)10 b Fw(;)2289 1559 y Fs(\\)2279 1593 y Fw(\034)2319 1607 y Ft(2)2359 1593 y Fw(\037)2416 1567 y Ft(\(1\))2525 1593 y Fw(q)2566 1607 y Ft(1)2605 1593 y Fx(\011)2676 1519 y Fr(\013)1152 1771 y Fi(.)50 b Fw(N)1356 1733 y Ft(2)1410 1771 y Fu(k)p Fw(')p Fu(k)1559 1733 y Ft(4)1559 1799 y Fv(L)1607 1780 y Fp(2)1643 1799 y FF(\\)p Fv(L)1738 1780 y Fm(1)1823 1697 y Fr(\012)1866 1771 y Fx(\011)10 b Fw(;)1996 1737 y Fs(\\)1987 1771 y Fw(\034)2027 1785 y Ft(2)2066 1771 y Fw(\037)2123 1744 y Ft(\(1\))2234 1771 y Fr(b)-53 b Fw(n)2287 1733 y Ft(2)2342 1771 y Fx(\011)2412 1697 y Fr(\013)2470 1771 y Fw(:)14 1978 y Fx(No)m(w)31 b(let)h(us)d(c)m(ho)s (ose)1447 2095 y Fw(\037)1504 2057 y Ft(\(1\))1598 2095 y Fx(\()p Fw(k)s Fx(\))1770 2092 y(:)1795 2095 y(=)50 b Fj(1)1970 2117 y FF(f)p Fv(k)r Fq(6)p Fv(N)2162 2098 y Fp(1)p Fm(\000)p Fn(\016)2274 2117 y FF(g)3514 2095 y Fx(\(4.29\))14 2266 y(for)30 b(some)h Fw(\016)e Fu(2)c Fx(\(0)p Fw(;)15 b Fx(1\).)43 b(Then)1501 2383 y(\()p Fw(\034)1576 2397 y Ft(2)1616 2383 y Fw(\037)1673 2345 y Ft(\(1\))1767 2383 y Fx(\))15 b Fw(n)1872 2345 y Ft(2)1962 2383 y Fi(6)50 b Fw(N)2166 2345 y FF(\000)p Fv(\016)14 2554 y Fx(implies)1384 2670 y Fu(j)p Fw(A)1477 2684 y Ft(1)1516 2670 y Fu(j)h Fi(.)f Fu(k)p Fw(')p Fu(k)1862 2633 y Ft(4)1862 2698 y Fv(L)1910 2679 y Fp(2)1946 2698 y FF(\\)p Fv(L)2041 2679 y Fm(1)2126 2670 y Fw(N)2209 2633 y Ft(2)p FF(\000)p Fv(\016)2352 2670 y Fw(:)14 2841 y Fx(Similarly)-8 b(,)31 b(w)m(e)g(\014nd)592 3072 y Fu(j)p Fw(A)685 3086 y Ft(2)724 3072 y Fu(j)51 b Fi(6)1015 2985 y Fr(X)921 3183 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1256 2994 y Fr(\014)1256 3049 y(\014)1286 2998 y(\012)1329 3072 y Fx(\011)10 b Fw(;)15 b(q)1491 3086 y Fv(j)1552 3037 y Fs(\\)1543 3072 y Fw(\034)1583 3086 y Ft(2)1622 3072 y Fw(\037)1679 3045 y Ft(\(1\))1788 3072 y Fw(p)1834 3086 y Fv(i)1862 3072 y Fw(p)1908 3086 y Ft(1)1947 3072 y Fw(W)2046 3024 y Ft(\()p Fv(p;)p Ft(2\))2033 3099 y(1)p Fv(i)2195 3072 y Fw(p)2241 3086 y Ft(1)2280 3072 y Fw(W)2379 3024 y Ft(\()p Fv(p;)p Ft(2\))2366 3099 y(1)p Fv(j)2528 3072 y Fw(p)2574 3086 y Ft(1)2613 3072 y Fw(p)2659 3086 y Fv(j)2720 3037 y Fs(\\)2711 3072 y Fw(\034)2751 3086 y Ft(2)2790 3072 y Fw(\037)2847 3045 y Ft(\(1\))2956 3072 y Fw(q)2997 3086 y Fv(i)3025 3072 y Fx(\011)3096 2998 y Fr(\013)3139 2994 y(\014)3139 3049 y(\014)800 3347 y Fi(6)1015 3261 y Fr(X)921 3458 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1256 3270 y Fr(\015)1256 3324 y(\015)1306 3347 y Fw(w)1373 3310 y Ft(\()p Fv(p;)p Ft(2\))1544 3347 y Fu(\003)20 b(j)p Fw(')p Fu(j)1718 3310 y Ft(2)1759 3270 y Fr(\015)1759 3324 y(\015)1809 3296 y Ft(2)1809 3383 y FF(1)1884 3347 y Fu(h)p Fx(\011)10 b Fw(;)2050 3313 y Fs(\\)2040 3347 y Fw(\034)2080 3361 y Ft(2)2120 3347 y Fw(\037)2177 3321 y Ft(\(1\))2286 3347 y Fw(q)2327 3361 y Ft(1)2366 3347 y Fx(\011)p Fu(i)800 3597 y Fi(.)50 b Fw(N)1004 3560 y Ft(2)1044 3597 y Fu(k)p Fw(')p Fu(k)1193 3560 y Ft(4)1193 3625 y Fv(L)1241 3606 y Fp(2)1277 3625 y FF(\\)p Fv(L)1372 3606 y Fm(1)1441 3597 y Fw(N)1524 3560 y FF(\000)p Fv(\016)800 3748 y Fx(=)g Fu(k)p Fw(')p Fu(k)1070 3710 y