Content-Type: multipart/mixed; boundary="-------------0304270344917" This is a multi-part message in MIME format. ---------------0304270344917 Content-Type: text/plain; name="03-197.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-197.keywords" spectral theory, Mourre method, limiting absorption principle ---------------0304270344917 Content-Type: application/postscript; name="mourre-abstract.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="mourre-abstract.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: C:\Travaux en cours\mourre-abstract\GGMfinal.dvi %%CreationDate: Sat Apr 26 12:14:32 2003 %%Pages: 46 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMMI12 CMR12 CMSY10 CMSY8 CMBX10 CMR10 CMMI10 %%+ CMSY7 CMR7 CMBX12 CMSY6 CMR9 CMMI8 CMR8 CMTI10 CMR6 CMMI6 CMEX10 %%+ LASY10 CMBX8 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: c:\texmf\miktex\bin\dvips.exe %+ "C:\Travaux en cours\mourre-abstract\GGMfinal.dvi" %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.04.26:1214 %%BeginProcSet: texc.pro %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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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 27 /sigma put dup 59 /comma put dup 61 /slash put dup 110 /n put dup 112 /p put dup 115 /s put dup 116 /t put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 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 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 71 /G put dup 76 /L put dup 77 /M 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 101 /e put dup 102 /f 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 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff 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 65 /A put dup 66 /B put dup 68 /D put dup 69 /E put dup 72 /H put dup 73 /I put dup 77 /M 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 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 11 /ff put dup 12 /fi put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 56 /eight put dup 58 /colon put dup 59 /semicolon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 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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 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 61 /equal put dup 73 /I put dup 82 /R put dup 91 /bracketleft put dup 93 /bracketright put dup 100 /d put dup 105 /i put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 15 /epsilon1 put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 65 /A put dup 66 /B put dup 70 /F put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 81 /Q put dup 83 /S put dup 86 /V put dup 105 /i put dup 106 /j put dup 107 /k put dup 110 /n put dup 112 /p put dup 113 /q put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def 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%%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 6 /plusminus put dup 48 /prime put dup 49 /infinity put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 14 /openbullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 27 /propersuperset put dup 29 /greatermuch put dup 33 /arrowright put dup 41 /arrowdblright put dup 44 /arrowdblboth put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 54 /negationslash put dup 55 /mapsto put dup 57 /existential put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 65 /A put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 75 /K put dup 91 /union 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 110 /backslash put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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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 15 /epsilon1 put dup 16 /zeta put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 102 /f put dup 103 /g put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 3 /Lambda put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 28 /oslash put dup 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: 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 /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 14 /openbullet put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 63 /perpendicular put dup 68 /D put dup 69 /E put dup 71 /G put dup 72 /H put dup 75 /K put dup 106 /bar put dup 110 /backslash put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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b(a)h(sp)s(ectral)g(gap,)h(whic)m(h)e(allo) m(ws)i(us)e(to)i(deduce)e(it)h(v)m(ery)g(easily)0 1517 y(from)34 b(our)f(main)h(result,)h(Theorem)f(3.5.)53 b(Finally)-8 b(,)36 b(App)s(endix)d(A)h(con)m(tains)h(more)f(tec)m (hnical)i(results)e(used)0 1630 y(in)c(other)h(parts)f(of)g(the)h(pap)s (er.)0 1916 y Fs(2)135 b(The)44 b Fe(C)569 1872 y Fx(1)614 1916 y Fd(\()p Fe(A)p Fd(\))g Fs(class)0 2119 y Fr(In)22 b(this)g(section)i(w)m(e)f(consider)f(a)h(linear)g(op)s(erator)f Fq(A)h Fr(and)f(de\014ne)f(a)i(regularit)m(y)h(prop)s(ert)m(y)e(of)g (linear)h(op)s(erators)0 2232 y(on)j(a)g(Hilb)s(ert)g(space)h Fp(H)f Fr(with)g(resp)s(ect)g(to)h Fq(A)f Fr(whic)m(h)g(is)g(an)g (extension)g(of)h(the)f Fq(C)2741 2199 y Fl(1)2780 2232 y Fr(\()p Fq(A)p Fr(\))g(prop)s(ert)m(y)g(\(see)h([ABG)q(]\))0 2344 y(when)e Fq(A)h Fr(is)h(selfadjoin)m(t.)40 b(Throughout)25 b(this)h(section)h Fq(A)g Fr(will)f(b)s(e)g(closed)g(and)g(densely)g (de\014ned)f(on)h(a)g(Hilb)s(ert)0 2457 y(space)31 b Fp(H)q Fr(.)40 b(Note)32 b(that)f(since)g Fq(A)f Fr(is)h(closed,)g Fp(D)s Fr(\()p Fq(A)1685 2424 y Fz(\003)1725 2457 y Fr(\))f(is)h(dense) f(in)g Fp(H)q Fr(.)0 2700 y Fj(2.1)112 b Fc(C)332 2664 y Fl(1)372 2700 y FB(\()p Fc(A)p FB(\))37 b Fj(class)h(of)g(b)s(ounded) h(op)s(erators)0 2872 y Fr(If)30 b Fq(S)g Fp(2)25 b Fq(B)5 b Fr(\()p Fp(H)q Fr(\))30 b(w)m(e)h(denote)g(b)m(y)f([)p Fq(A;)15 b(S)5 b Fr(])32 b(the)e(sesquilinear)h(form)f(on)g Fp(D)s Fr(\()p Fq(A)2481 2839 y Fz(\003)2521 2872 y Fr(\))20 b Fp(\002)g(D)s Fr(\()p Fq(A)p Fr(\))31 b(de\014ned)e(b)m(y:)701 3070 y(\()p Fq(u;)15 b Fr([)p Fq(A;)g(S)5 b Fr(])p Fq(v)s Fr(\))28 b(:=)d(\()p Fq(A)1381 3033 y Fz(\003)1421 3070 y Fq(u;)15 b(S)5 b(v)s Fr(\))22 b Fp(\000)e Fr(\()p Fq(S)1865 3033 y Fz(\003)1904 3070 y Fq(u;)15 b(Av)s Fr(\))p Fq(;)37 b(u)26 b Fp(2)e(D)s Fr(\()p Fq(A)2547 3033 y Fz(\003)2587 3070 y Fr(\))p Fq(;)36 b(v)29 b Fp(2)24 b(D)s Fr(\()p Fq(A)p Fr(\))p Fq(:)0 3269 y Fh(De\014nition)35 b(2.1)46 b Fk(A)n(n)g(op)-5 