Ft(4)1070 3776 y Fv(L)1118 3757 y Fp(2)1154 3776 y FF(\\)p Fv(L)1249 3757 y Fm(1)1319 3748 y Fw(N)1402 3710 y Ft(2)p FF(\000)p Fv(\016)1545 3748 y Fw(:)14 3956 y Fx(Th)m(us)29 b(w)m(e)i(ha)m(v)m(e)h (pro)m(v)m(en)1411 4072 y Fu(j)p Fw(A)p Fu(j)51 b Fi(.)f Fu(k)p Fw(')p Fu(k)1850 4035 y Ft(4)1850 4100 y Fv(L)1898 4082 y Fp(2)1934 4100 y FF(\\)p Fv(L)2029 4082 y Fm(1)2098 4072 y Fw(N)2181 4035 y Ft(2)p FF(\000)p Fv(\016)2325 4072 y Fw(:)14 4244 y Fx(Going)31 b(bac)m(k)h(to)f(\(4.27\))r(,)g(w)m (e)f(see)h(that)447 4397 y Fr(\014)447 4452 y(\014)477 4401 y(\012)520 4475 y Fx(\011)10 b Fw(;)15 b(p)687 4489 y Ft(1)726 4475 y Fw(p)772 4489 y Ft(2)811 4475 y Fw(W)910 4427 y Ft(\()p Fv(p;)p Ft(2\))897 4501 y(12)1077 4475 y Fr(b)-53 b Fw(\027)1150 4438 y Fr(d)1140 4475 y Fw(\037)1197 4448 y Ft(\(1\))1307 4475 y Fw(q)1348 4489 y Ft(1)1387 4475 y Fw(q)1428 4489 y Ft(2)1467 4475 y Fx(\011)1537 4401 y Fr(\013)1580 4397 y(\014)1580 4452 y(\014)1661 4475 y Fi(.)50 b Fu(k)p Fw(')p Fu(k)1931 4437 y Ft(2)1931 4503 y Fv(L)1979 4484 y Fp(2)2015 4503 y FF(\\)p Fv(L)2110 4484 y Fm(1)2180 4475 y Fw(N)2263 4437 y FF(\000)p Fv(\016)r(=)p Ft(2)2446 4475 y Fx(+)20 b Fu(k)p Fw(')p Fu(k)2686 4489 y FF(1)2762 4475 y Fw(N)2845 4437 y FF(\000)p Ft(1)p Fv(=)p Ft(2)3025 4475 y Fw(a)3073 4437 y Ft(1)p FF(\000)p Fv(p=)p Ft(2)3289 4475 y Fw(:)155 4703 y Fx(What)31 b(remains)g(is)f (to)h(estimate)h(is)f(the)f(term)h(of)f(\(I)s(I)s(I\))2059 4661 y Ft(\()p Fv(p;)p Ft(2\))2239 4703 y Fx(con)m(taining)i Fw(\037)2738 4670 y Ft(\(2\))2832 4703 y Fx(,)97 4944 y Fr(\014)97 4999 y(\014)127 4948 y(\012)170 5022 y Fx(\011)10 b Fw(;)15 b(p)337 5036 y Ft(1)377 5022 y Fw(p)423 5036 y Ft(2)462 5022 y Fw(W)561 4974 y Ft(\()p Fv(p;)p Ft(2\))548 5048 y(12)728 5022 y Fr(b)-54 b Fw(\027)801 4985 y Fr(d)791 5022 y Fw(\037)848 4995 y Ft(\(2\))957 5022 y Fw(q)998 5036 y Ft(1)1037 5022 y Fw(q)1078 5036 y Ft(2)1117 5022 y Fx(\011)1188 4948 y Fr(\013)1231 4944 y(\014)1231 4999 y(\014)1312 5022 y Fx(=)1540 4960 y(1)p 1443 5001 240 4 v 1443 5084 a Fw(N)30 b Fu(\000)20 b Fx(1)1692 4890 y Fr(\014)1692 4944 y(\014)1692 4999 y(\014)1692 5054 y(\014)1723 4894 y(\034)1791 5022 y Fx(\011)25 b Fw(;)1977 4908 y Fv(N)1942 4935 y Fr(X)1951 5131 y Fv(i)p Ft(=2)2089 5022 y Fw(p)2135 5036 y Ft(1)2174 5022 y Fw(p)2220 5036 y Fv(i)2248 5022 y Fw(W)2347 4974 y Ft(\()p Fv(p;)p Ft(2\))2334 5049 y(1)p Fv(i)2511 5022 y Fw(q)2552 5036 y Fv(i)2580 5022 y Fw(q)2621 5036 y Ft(1)2685 4985 y Fr(d)2675 5022 y Fw(\037)2732 4995 y Ft(\(2\))2844 5022 y Fr(b)-54 b Fw(\027)2892 4984 y Ft(1)p Fv(=)p Ft(2)3020 5022 y Fr(b)g Fw(\027)3068 4984 y Ft(1)p Fv(=)p Ft(2)3193 5022 y Fw(q)3234 5036 y Ft(1)3273 5022 y Fx(\011)3344 4894 y Fr(\035)3412 4890 y(\014)3412 4944 y(\014)3412 4999 y(\014)3412 5054 y(\014)834 5367 y Fi(6)1062 5306 y Fx(1)p 965 5347 V 965 5430 a Fw(N)30 b Fu(\000)20 b Fx(1)1229 5290 y Fr(\015)1229 5345 y(\015)1283 5367 y(b)-54 b Fw(\027)1331 5330 y Ft(1)p Fv(=)p Ft(2)1456 5367 y Fw(q)1497 5381 y Ft(1)1536 5367 y Fx(\011)1607 5290 y Fr(\015)1607 5345 y(\015)1657 5180 y(v)1657 5231 y(u)1657 5286 y(u)1657 5340 y(t)p 1753 5180 1871 4 v 1805 5254 a Fv(N)1770 5281 y Fr(X)1753 5477 y Fv(i;j)t Ft(=2)1934 5294 y Fr(\012)1977 5367 y Fx(\011)10 b Fw(;)15 b(p)2144 5381 y Ft(1)2184 5367 y Fw(p)2230 5381 y Fv(i)2258 5367 y Fw(W)2357 5320 y Ft(\()p Fv(p;)p Ft(2\))2344 5395 y(1)p Fv(i)2505 5367 y Fw(q)2546 5381 y Ft(1)2586 5367 y Fw(q)2627 5381 y Fv(i)2679 5330 y Fr(d)2669 5367 y Fw(\037)2726 5341 y Ft(\(2\))2838 5367 y Fr(b)-53 b Fw(\027)21 b(q)2943 5381 y Ft(1)2982 5367 y Fw(q)3023 5381 y Fv(j)3059 5367 y Fw(W)3158 5320 y Ft(\()p Fv(p)p FF(\000)p Ft(2\))3145 5395 y(1)p Fv(j)3342 5367 y Fw(p)3388 5381 y Fv(j)3424 5367 y Fw(p)3470 5381 y Ft(1)3509 5367 y Fx(\011)3580 5294 y Fr(\013)3638 5367 y Fw(:)p Black 1835 6000 a Fx(29)p Black eop end %%Page: 30 30 TeXDict begin 30 29 bop Black Black 14 162 a Fx(Using)1108 198 y Fr(\015)1108 252 y(\015)1161 275 y(b)-54 b Fw(\027)1209 238 y Ft(1)p Fv(=)p Ft(2)1334 275 y Fw(q)1375 289 y Ft(1)1414 275 y Fx(\011)1485 198 y Fr(\015)1485 252 y(\015)1586 275 y Fi(6)1707 193 y Fr(p)p 1798 193 536 4 v 82 x Fu(h)p Fx(\011)10 b Fw(;)18 b Fr(b)-54 b Fw(n)2009 249 y FF(\000)p Ft(1)2121 275 y Fr(b)h Fw(n)2174 249 y Ft(2)2228 275 y Fx(\011)p Fu(i)50 b Fx(=)2506 193 y Fr(p)p 2597 193 57 4 v 82 x Fw(\014)14 435 y Fx(w)m(e)31 b(\014nd)898 504 y Fr(\014)898 558 y(\014)929 507 y(\012)971 581 y Fx(\011)10 b Fw(;)15 b(p)1138 595 y Ft(1)1178 581 y Fw(p)1224 595 y Ft(2)1263 581 y Fw(W)1362 533 y Ft(\()p Fv(p;)p Ft(2\))1349 607 y(12)1529 581 y Fr(b)-54 b Fw(\027)1602 544 y Fr(d)1592 581 y Fw(\037)1649 555 y Ft(\(2\))1758 581 y Fw(q)1799 595 y Ft(1)1838 581 y Fw(q)1879 595 y Ft(2)1918 581 y Fx(\011)1989 507 y Fr(\013)2032 504 y(\014)2032 558 y(\014)2113 581 y Fi(6)2298 451 y Fu(p)p 2373 451 V 2373 519 a Fw(\014)p 2244 560 240 4 v 2244 643 a(N)30 b Fu(\000)20 b Fx(1)2493 503 y Fu(p)p 2569 503 253 4 v 78 x Fw(A)h Fx(+)e Fw(B)h(;)652 b Fx(\(4.30\))14 770 y(where)776 960 y Fw(A)895 957 y Fx(:)920 960 y(=)1135 874 y Fr(X)1041 1071 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1376 887 y Fr(\012)1419 960 y Fx(\011)10 b Fw(;)15 b(p)1586 974 y Ft(1)1625 960 y Fw(p)1671 974 y Fv(i)1699 960 y Fw(W)1798 912 y Ft(\()p Fv(p;)p Ft(2\))1785 987 y(1)p Fv(i)1947 960 y Fw(q)1988 974 y Ft(1)2027 960 y Fw(q)2068 974 y Fv(i)2121 923 y Fr(d)2111 960 y Fw(\037)2168 934 y Ft(\(2\))2280 960 y Fr(b)-54 b Fw(\027)21 b(q)2384 974 y Fv(j)2420 960 y Fw(W)2519 912 y Ft(\()p Fv(p;)p Ft(2\))2506 987 y(1)p Fv(j)2668 960 y Fw(p)2714 974 y Fv(j)2751 960 y Fw(p)2797 974 y Ft(1)2836 960 y Fx(\011)2906 887 y Fr(\013)2964 960 y Fw(;)771 1295 y(B)895 1292 y Fx(:)920 1295 y(=)1075 1181 y Fv(N)1041 1208 y Fr(X)1050 1404 y Fv(i)p Ft(=2)1188 1221 y Fr(\012)1231 1295 y Fx(\011)10 b Fw(;)15 b(p)1398 1309 y Ft(1)1437 1295 y Fw(p)1483 1309 y Fv(i)1511 1295 y Fw(W)1610 1247 y Ft(\()p Fv(p;)p Ft(2\))1597 1322 y(1)p Fv(i)1759 1295 y Fw(q)1800 1309 y Ft(1)1839 1295 y Fw(q)1880 1309 y Fv(i)1933 1258 y Fr(d)1923 1295 y Fw(\037)1980 1268 y Ft(\(2\))2092 1295 y Fr(b)-54 b Fw(\027)21 b(W)2254 1247 y Ft(\()p Fv(p;)p Ft(2\))2241 1322 y(1)p Fv(i)2403 1295 y Fw(p)2449 1309 y Fv(i)2477 1295 y Fw(p)2523 1309 y Ft(1)2562 1295 y Fx(\011)2633 