b(er)g(ator)49 b Fq(S)55 b Fp(2)49 b Fq(B)5 b Fr(\()p Fp(H)q Fr(\))46 b Fk(is)h Fr(of)e(class)h Fq(C)2220 3236 y Fl(1)2259 3269 y Fr(\()p Fq(A)p Fr(\))h Fk(if)f(the)g(sesquiline)-5 b(ar)47 b(form)g Fr([)p Fq(A;)15 b(S)5 b Fr(])47 b Fk(is)0 3382 y(c)-5 b(ontinuous)46 b(for)g(the)f(top)-5 b(olo)g(gy)48 b(of)e Fp(H)30 b(\002)f(H)q Fk(.)78 b(If)45 b(this)h(is)f(the)h(c)-5 b(ase,)48 b(we)d(denote)h(by)f Fr([)p Fq(A;)15 b(S)5 b Fr(])3270 3349 y Fz(\016)3356 3382 y Fk(the)45 b(unique)0 3495 y(b)-5 b(ounde)g(d)31 b(op)-5 b(er)g(ator)32 b(on)d Fp(H)h Fk(asso)-5 b(ciate)g(d)31 b(to)f(the)g(quadr)-5 b(atic)30 b(form)g Fr([)p Fq(A;)15 b(S)5 b Fr(])30 b Fk(\(note)g(that)g Fp(D)s Fr(\()p Fq(A)3056 3462 y Fz(\003)3096 3495 y Fr(\))12 b Fp(\002)g(D)s Fr(\()p Fq(A)p Fr(\))30 b Fk(is)f(dense)0 3608 y(in)k Fp(H)20 b(\002)g(H)q Fk(\).)42 b(We)32 b(denote)h(by)g Fq(C)1131 3575 y Fl(1)1170 3608 y Fr(\()p Fq(A)p Fr(\))g Fk(the)g(line)-5 b(ar)34 b(sp)-5 b(ac)g(e)1041 3806 y Fq(C)1113 3769 y Fl(1)1152 3806 y Fr(\()p Fq(A)p Fr(\))26 b(:=)f Fp(f)p Fq(S)31 b Fp(2)25 b Fq(B)5 b Fr(\()p Fp(H)q Fr(\))p Fp(j)p Fq(S)37 b Fk(is)c(of)g(class)g Fq(C)2490 3769 y Fl(1)2529 3806 y Fr(\()p Fq(A)p Fr(\))p Fp(g)p Fq(:)0 4013 y Fh(Prop)s(osition)j (2.2)46 b Fk(A)n(n)39 b(op)-5 b(er)g(ator)42 b Fq(S)g Fp(2)37 b Fq(B)5 b Fr(\()p Fp(H)q Fr(\))39 b Fk(is)g(of)h(class)g Fq(C)2236 3980 y Fl(1)2275 4013 y Fr(\()p Fq(A)p Fr(\))g Fk(if)e(and)j(only)f(if)f Fq(S)44 b Fk(maps)c Fp(D)s Fr(\()p Fq(A)p Fr(\))g Fk(into)0 4126 y(itself)33 b(and)g Fq(AS)26 b Fp(\000)20 b Fq(S)5 b(A)25 b Fr(:)g Fp(D)s Fr(\()p Fq(A)p Fr(\))h Fp(!)f(H)34 b Fk(extends)f(to)g(a)g(b)-5 b(ounde)g(d)34 b(op)-5 b(er)g(ator)36 b(on)d Fp(H)q Fk(.)41 b(In)33 b(this)g(c)-5 b(ase)1026 4325 y Fq(AS)30 b Fr(=)25 b Fq(S)5 b(A)20 b Fr(+)g([)p Fq(A;)15 b(S)5 b Fr(])1735 4287 y Fz(\016)1808 4325 y Fk(as)34 b(an)f(identity)g(on)g Fp(D)s Fr(\()p Fq(A)p Fr(\))p Fq(:)0 4532 y Fh(Pro)s(of.)47 b Fr(If)30 b Fq(S)h Fp(2)24 b Fq(C)664 4499 y Fl(1)703 4532 y Fr(\()p Fq(A)p Fr(\))32 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Fr(\))d Fp(\\)e(D)s Fr(\()p Fq(A)1111 613 y Fl(2)1151 599 y Fr(\))31 b(then)f Fq(S)5 b(u)25 b Fp(2)g(D)s Fr(\()p Fq(A)1824 613 y Fl(1)1864 599 y Fr(\))20 b Fp(\\)g(D)s Fr(\()p Fq(A)2176 613 y Fl(2)2216 599 y Fr(\))30 b(and,)g(b)m(y)h(Prop)s(osition)f(2.2,)129 802 y Fp(k)p Fq(AS)5 b(u)p Fp(k)26 b(\024)f(k)p Fr(\()p Fq(AS)h Fp(\000)20 b Fq(S)5 b(A)p Fr(\))p Fq(u)p Fp(k)21 b Fr(+)f Fp(k)p Fq(S)5 b(Au)p Fp(k)27 b Fr(=)e Fp(k)p Fr([)p Fq(A)1748 816 y Fl(1)1788 802 y Fq(;)15 b(S)5 b Fr(])1914 764 y Fz(\016)1954 802 y Fq(u)20 b Fr(+)g([)p Fq(A)2210 816 y Fl(2)2250 802 y Fq(;)15 b(S)5 b Fr(])2376 764 y Fz(\016)2416 802 y Fq(u)p Fp(k)21 b Fr(+)f Fp(k)p Fq(S)5 b(Au)p Fp(k)26 b(\024)f Fq(C)7 b Fr(\()p Fp(k)p Fq(u)p Fp(k)21 b Fr(+)f Fp(k)p Fq(Au)p Fp(k)p Fr(\))p Fq(:)0 1004 y Fr(Th)m(us)k Fq(S)5 b Fp(D)s Fr(\()p Fq(A)p Fr(\))25 b Fp(\032)g(D)s Fr(\()p Fq(A)p Fr(\))h(and)e(for)g Fq(u)h Fp(2)g(D)s Fr(\()p Fq(A)p Fr(\))g(w)m(e)h(ha)m(v)m(e)f(\()p Fq(AS)14 b Fp(\000)9 b Fq(S)c(A)p Fr(\))p Fq(u)26 b 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Fl(1)2522 4991 y Fr(\)d)p Fq(s)1242 5227 y Fr(=)1396 5112 y Ff(Z)1479 5139 y