1221 y Fr(\013)2691 1295 y Fw(:)14 1561 y Fx(Since)1460 1674 y Fw(\037)1517 1637 y Ft(\(2\))1611 1674 y Fx(\()p Fw(k)s Fx(\))51 b(=)g Fj(1)1958 1696 y FF(f)p Fv(k)r(>N)2150 1677 y Fp(1)p Fm(\000)p Fn(\016)2261 1696 y FF(g)14 1834 y Fx(w)m(e)31 b(\014nd)1327 1947 y Fw(\037)1384 1910 y Ft(\(2\))1493 1947 y Fw(\027)56 b Fi(6)50 b Fw(\037)1772 1910 y Ft(\(2\))1882 1947 y Fw(n)1937 1910 y FF(\000)p Ft(1)2081 1947 y Fi(6)g Fw(N)2285 1910 y Fv(\016)r(=)p Ft(2)2409 1947 y Fw(:)14 2125 y Fx(Th)m(us,)30 b Fu(k)p Fw(q)356 2139 y Ft(1)395 2125 y Fw(q)436 2139 y Fv(i)489 2088 y Fr(d)479 2125 y Fw(\037)536 2099 y Ft(\(2\))648 2125 y Fr(b)-54 b Fw(\027)6 b Fu(k)51 b Fi(6)f Fw(N)996 2092 y Fv(\016)r(=)p Ft(2)1135 2125 y Fx(and)30 b(w)m(e)h(get)97 2427 y Fw(B)55 b Fi(6)50 b Fw(N)425 2390 y Fv(\016)r(=)p Ft(2)583 2314 y Fv(N)549 2341 y Fr(X)558 2536 y Fv(i)p Ft(=2)695 2354 y Fr(\012)738 2427 y Fx(\011)10 b Fw(;)15 b(p)905 2441 y Ft(1)945 2427 y Fw(p)991 2441 y Fv(i)1019 2354 y Fr(\000)1060 2427 y Fw(W)1159 2379 y Ft(\()p Fv(p;)p Ft(2\))1146 2454 y(1)p Fv(i)1308 2354 y Fr(\001)1350 2376 y Ft(2)1389 2427 y Fw(p)1435 2441 y Fv(i)1463 2427 y Fw(p)1509 2441 y Ft(1)1548 2427 y Fx(\011)1619 2354 y Fr(\013)1713 2427 y Fi(6)50 b Fw(N)1917 2390 y Ft(1+)p Fv(\016)r(=)p Ft(2)2131 2350 y Fr(\015)2131 2405 y(\015)2181 2354 y(\000)2223 2427 y Fw(w)2290 2390 y Ft(\()p Fv(p;)p Ft(2\))2440 2354 y Fr(\001)2481 2376 y Ft(2)2541 2427 y Fu(\003)21 b(j)p Fw(')p Fu(j)2716 2390 y Ft(2)2756 2350 y Fr(\015)2756 2405 y(\015)2807 2463 y FF(1)1731 2666 y Fi(6)50 b Fw(N)1935 2628 y Ft(1+)p Fv(\016)r(=)p Ft(2)2149 2666 y Fu(k)p Fw(w)2261 2628 y Ft(\()p Fv(p;)p Ft(2\))2411 2666 y Fu(k)2456 2628 y Ft(2)2456 2688 y(2)2511 2666 y Fu(k)p Fw(')p Fu(k)2660 2628 y Ft(2)2660 2688 y FF(1)2787 2666 y Fi(.)g Fw(N)2991 2628 y Ft(1+)p Fv(\016)r(=)p Ft(2)3205 2666 y Fw(a)3253 2628 y Ft(2)p FF(\000)p Fv(p)3398 2666 y Fu(k)p Fw(')p Fu(k)3547 2628 y Ft(2)3547 2688 y FF(1)3638 2666 y Fw(;)14 2857 y Fx(b)m(y)32 b(\(4.23b\))r(.)155 2970 y(Next,)g(using)e(Lemma)g (3.10,)i(w)m(e)f(\014nd)414 3179 y Fw(A)51 b Fx(=)748 3092 y Fr(X)654 3290 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)989 3105 y Fr(\012)1032 3179 y Fx(\011)10 b Fw(;)15 b(p)1199 3193 y Ft(1)1238 3179 y Fw(p)1284 3193 y Fv(i)1312 3179 y Fw(q)1353 3193 y Fv(j)1389 3179 y Fw(W)1488 3131 y Ft(\()p Fv(p;)p Ft(2\))1475 3206 y(1)p Fv(i)1662 3141 y Fr(d)1652 3179 y Fw(\037)1709 3152 y Ft(\(2\))1821 3179 y Fr(b)-53 b Fw(\027)1870 3141 y Ft(1)p Fv(=)p Ft(2)1994 3179 y Fw(q)2035 3193 y Ft(1)2100 3141 y Fr(d)2090 3179 y Fw(\037)2147 3152 y Ft(\(2\))2259 3179 y Fr(b)f Fw(\027)2307 3141 y Ft(1)p Fv(=)p Ft(2)2432 3179 y Fw(W)2531 3131 y Ft(\()p Fv(p;)p Ft(2\))2518 3206 y(1)p Fv(j)2680 3179 y Fw(q)2721 3193 y Fv(i)2749 3179 y Fw(p)2795 3193 y Fv(j)2831 3179 y Fw(p)2877 3193 y Ft(1)2916 3179 y Fx(\011)2987 3105 y Fr(\013)533 3454 y Fx(=)748 3368 y Fr(X)654 3565 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)989 3381 y Fr(\012)1032 3454 y Fx(\011)10 b Fw(;)15 b(p)1199 3468 y Ft(1)1238 3454 y Fw(p)1284 3468 y Fv(i)1312 3454 y Fw(q)1353 3468 y Fv(j)1413 3420 y Fs(\\)1404 3454 y Fw(\034)1444 3468 y Ft(2)1483 3454 y Fw(\037)1540 3428 y Ft(\(2\))1669 3454 y Fr(c)-110 b Fw(\034)1690 3468 y Ft(2)1729 3454 y Fw(\027)1780 3412 y Ft(1)p Fv(=)p Ft(2)1905 3454 y Fw(W)2004 3406 y Ft(\()p Fv(p;)p Ft(2\))1991 3481 y(1)p Fv(i)2153 3454 y Fw(q)2194 3468 y Ft(1)2233 3454 y Fw(W)2332 3406 y Ft(\()p Fv(p;)p Ft(2\))2319 3481 y(1)p Fv(j)2505 3420 y Fs(\\)2496 3454 y Fw(\034)2536 3468 y Ft(2)2575 3454 y Fw(\037)2632 3428 y Ft(\(2\))2761 3454 y Fr(c)f Fw(\034)2781 3468 y Ft(2)2821 3454 y Fw(\027)2871 3412 y Ft(1)p Fv(=)p Ft(2)2996 3454 y Fw(q)3037 3468 y Fv(i)3065 3454 y Fw(p)3111 3468 y Fv(j)3147 3454 y Fw(p)3193 3468 y Ft(1)3233 3454 y Fx(\011)3303 3381 y Fr(\013)533 3700 y Fx(=)50 b Fw(A)722 3714 y Ft(1)782 3700 y Fx(+)20 b Fw(A)941 3714 y Ft(2)996 3700 y Fw(;)14 3890 y Fx(where,)30 b(as)h(ab)s(o)m(v)m(e,)h(the)e(splitting)h Fw(A)26 b Fx(=)f Fw(A)1470 3904 y Ft(1)1530 3890 y Fx(+)20 b Fw(A)1689 3904 y Ft(2)1758 3890 y Fx(arises)31 b(from)f(writing)g Fw(q)2576 3904 y Ft(1)2641 3890 y Fx(=)25 b Fj(1)19 b Fu(\000)h Fw(p)2947 3904 y Ft(1)2987 3890 y Fx(.)40 b(Th)m(us,)14 4103 y Fu(j)p Fw(A)107 4117 y Ft(1)147 4103 y Fu(j)51 b Fi(6)438 4017 y Fr(X)344 4214 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)679 4026 y Fr(\014)679 4080 y(\014)709 4030 y(\012)752 4103 y Fx(\011)10 b Fw(;)15 b(p)919 4117 y Ft(1)958 4103 y Fw(p)1004 4117 y Fv(i)1032 4103 y Fw(q)1073 4117 y Fv(j)1134 4069 y Fs(\\)1124 4103 y Fw(\034)1164 4117 y Ft(2)1204 4103 y Fw(\037)1261 4077 y Ft(\(2\))1389 4103 y Fr(c)-110 b Fw(\034)1410 4117 y Ft(2)1449 4103 y Fw(\027)1500 4061 y Ft(1)p Fv(=)p Ft(2)1625 4103 y Fw(W)1724 4055 y Ft(\()p Fv(p;)p Ft(2\))1711 4130 y(1)p Fv(i)1873 4103 y Fw(W)1972 4055 y Ft(\()p Fv(p;)p Ft(2\))1959 4130 y(1)p Fv(j)2145 4069 y Fs(\\)2136 4103 y Fw(\034)2176 4117 y Ft(2)2215 4103 y Fw(\037)2272 4077 y Ft(\(2\))2401 4103 y Fr(c)f Fw(\034)2421 4117 y Ft(2)2461 4103 y Fw(\027)2511 4061 y Ft(1)p Fv(=)p Ft(2)2637 4103 y Fw(q)2678 4117 y Fv(i)2705 4103 y Fw(p)2751 4117 y Fv(j)2788 4103 y Fw(p)2834 4117 y Ft(1)2873 4103 y Fx(\011)2943 4030 y Fr(\013)2986 4026 y(\014)2986 4080 y(\014)223 4399 y Fx(=)438 4313 y Fr(X)344 4510 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)679 4322 y Fr(\014)679 4376 y(\014)709 4325 y(\012)752 4399 y Fx(\011)10 b Fw(;)15 b(p)919 4413 y Ft(1)958 4399 y Fw(p)1004 4413 y Fv(i)1032 4399 y Fw(q)1073 4413 y Fv(j)1134 4365 y Fs(\\)1124 4399 y Fw(\034)1164 4413 y Ft(2)1204 4399 y Fw(\037)1261 4373 y Ft(\(2\))1389 4399 y Fr(c)-110 b Fw(\034)1410 4413 y Ft(2)1449 4399 y Fw(\027)1500 4357 y Ft(1)p Fv(=)p Ft(2)1625 4277 y Fr(q)p 1716 4277 248 4 v 122 x Fw(W)1815 4351 y Ft(\()p Fv(p;)p Ft(2\))1802 4426 y(1)p Fv(i)1964 4283 y Fr(q)p 2055 4283 V 116 x Fw(W)2154 4351 y Ft(\()p Fv(p;)p Ft(2\))2141 4426 y(1)p Fv(j)2303 4277 y Fr(q)p 2394 4277 V 122 x Fw(W)2493 4351 y Ft(\()p Fv(p;)p Ft(2\))2480 4426 y(1)p Fv(i)2641 4283 y Fr(q)p 2732 4283 V 116 x Fw(W)2831 4351 y Ft(\()p Fv(p;)p Ft(2\))2818 4426 y(1)p Fv(j)3005 4365 y Fs(\\)2995 4399 y Fw(\034)3035 4413 y Ft(2)3075 4399 y Fw(\037)3132 4373 y Ft(\(2\))3260 4399 y