Fm(t)1442 5301 y Fl(0)1508 5227 y Fr(\()p Fq(W)1642 5190 y Fz(\003)1629 5250 y Fl(2)p Fm(;t)p Fz(\000)p Fm(s)1802 5227 y Fq(u)1854 5241 y Fl(2)1893 5227 y Fq(;)1933 5241 y Fl(2)1973 5227 y Fr([)p Fq(S;)g Fr(i)p Fq(A)p Fr(])2212 5190 y Fz(\016)2212 5250 y Fl(1)2253 5227 y Fq(W)2339 5241 y Fl(1)p Fm(;s)2430 5227 y Fq(u)2482 5241 y Fl(1)2522 5227 y Fr(\)d)p Fq(s:)1844 5517 y Fr(19)p eop end %%Page: 20 20 TeXDict begin 20 19 bop 0 162 a Fr(This)30 b(giv)m(es:)1042 318 y Fq(S)5 b(W)1189 332 y Fl(1)p Fm(;t)1293 318 y Fp(\000)20 b Fq(W)1470 332 y Fl(2)p Fm(;t)1555 318 y Fq(S)30 b Fr(=)1737 203 y Ff(Z)1820 229 y Fm(t)1783 391 y Fl(0)1865 318 y Fq(W)1951 332 y Fl(2)p Fm(;t)p Fz(\000)p Fm(s)t Fl(2)2162 318 y Fr([)p Fq(S;)15 b Fr(i)p Fq(A)p Fr(])2401 280 y Fz(\016)2401 340 y Fl(1)2442 318 y Fq(W)2528 332 y Fl(1)p Fm(;s)2619 318 y Fr(d)p Fq(s;)-2738 b Fr(\(2.19\))0 517 y(as)31 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865 y Fp(g)0 977 y Fr(\(w)m(e)h(use)f ([ABG)q(,)g(Prop.)42 b(2.7.3)33 b(and)d(Th.)42 b(3.3.23]\).)k(Note)32 b(that)g Fp(f)p Fq(U)2339 991 y Fm(t)2369 977 y Fp(g)f Fr(restricts)h(to)g(a)f Fq(C)3049 991 y Fl(0)3089 977 y Fr(-semigroup)g(on)g Fq(F)3740 991 y Fl(1)0 1090 y Fr(and)36 b(extends)g(to)h(a)g Fq(C)784 1104 y Fl(0)824 1090 y Fr(-semigroup)f(on)h Fq(F)1486 1104 y Fz(\000)p Fl(1)1580 1090 y Fr(,)i(b)s(oth)c(still)j(denoted)e(b)m(y)h Fp(f)p Fq(U)2637 1104 y Fm(t)2667 1090 y Fp(g)g Fr(\(see)g([ABG)q(,)h (Prop.)59 b(3.3.8]\).)0 1203 y(F)-8 b(or)31 b(0)26 b Fq(<)f(s)g(<)g Fr(1,)31 b(1)25 b Fp(\024)g Fq(p)g Fp(\024)g Fr(+)p Fp(1)30 b Fr(w)m(e)h(set:)804 1471 y Fp(k)p Fq(f)10 b Fp(k)949 1485 y Fm(s;p)1066 1471 y Fr(:=)1187 1327 y Ff(\()1296 1425 y Fp(k)p Fq(f)g Fp(k)1441 1439 y Fl(0)1500 1425 y Fr(+)20 b(\()1626 1357 y Ff(R)1682 1383 y Fl(1)1666 1453 y(0)1737 1425 y Fp(k)p Fq(t)1815 1392 y Fz(\000)p Fm(s)1907 1425 y Fr(\()p Fq(U)2004 1439 y Fm(t)2054 1425 y Fp(\000)g Fr(1)-20 b(l\))p Fq(f)10 b Fp(k)2330 1381 y Fm(p)2330 1450 y Fl(0)2380 1390 y(d)p Fm(t)p 2380 1405 65 4 v 2400 1457 a(t)2455 1425 y Fr(\))2501 1353 y Fi(1)p 2500 1365 33 4 v 2500 1406 a Fg(p)2546 1425 y Fq(;)36 b(p)25 b(<)g Fp(1)p Fq(;)1296 1538 y Fp(k)p Fq(f)10 b Fp(k)1441 1552 y Fl(0)1500 1538 y Fr(+)20 b(sup)1728 1560 y Fl([0)p Fm(;)p Fl(1])1877 1538 y Fp(k)p Fq(t)1955 1505 y Fz(\000)p Fm(s)2047 1538 y Fr(\()p Fq(U)2144 1552 y Fm(t)2194 1538 y Fp(\000)g Fr(1)-20 b(l\))p Fq(f)10 b Fp(k)2470 1552 y Fl(0)2510 1538 y Fq(;)36 b(p)25 b Fr(=)g(+)p Fp(1)p Fq(:)0 1745 y Fr(Then)i Fq(F)293 1759 y Fm(s;p)414 1745 y Fr(is)h(the)h(space)f(of)h Fq(f)34 b Fp(2)25 b Fq(F)41 b Fr(suc)m(h)28 b(that)h Fp(k)p Fq(f)10 b Fp(k)1807 1759 y Fm(s;p)1924 1745 y Fq(<)25 b Fp(1)k Fr(equipp)s(ed)d(with)i(the)h(norm)e Fp(k)p Fq(f)10 b Fp(k)3266 1759 y Fm(s;p)3358 1745 y Fr(.)40 b(Similarly)0 1857 y(w)m(e)31 b(set:)721 2017 y Fp(k)p Fq(f)10 b Fp(k)866 2031 y Fz(\000)p Fm(s;p)1039 2017 y Fr(:=)1160 1873 y Ff(\()1268 1971 y Fp(k)p Fq(f)g Fp(k)1413 1985 y Fz(\000)p Fl(1)1528 1971 y Fr(+)20 b(\()1654 1902 y Ff(R)1709 1928 y Fl(1)1693 1998 y(0)1764 1971 y Fp(k)p Fq(t)1842 1938 y Fz(\000)p Fm(s)1934 1971 y Fr(\()p Fq(U)2031 1985 y Fm(t)2081 1971 y Fp(\000)g Fr(1)-20 b(l)q(\))p Fq(f)10 b Fp(k)2358 1926 y Fm(p)2358 1995 y Fz(\000)p Fl(1)2462 1935 y(d)p Fm(t)p 2462 1950 65 4 v 2482 2002 a(t)2537 1971 y Fr(\))2583 1898 y Fi(1)p 2582 1910 33 4 v 2582 1951 a Fg(p)2628 1971 y Fq(;)36 b(p)25 b(<)g Fp(1)p Fq(;)1268 2083 y Fp(k)p Fq(f)10 b Fp(k)1413 2097 y Fz(\000)p Fl(1)1528 2083 y Fr(+)20 b(sup)1756 2105 y Fl([0)p Fm(;)p Fl(1])1904 2083 y Fp(k)p Fq(t)1982 2050 y Fz(\000)p Fm(s)2074 2083 y Fr(\()p Fq(U)2171 2097 y Fm(t)2222 2083 y Fp(\000)f Fr(1)-20 b(l)q(\))p Fq(f)10 b Fp(k)2498 2097 y Fz(\000)p Fl(1)2592 2083 y Fq(;)36 b(p)25 b Fr(=)g(+)p Fp(1)p Fq(:)0 2260 y Fr(Then)35 b Fq(F)301 2274 y Fz(\000)p Fm(s;p)484 2260 y Fr(is)h(the)h(space)f(of)g Fq(f)44 b Fp(2)35 b Fq(F)1344 2274 y Fz(\000)p Fl(1)1475 2260 y Fr(suc)m(h)g(that)p Fp(k)p Fq(f)10 b Fp(k)1996 2274 y Fz(\000)p Fm(s;p)2179 2260 y Fq(<)34 b Fp(1)p Fr(.)58 b(Finally)37 b(if)f(w)m(e)g(denote)h(b) m(y)f Fq(F)3503 2227 y Fz(\003)p Fl(0)3490 2282 y Fm(s;)p Fz(1)3653 2260 y Fr(the)0 2373 y(closure)41 b(of)f Fq(F)498 2340 y Fz(\003)485 2396 y Fl(1)578 2373 y Fr(in)g Fq(F)765 2340 y Fz(\003)752 2395 y Fm(s;)p Fz(1)879 2373 y Fr(,)j(then)d Fq(F)1222 2387 y Fz(\000)p Fm(s;)p Fl(1)1409 2373 y Fr(is)g (canonically)i(iden)m(ti\014ed)f(with)f(the)g(dual)g(of)g Fq(F)3178 2340 y Fz(\003)p Fl(0)3165 2395 y Fm(s;)p Fz(1)3333 2373 y Fr(\(see)h([ABG)q(,)0 2486 y(Theorem)30 b(2.4.2]\).)141 2648 y(W)-8 b(e)46 b(will)f(assume)g(in)g(this)f(subsection)h(that)h Fq(A)f Fr(is)g(symmetric)g(\(hence)g(maximal)h(symmetric,)j(b)s(e-)0 2761 y(cause)34 b(it)g(generates)g(a)g Fq(C)886 2775 y Fl(0)925 2761 y Fr(-semigroup\))g(and)e(that)i Fp(G)39 b Fr(is)33 b(b-stable)h(under)d Fp(f)p Fq(W)2746 2728 y Fz(\003)2733 2784 y Fm(t)2786 2761 y Fp(g)p Fr(.)49 b(Then)33 b Fp(f)p Fq(W)3290 2728 y Fz(\003)3277 2784 y Fm(t)3329 2761 y Fp(g)h Fr(induces)e(a)0 2874 y Fq(C)65 2888 y Fl(0)104 2874 y Fp(\000)p Fr(semigroup)22 b(on)f Fp(G)27 b Fr(and)22 b Fp(f)p Fq(W)1100 2888 y Fm(t)1130 2874 y Fp(g)g Fr(induces)f(a)h Fq(C)1644 2888 y Fl(0)1683 2874 y Fp(\000)p Fr(semigroup)g(on)f Fp(G)2357 2841 y Fz(\003)2397 2874 y Fr(.)38 b(W)-8 b(e)23 b(denote)f(b)m(y)g Fp(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)3285 2841 y Fz(\003)3326 2874 y Fr(\))25 b Fp(\021)g(D)s Fr(\()p Fq(A)3658 2888 y Fz(G)3704 2869 y Fo(\003)3744 2874 y Fr(\))0 2987 y(the)k(domain)f (of)h(the)g(generator)g(of)g(the)g(semigroup)f(induced)g(b)m(y)g Fp(f)p Fq(W)2417 3001 y Fm(t)2447 2987 y Fp(g)h Fr(in)f Fp(G)2684 2954 y Fz(\003)2724 2987 y Fr(.)40 b(Then)28 b(the)g(spaces)h Fp(G)3510 3001 y Fz(\006)p Fl(1)3633 2987 y Fr(and)0 3100 y Fp(G)59 3067 y Fz(\003)54 3123 y(\006)p Fl(1)171 3100 y Fr(and)21 b(the)i(Beso)m(v)h(scales)f Fp(G)1041 3123 y Fm(s;p)1155 3100 y Fr(and)f Fp(G)1383 3067 y Fz(\003)1378 3123 y Fm(s;p)1492 3100 y Fr(\()p Fp(\000)p Fr(1)k Fq(<)f(s)g(<)g Fr(1,)f(1)i Fp(\024)f Fq(p)g Fp(\024)g Fr(+)p Fp(1)p Fr(\))d(are)h(de\014ned)e(as)i (explained)f(ab)s(o)m(v)m(e,)0 3213 y(taking)37 b Fq(F)48 b Fr(=)35 b Fp(G)42 b Fr(and)35 b(the)i(semigroup)f Fp(f)p Fq(U)1487 3227 y Fm(t)1517 3213 y Fp(g)f Fr(:=)g Fp(f)p Fq(W)1872 3180 y Fz(\003)1859 3235 y Fm(t)1912 3213 y Fp(g)h Fr(acting)i(on)e Fp(G)5 b Fr(.)59 b(With)36 b(the)h(notations)g (in)m(tro)s(duced)0 3326 