Fr(c)g Fw(\034)3281 4413 y Ft(2)3320 4399 y Fw(\027)3371 4357 y Ft(1)p Fv(=)p Ft(2)3496 4399 y Fw(q)3537 4413 y Fv(i)3565 4399 y Fw(p)3611 4413 y Fv(j)3647 4399 y Fw(p)3693 4413 y Ft(1)3732 4399 y Fx(\011)3803 4325 y Fr(\013)3846 4322 y(\014)3846 4376 y(\014)223 4675 y Fi(6)438 4588 y Fr(X)344 4786 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)679 4601 y Fr(\012)722 4675 y Fx(\011)10 b Fw(;)15 b(q)884 4689 y Fv(j)944 4640 y Fs(\\)935 4675 y Fw(\034)975 4689 y Ft(2)1014 4675 y Fw(\037)1071 4648 y Ft(\(2\))1200 4675 y Fr(c)-110 b Fw(\034)1221 4689 y Ft(2)1260 4675 y Fw(\027)1310 4633 y Ft(1)p Fv(=)p Ft(2)1436 4675 y Fw(p)1482 4689 y Ft(1)1521 4675 y Fw(p)1567 4689 y Fv(i)1595 4597 y Fr(\014)1595 4652 y(\014)1625 4675 y Fw(W)1724 4627 y Ft(\()p Fv(p;)p Ft(2\))1711 4702 y(1)p Fv(i)1873 4597 y Fr(\014)1873 4652 y(\014)1903 4597 y(\014)1903 4652 y(\014)1933 4675 y Fw(W)2032 4627 y Ft(\()p Fv(p;)p Ft(2\))2019 4702 y(1)p Fv(j)2181 4597 y Fr(\014)2181 4652 y(\014)2212 4675 y Fw(p)2258 4689 y Fv(i)2286 4675 y Fw(p)2332 4689 y Ft(1)2395 4640 y Fs(\\)2386 4675 y Fw(\034)2426 4689 y Ft(2)2465 4675 y Fw(\037)2522 4648 y Ft(\(2\))2651 4675 y Fr(c)f Fw(\034)2671 4689 y Ft(2)2711 4675 y Fw(\027)2761 4633 y Ft(1)p Fv(=)p Ft(2)2887 4675 y Fw(q)2928 4689 y Fv(j)2964 4675 y Fx(\011)3034 4601 y Fr(\013)3092 4675 y Fw(;)14 4962 y Fx(b)m(y)30 b(Cauc)m(h)m(y-Sc)m(h)m(w)m(arz)i(and)e(symmetry)g (of)h(\011.)40 b(Using)32 b(\(4.28\))h(w)m(e)d(get)1043 5165 y Fu(j)p Fw(A)1136 5179 y Ft(1)1176 5165 y Fu(j)51 b Fi(6)f Fw(N)1456 5127 y Ft(2)1511 5087 y Fr(\015)1511 5142 y(\015)1561 5087 y(\014)1561 5142 y(\014)1592 5165 y Fw(w)1659 5127 y Ft(\()p Fv(p;)p Ft(2\))1809 5087 y Fr(\014)1809 5142 y(\014)1859 5165 y Fu(\003)21 b(j)p Fw(')p Fu(j)2034 5127 y Ft(2)2074 5087 y Fr(\015)2074 5142 y(\015)2125 5114 y Ft(2)2125 5201 y FF(1)2214 5091 y Fr(\012)2257 5165 y Fx(\011)10 b Fw(;)35 b Fr(c)-111 b Fw(\034)2418 5179 y Ft(2)2458 5165 y Fw(\027)21 b(q)2565 5179 y Ft(1)2604 5165 y Fx(\011)2674 5091 y Fr(\013)1252 5321 y Fi(6)50 b Fw(N)1456 5284 y Ft(2)1496 5321 y Fu(k)p Fw(w)1608 5284 y Ft(\()p Fv(p;)p Ft(2\))1758 5321 y Fu(k)1803 5284 y Ft(2)1803 5344 y Fv(p)1858 5321 y Fu(k)p Fw(')p Fu(k)2007 5284 y Ft(4)2007 5349 y Fv(L)2055 5330 y Fp(2)2091 5349 y FF(\\)p Fv(L)2186 5330 y Fm(1)2271 5321 y Fu(h)p Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)15 b Fx(\011)p Fu(i)1252 5470 y Fi(.)50 b Fw(N)1456 5433 y Ft(2)1511 5470 y Fu(k)p Fw(')p Fu(k)1660 5433 y Ft(4)1660 5498 y Fv(L)1708 5479 y Fp(2)1744 5498 y FF(\\)p Fv(L)1839 5479 y Fm(1)1908 5470 y Fw(\014)20 b(:)p Black 1835 6000 a Fx(30)p Black eop end %%Page: 31 31 TeXDict begin 31 30 bop Black Black 14 162 a Fx(Similarly)-8 b(,)336 403 y Fu(j)p Fw(A)429 417 y Ft(2)469 403 y Fu(j)51 b Fi(6)760 317 y Fr(X)666 515 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1001 326 y Fr(\014)1001 381 y(\014)1031 330 y(\012)1074 403 y Fx(\011)10 b Fw(;)15 b(p)1241 417 y Fv(i)1269 403 y Fw(q)1310 417 y Fv(j)1371 369 y Fs(\\)1362 403 y Fw(\034)1402 417 y Ft(2)1441 403 y Fw(\037)1498 377 y Ft(\(2\))1627 403 y Fr(c)-111 b Fw(\034)1647 417 y