y(after)31 b(De\014nition)g(2.32)h(w)m(e)f(ha) m(v)m(e)g Fp(G)1227 3340 y Fl(1)1292 3326 y Fr(=)25 b Fp(D)s Fr(\()p Fq(A)1564 3293 y Fz(\003)1604 3326 y Fr(;)15 b Fp(G)5 b Fr(\))31 b(and)f Fp(G)2005 3293 y Fz(\003)2000 3349 y Fl(1)2070 3326 y Fr(=)25 b Fp(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)2441 3293 y Fz(\003)2481 3326 y Fr(\).)141 3439 y(W)-8 b(e)32 b(will)e(denote)h(b)m(y)g Fp(E)38 b Fr(the)31 b(space:)1666 3552 y Fp(E)j Fr(:=)25 b Fp(G)1928 3514 y Fz(\003)1923 3577 y Fl(1)p Fm(=)p Fl(2)p Fm(;)p Fl(1)2088 3552 y Fq(;)0 3719 y Fr(and)30 b(as)g(recalled)i(ab)s(o)m(v)m (e)g Fp(E)936 3686 y Fz(\003)1000 3719 y Fr(=)25 b Fp(G)1150 3737 y Fz(\000)p Fl(1)p Fm(=)p Fl(2)p Fm(;)p Fz(1)1405 3719 y Fr(.)141 3832 y(F)-8 b(or)31 b(later)h(use)e(w)m(e)h(pro)m(v)m (e)g(the)f(follo)m(wing)i(lemma.)0 4019 y Fh(Lemma)j(3.4)46 b Fk(Assume)37 b(that)h Fq(A)g Fk(is)f(symmetric)h(and)g(that)h Fp(G)j Fk(is)37 b Fr(b-)p Fk(stable)h(under)g Fp(f)p Fq(W)3056 3986 y Fz(\003)3043 4042 y Fm(t)3095 4019 y Fp(g)p Fk(.)56 b(Then)38 b Fp(D)s Fr(\()p Fq(A)p Fr(\))f Fk(is)0 4132 y(dense)c(in)f Fp(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)637 4099 y Fz(\003)678 4132 y Fr(\))p Fk(,)33 b(in)f Fp(E)41 b Fk(and)33 b(in)g Fp(E)28 b(\\)20 b(H)33 b Fk(for)g(the)g(interse)-5 b(ction)34 b(top)-5 b(olo)g(gy.)0 4320 y Fh(Pro)s(of.)46 b Fr(F)-8 b(or)26 b Fq(\025)g Fp(\035)f Fr(1)h(the)g(op)s(erator)g(\()p Fq(A)11 b Fr(+)g(i)p Fq(\025)p Fr(\))1575 4287 y Fz(\000)p Fl(1)1697 4320 y Fr(is)26 b(equal)g(to)h(the)f(restriction)h(to)f Fp(H)h Fr(of)f(\()p Fq(A)3121 4334 y Fz(G)3167 4315 y Fo(\003)3218 4320 y Fr(+)11 b(i)p Fq(\025)p Fr(\))3413 4287 y Fz(\000)p Fl(1)3508 4320 y Fr(.)39 b(Since)0 4433 y Fp(H)29 b Fr(is)f(dense)f(in) h Fp(G)603 4400 y Fz(\003)643 4433 y Fr(,)h Fp(D)s Fr(\()p Fq(A)p Fr(\))c(=)g(\()p Fq(A)16 b Fr(+)f(i)p Fq(\025)p Fr(\))1347 4400 y Fz(\000)p Fl(1)1442 4433 y Fp(H)26 b Fr(=)f(\()p Fq(A)1744 4447 y Fz(G)1790 4428 y Fo(\003)1846 4433 y Fr(+)15 b(i)p Fq(\025)p Fr(\))2045 4400 y Fz(\000)p Fl(1)2140 4433 y Fp(H)29 b Fr(is)f(dense)g(in)f(\()p Fq(A)2787 4447 y Fz(G)2833 4428 y Fo(\003)2889 4433 y Fr(+)15 b(i)p Fq(\025)p Fr(\))3088 4400 y Fz(\000)p Fl(1)3183 4433 y Fp(G)3242 4400 y Fz(\003)3307 4433 y Fr(=)25 b Fp(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)3678 4400 y Fz(\003)3719 4433 y Fr(\).)0 4546 y(Since)30 b Fp(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)512 4513 y Fz(\003)553 4546 y Fr(\))25 b(=)g Fp(G)768 4513 y Fz(\003)763 4569 y Fl(1)839 4546 y Fr(is)30 b(dense)g(in)g Fp(E)j Fr(=)25 b Fp(G)1520 4513 y Fz(\003)1515 4576 y Fl(1)p Fm(=)p Fl(2)p Fm(;)p Fl(1)1680 4546 y Fr(,)31 b Fp(D)s Fr(\()p Fq(A)p Fr(\))g(is)f(dense)g (in)g Fp(E)8 b Fr(.)141 4669 y(Finally)36 b Fp(f)p Fq(W)586 4683 y Fm(t)616 4669 y Fp(g)g Fr(is)f(a)g Fq(C)938 4683 y Fl(0)978 4669 y Fp(\000)p Fr(semigroup)f(on)h Fp(G)1678 4636 y Fz(\003)1753 4669 y Fr(and)g(on)g Fp(D)s Fr(\()p Fq(A;)15 b Fp(G)2341 4636 y Fz(\003)2381 4669 y Fr(\))36 b(hence)f(on)g Fp(E)43 b Fr(b)m(y)35 b(real)h(in)m(terp)s(olation.)0 4782 y(Let)f Fq(R)236 4796 y Fm(\017)301 4782 y Fr(=)d Fq(\017)441 4749 y Fz(\000)p Fl(1)550 4713 y Ff(R)606 4739 y Fm(\017)589 4809 y Fl(0)653 4782 y