Ft(2)1686 403 y Fw(\027)1737 361 y Ft(1)p Fv(=)p Ft(2)1862 403 y Fw(p)1908 417 y Ft(1)1947 403 y Fw(W)2046 355 y Ft(\()p Fv(p;)p Ft(2\))2033 431 y(1)p Fv(i)2195 403 y Fw(p)2241 417 y Ft(1)2280 403 y Fw(W)2379 355 y Ft(\()p Fv(p;)p Ft(2\))2366 431 y(1)p Fv(j)2528 403 y Fw(p)2574 417 y Ft(1)2638 369 y Fs(\\)2629 403 y Fw(\034)2669 417 y Ft(2)2708 403 y Fw(\037)2765 377 y Ft(\(2\))2894 403 y Fr(c)g Fw(\034)2914 417 y Ft(2)2953 403 y Fw(\027)3004 361 y Ft(1)p Fv(=)p Ft(2)3129 403 y Fw(q)3170 417 y Fv(i)3198 403 y Fw(p)3244 417 y Fv(j)3280 403 y Fx(\011)3351 330 y Fr(\013)3394 326 y(\014)3394 381 y(\014)545 665 y Fi(6)760 579 y Fr(X)666 777 y Ft(2)p Fq(6)p Fv(i)p FF(6)p Ft(=)p Fv(j)t Fq(6)p Fv(N)1001 588 y Fr(\015)1001 643 y(\015)1051 665 y Fw(w)1118 628 y Ft(\()p Fv(p;)p Ft(2\))1289 665 y Fu(\003)20 b(j)p Fw(')p Fu(j)1463 628 y Ft(2)1504 588 y Fr(\015)1504 643 y(\015)1554 614 y Ft(2)1554 701 y FF(1)1629 592 y Fr(\012)1672 665 y Fx(\011)10 b Fw(;)35 b Fr(c)-111 b Fw(\034)1833 679 y Ft(2)1872 665 y Fw(\027)21 b(q)1979 679 y Ft(1)2018 665 y Fx(\011)2089 592 y Fr(\013)545 919 y Fi(6)50 b Fw(N)749 882 y Ft(2)789 919 y Fu(k)p Fw(w)901 882 y Ft(\()p Fv(p)p Ft(\))996 919 y Fu(k)1041 882 y Ft(2)1041 942 y Fv(p)1097 919 y Fu(k)p Fw(')p Fu(k)1246 882 y Ft(4)1246 947 y Fv(L)1294 928 y Fp(2)1330 947 y FF(\\)p Fv(L)1425 928 y Fm(1)1509 919 y Fu(h)p Fx(\011)10 b Fw(;)17 b Fr(b)-53 b Fw(n)15 b Fx(\011)p Fu(i)545 1068 y Fi(.)50 b Fw(N)749 1031 y Ft(2)804 1068 y Fu(k)p Fw(')p Fu(k)953 1031 y Ft(4)953 1096 y Fv(L)1001 1077 y Fp(2)1037 1096 y FF(\\)p Fv(L)1132 1077 y Fm(1)1216 1068 y Fw(\014)21 b(:)14 1287 y Fx(Plugging)31 b(all)g(this)g(bac)m(k)g(in)m(to)g(\(4.30\))s(,)f(w)m (e)h(\014nd)e(that)378 1452 y Fr(\014)378 1507 y(\014)408 1456 y(\012)451 1529 y Fx(\011)10 b Fw(;)15 b(p)618 1543 y Ft(1)658 1529 y Fw(p)704 1543 y Ft(2)743 1529 y Fw(W)842 1481 y Ft(\()p Fv(p;)p Ft(2\))829 1555 y(12)1009 1529 y Fr(b)-54 b Fw(\027)1082 1492 y Fr(d)1072 1529 y Fw(\037)1129 1503 y Ft(\(2\))1238 1529 y Fw(q)1279 1543 y Ft(1)1318 1529 y Fw(q)1359 1543 y Ft(2)1398 1529 y Fx(\011)1469 1456 y Fr(\013)1512 1452 y(\014)1512 1507 y(\014)1593 1529 y Fi(.)50 b Fw(\014)1770 1456 y Fr(\000)1812 1529 y Fu(k)p Fw(')p Fu(k)1961 1492 y Ft(2)1961 1557 y Fv(L)2009 1538 y Fp(2)2045 1557 y FF(\\)p Fv(L)2140 1538 y Fm(1)2229 1529 y Fx(+)20 b Fu(k)p Fw(')p Fu(k)2469 1543 y FF(1)2545 1456 y Fr(\001)2607 1529 y Fx(+)g Fu(k)p Fw(')p Fu(k)2847 1543 y FF(1)2923 1529 y Fw(a)2971 1492 y Ft(2)p FF(\000)p Fv(p)3101 1529 y Fw(N)3184 1492 y Fv(\016)r(=)p Ft(2)p FF(\000)p Ft(1)155 1753 y Fx(Summarizing:)406 1912 y Fr(\014)406 1967 y(\014)436 1990 y Fx(\(I)s(I)s(I\))610 1948 y Ft(\()p Fv(p;)p Ft(2\))760 1912 y Fr(\014)760 1967 y(\014)841 1990 y Fi(.)962 1916 y Fr(\000)1004 1990 y Fx(1)g(+)g Fu(k)p Fw(')p Fu(k)1309 1952 y Ft(2)1309 2018 y Fv(L)1357 1999 y Fp(2)1393 2018 y FF(\\)p Fv(L)1488 1999 y Fm(1)1557 1916 y Fr(\001)1599 1889 y(\020)1653 1990 y Fw(\014)26 b Fx(+)20 b Fw(a)1869 1952 y Ft(2)p FF(\000)p Fv(p)2014 1990 y Fw(N)2097 1952 y Fv(\016)r(=)p Ft(2)p FF(\000)p Ft(1)2315 1990 y Fx(+)g Fw(N)2489 1952 y FF(\000)p