Fq(W)739 4796 y Fm(t)769 4782 y Fr(d)p Fq(t)p Fr(.)52 b(Then)34 b Fq(R)1241 4796 y Fm(\017)1306 4782 y Fr(:)e Fp(H)h(!)f(D)s Fr(\()p Fq(A)p Fr(\),)k(and)e(b)m(y)h(semigroup)f(theory)h(s-)15 b(lim)3116 4796 y Fm(\017)p Fz(!)p Fl(0)3270 4782 y Fq(R)3339 4796 y Fm(\017)3404 4782 y Fr(=)32 b(1)-20 b(l)35 b(in)f Fp(H)0 4895 y Fr(and)c(in)g Fp(E)8 b Fr(,)30 b(so)h(that)g Fp(D)s Fr(\()p Fq(A)p Fr(\))g(is)f(also)i(dense)e(in)g Fp(E)e(\\)20 b(H)31 b Fr(for)f(the)g(in)m(tersection)j(top)s(ology)-8 b(.)42 b Fb(2)141 5007 y Fr(Before)31 b(stating)h(our)e(next)g (results,)h(w)m(e)g(in)m(tro)s(duce)f(t)m(w)m(o)i(more)e(notations:)680 5212 y Fq(J)739 5174 y Fz(\016)730 5234 y(\006)814 5212 y Fr(=)25 b Fp(f)p Fq(\025)c Fp(\006)f Fr(i)p Fq(\026)25 b Fp(j)h Fq(\025)f Fp(2)g Fq(J)o(;)46 b(\026)25 b(>)g Fr(0)p Fp(g)p Fq(;)77 b(J)1978 5226 y Fz(\006)2062 5212 y Fr(=)25 b Fp(f)p Fq(\025)c Fp(\006)f Fr(i)p Fq(\026)25 b Fp(j)h Fq(\025)f Fp(2)g Fq(J)o(;)46 b(\026)25 b Fp(\025)g Fr(0)p Fp(g)p Fq(:)-3099 b Fr(\(3.7\))1844 5517 y(26)p eop end %%Page: 27 27 TeXDict begin 27 26 bop 0 162 a Fh(Theorem)70 b(3.5)46 b Fk(Assume,)28 b(b)-5 b(esides)28 b Fh(\(M1\))p Fk({)p Fh(\(M5\))p Fk(,)g(that)h Fq(A)f Fk(is)f(symmetric)i(and)f(that)h Fp(G)k Fk(is)27 b Fr(b-)p Fk(stable)h(under)0 275 y Fp(f)p Fq(W)144 242 y Fz(\003)131 298 y Fm(t)183 275 y Fp(g)p Fk(.)43 b(Then:)0 388 y Fr(\(i\))33 b Fk(if)g Fq(I)f Fp(\032)25 b Fq(J)42 b Fk(is)32 b(c)-5 b(omp)g(act,)35 b(ther)-5 b(e)34 b(is)e(a)h(c)-5 b(onstant)35 b Fq(C)1784 402 y Fm(I)1856 388 y Fk(such)e(that)1455 580 y Fp(j)p Fr(\()p Fq(u;)15 b(R)q Fr(\()p Fq(z)t Fr(\))p Fq(u)p Fr(\))p Fp(j)28 b(\024)d Fq(C)2094 594 y Fm(I)2134 580 y Fp(k)p Fq(u)p Fp(k)2276 543 y Fl(2)2276 603 y Fz(E)0 580 y Fr(\(3.8\))0 772 y Fk(for)33 b(al)5 b(l)33 b Fq(u)26 b Fp(2)e(E)29 b(\\)20 b(H)33 b Fk(and)g Fq(z)d Fr(=)25 b Fq(\025)20 b Fr(+)g(i)p Fq(\026;)48 b(\025)25 b Fp(2)g Fq(I)7 b(;)48 b(\026)25 b Fp(6)p Fr(=)g(0)33 b Fk(r)-5 b(e)g(al.)0 885 y Fr(\(ii\))40 b Fk(for)g(e)-5 b(ach)40 b Fq(z)i Fr(=)37 b Fq(\025)25 b Fr(+)f(i)p Fq(\026)40 b Fk(with)g Fq(\025)d Fp(2)g Fq(J)o(;)54 b(\026)37 b Fp(6)p Fr(=)g(0)p Fk(,)k(the)f(r)-5 b(estriction)41 b(of)e(the)h (sesquiline)-5 b(ar)40 b(form)g Fr(\()p Fq(u;)15 b(v)s Fr(\))39 b Fp(7!)0 998 y Fr(\()p Fq(u;)15 b(R)q Fr(\()p Fq(z)t Fr(\))p Fq(v)s Fr(\))47 b Fk(to)f Fp(E)37 b(\\)29 b(H)45 b Fk(extends)h(to)g(a)f(c)-5 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5074 y Fp(\024)25 b(k)p Fr(\()p Fq(H)2452 5088 y Fm(")2509 5074 y Fp(\000)20 b Fq(z)t Fr(\))p Fq(u)p Fp(k)2778 5041 y Fl(2)2839 5074 y Fr(+)g Fq(C)7 b Fp(j)p Fq(")p Fp(jkh)p Fq(H)g Fp(i)p Fq(u)p Fp(k)3389 5041 y Fl(2)3430 5074 y Fq(;)31 b Fr(or)931 5268 y(\()p Fq(u;)15 b Fr([\()p Fq(H)29 b Fp(\000)20 b Fq(\025)p Fr(\))1402 5230 y Fl(2)1462 5268 y Fp(\000)f Fq(C)7 b Fp(j)p Fq(")p Fp(j)p Fr(\(1)22 b(+)e Fq(H)1992 5230 y Fl(2)2031 5268 y Fr(\)])p Fq(u)p Fr(\))26 b Fp(\024)f(k)p Fr(\()p Fq(H)2456 5282 y Fm(")2514 5268 y Fp(\000)20 b Fq(z)t Fr(\))p Fq(u)p Fp(k)2783 5230 y Fl(2)2823 5268 y Fq(:)1844 5517 y Fr(29)p eop end %%Page: 30 30 TeXDict begin 30 29 bop 0 162 a Fr(F)-8 b(rom)32 b(Prop)s(osition)f (2.23)i(w)m(e)f(get)h Fq(\036)27 b Fp(2)g Fq(C)1452 129 y