Fv(\016)r(=)p Ft(2)2673 1990 y Fx(+)g Fw(N)2847 1952 y FF(\000)p Ft(1)p Fv(=)p Ft(2)3012 1990 y Fw(a)3060 1952 y Ft(1)p FF(\000)p Fv(p=)p Ft(2)3260 1889 y Fr(\021)3329 1990 y Fw(;)14 2226 y Fx(from)30 b(whic)m(h)g(w)m(e)h(deduce)97 2393 y Fr(\014)97 2447 y(\014)127 2470 y Fx(\(I)s(I)s(I\))302 2428 y Ft(\()p Fv(p)p Ft(\))396 2393 y Fr(\014)396 2447 y(\014)477 2470 y Fi(.)50 b Fu(k)p Fw(')p Fu(k)747 2484 y FF(1)823 2470 y Fu(kr)944 2484 y Ft(1)984 2470 y Fw(q)1025 2484 y Ft(1)1064 2470 y Fx(\011)p Fu(k)1180 2432 y Ft(2)740 2642 y Fx(+)831 2568 y Fr(\000)873 2642 y Fx(1)20 b(+)g Fu(k)p Fw(')p Fu(k)1178 2656 y Fv(X)1236 2665 y Fp(1)1272 2656 y FF(\\)p Fv(L)1367 2637 y Fm(1)1436 2568 y Fr(\001)1478 2541 y(\020)1532 2642 y Fw(\014)26 b Fx(+)20 b Fw(a)1748 2604 y Ft(2)p FF(\000)p Fv(p)1893 2642 y Fw(N)1976 2604 y Fv(\016)r(=)p Ft(2)p FF(\000)p Ft(1)2194 2642 y Fx(+)g Fw(N)2368 2604 y FF(\000)p Fv(\016)r(=)p Ft(2)2552 2642 y Fx(+)g Fw(N)2726 2604 y FF(\000)p Ft(1)p Fv(=)p Ft(2)2891 2642 y Fw(a)2939 2604 y Ft(1)p FF(\000)p Fv(p=)p Ft(2)3159 2642 y Fx(+)g Fw(a)3298 2604 y Ft(2)p FF(\000)p Ft(2)p Fv(p=p)3530 2613 y Fp(0)3569 2541 y Fr(\021)3638 2642 y Fw(:)14 2894 y Fx(Let)31 b(us)f(set)h Fw(a)25 b Fu(\021)g Fw(a)653 2908 y Fv(N)745 2894 y Fx(=)g Fw(N)924 2861 y Fv(\020)994 2894 y Fx(and)30 b(optimize)i(in)e Fw(\016)k Fx(and)c Fw(\020)7 b Fx(.)40 b(This)30 b(yields)g(the)h(relations)998 3158 y Fw(\020)7 b Fx(\(2)20 b Fu(\000)g Fw(p)p Fx(\))h(+)f Fw(\016)54 b Fx(=)c(1)15 b Fw(;)198 b Fu(\000)2009 3096 y Fw(\016)p 2008 3137 46 4 v 2008 3220 a Fx(2)2114 3158 y(=)50 b(2)p Fw(\020)2327 3030 y Fr(\022)2394 3158 y Fx(1)20 b Fu(\000)2580 3096 y Fw(p)p 2560 3137 86 4 v 2560 3220 a(p)2606 3234 y Ft(0)2655 3030 y Fr(\023)2737 3158 y Fw(;)14 3422 y Fx(whic)m(h)30 b(imply)1429 3530 y Fw(\016)p 1428 3571 46 4 v 1428 3654 a Fx(2)1534 3592 y(=)1812 3530 y Fw(p=p)1949 3544 y Ft(0)2009 3530 y Fu(\000)20 b Fx(1)p 1666 3571 627 4 v 1666 3654 a(2)p Fw(p=p)1848 3668 y Ft(0)1908 3654 y Fu(\000)g Fw(p=)p Fx(2)g Fu(\000)g Fx(1)2317 3592 y Fw(;)14 3820 y Fx(with)30 b Fw(\016)f Fi(6)c Fx(1.)41 b(Th)m(us,)692 3979 y Fr(\014)692 4033 y(\014)722 4056 y Fx(\(I)s(I)s(I\))896 4014 y Ft(\()p Fv(p)p Ft(\))991 3979 y Fr(\014)991 4033 y(\014)1072 4056 y Fi(.)50 b Fu(k)p Fw(')p Fu(k)1342 4070 y FF(1)1418 4056 y Fu(kr)1539 4070 y Ft(1)1579 4056 y Fw(q)1620 4070 y Ft(1)1659 4056 y Fx(\011)p Fu(k)1775 4019 y Ft(2)1835 4056 y Fx(+)1925 3982 y Fr(\000)1967 4056 y Fx(1)21 b(+)f Fu(k)p Fw(')p Fu(k)2273 4070 y Fv(X)2331 4079 y Fp(1)2367 4070 y FF(\\)p Fv(L)2462 4051 y Fm(1)2531 3982 y Fr(\001)2573 3955 y(\020)2627 4056 y Fw(\014)25 b Fx(+)20 b Fw(N)2877 4019 y FF(\000)p Fv(\021)2974 3955 y Fr(\021)3043 4056 y Fw(;)14 4298 y Fx(where)30 b Fw(\021)f Fx(=)c Fw(\016)s(=)p Fx(2)32 b(satis\014es)f(\(4.4\))q(.)14 4534 y Fg(Conclusion)j(of)f(the) g(pr)-5 b(o)g(of.)42 b Fx(W)-8 b(e)32 b(ha)m(v)m(e)f(sho)m(wn)f(that) 778 4728 y(_)755 4752 y Fw(\014)56 b Fi(.)50 b Fu(k)p Fw(')p Fu(k)1132 4772 y Fv(L)1180 4753 y Fp(2)1216 4772 y FF(\\)p Fv(L)1311 4753 y Fm(1)1380 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