Fl(1)1491 162 y Fr(\()p Fq(H)1609 129 y Fz(0)1632 162 y Fr(\).)44 b(In)31 b(particular)h Fq(\036)2326 129 y Fz(?)2385 162 y Fp(D)e(\032)c(D)s Fr(,)32 b(cf.)g(Prop)s(osition)f (2.2,)i(so)f(that)0 275 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Fq(u)p Fp(k)h Fr(+)f Fq(C)7 b Fp(j)p Fq(")p Fp(jk)p Fq(u)p Fp(k)p Fq(:)p Fb(2)141 1548 y Fr(The)30 b(next)h(prop)s(osition)f(is)g(the)h(main)f(tec)m(hnical)i(result)e(of) h(this)f(section.)0 1760 y Fh(Prop)s(osition)36 b(3.11)47 b Fk(Ther)-5 b(e)28 b(ar)-5 b(e)28 b Fq(C)q(;)15 b(")1350 1774 y Fl(0)1416 1760 y Fq(>)25 b Fr(0)i Fk(such)h(that)g(for)g Fr(0)e Fq(<)f Fp(j)p Fq(")p Fp(j)h(\024)f Fq(")2529 1774 y Fl(0)2569 1760 y Fq(;)42 b(\025)26 b Fp(2)e Fq(I)35 b Fk(and)28 b Fq(\026)f Fk(r)-5 b(e)g(al)29 b(with)f Fq(\026")d Fp(\025)g Fr(0)p Fk(,)0 1873 y(the)38 b(op)-5 b(er)g(ator)40 b Fq(H)594 1887 y Fm(")654 1873 y Fp(\000)24 b Fq(z)38 b Fr(:)c Fp(D)j(!)d(H)k Fk(is)f(bije)-5 b(ctive)37 b(and)h(its)g(inverse)f Fq(R)2393 1887 y Fm(")2464 1873 y Fp(\021)c Fq(R)2637 1887 y Fm(")2674 1873 y Fr(\()p Fq(z)t Fr(\))38 b Fk(extends)h(to)f(a)f(c)-5 b(ontinuous)0 1986 y(op)g(er)g(ator)36 b Fq(R)427 2000 y Fm(")489 1986 y Fr(:)25 b Fp(G)598 1953 y Fz(\003)663 1986 y Fp(!)h(G)38 b Fk(satisfying)33 b(for)g(e)-5 b(ach)33 b Fq(f)i Fp(2)25 b(G)1850 1953 y Fz(\003)1890 1986 y Fk(:)1049 2190 y Fp(j)p Fq(")p Fp(j)1141 2153 y Fl(1)p Fm(=)p Fl(2)1252 2190 y Fp(k)p Fq(R)1366 2204 y Fm(")1403 2190 y Fq(f)10 b Fp(k)1503 2204 y Fz(G)1578 2190 y Fp(\024)25 b Fq(C)7 b Fp(j=)p Fr(\()p Fq(f)e(;)15 b(R)2031 2204 y Fm(")2067 2190 y Fq(f)10 b Fr(\))p Fp(j)2182 2153 y Fl(1)p Fm(=)p Fl(2)2312 2190 y Fr(+)20 b Fq(C)7 b Fp(k)p Fq(f)j Fp(k)2620 2204 y Fz(G)2666 2185 y Fo(\003)2705 2190 y Fq(:)-2730 b Fr(\(3.15\))0 2403 y Fh(Pro)s(of.)47 b Fr(By)31 b(using)f(1)-20 b(l)760 2417 y Fm(J)809 2403 y Fr(\()p Fq(H)7 b Fr(\))962 2370 y Fz(?)1047 2403 y Fp(\024)25 b Fq(\036)1197 2370 y Fz(?)p Fl(2)1322 2403 y Fr(in)30 b(Lemma)h(3.10)h(w)m(e)e(get)423 2607 y Fp(k)p Fr(1)-20 b(l)519 2621 y Fm(J)568 2607 y Fr(\()p Fq(H)7 b Fr(\))721 2570 y Fz(?)781 2607 y Fp(h)p Fq(H)g Fp(i)934 2570 y Fl(1)p Fm(=)p Fl(2)1044 2607 y Fq(u)p Fp(k)1141 2570 y Fl(2)1207 2607 y Fp(\024)25 b(k)p Fq(u)p Fp(kk)p Fr(1)-20 b(l)1541 2621 y Fm(J)1590 2607 y Fr(\()p Fq(H)7 b Fr(\))1743 2570 y Fz(?)1803 2607 y Fp(h)p Fq(H)g Fp(i)p Fq(u)p Fp(k)27 b(\024)d Fq(C)7 b Fp(k)p Fq(u)p Fp(kk)p Fr(\()p Fq(H)2545 2621 y Fm(")2603 2607 y Fp(\000)20 b Fq(z)t Fr(\))p Fq(u)p Fp(k)h Fr(+)f Fq(C)7 b Fp(j)p Fq(")p Fp(jk)p Fq(u)p Fp(k)3290 2570 y Fl(2)3331 2607 y Fq(:)0 2811 y Fr(Inserting)30 b(this)g(in)m(to)h (the)g(estimate)h(of)e(Lemma)h(3.9)g(and)f(taking)h(in)m(to)g(accoun)m (t)h(that)f Fp(k)p Fq(u)p Fp(k)26 b(\024)f(k)p Fq(u)p Fp(k)3418 2825 y Fz(G)3469 2811 y Fr(,)31 b(w)m(e)f(get)0 2924 y(for)g Fq(")181 2938 y Fl(0)251 2924 y Fr(small)h(enough:)82 3128 y Fp(j)p Fq(")p Fp(jk)p Fq(u)p Fp(k)316 3091 y Fl(2)316 3151 y Fz(G)388 3128 y Fr(+)20 b Fp(j)p Fq(\026)p Fp(jk)p Fq(u)p Fp(k)726 3091 y Fl(2)792 3128 y Fp(\024)25 b Fq(C)7 b Fp(j=)p Fr(\(\()p Fq(H)1197 3142 y Fm(")1254 3128 y Fp(\000)19 b Fq(z)t Fr(\))p Fq(u;)c(u)p Fr(\))p Fp(j)22 b Fr(+)e Fq(C)7 b Fp(j)p Fq(")p Fp(jk)p Fq(u)p Fp(kk)p Fr(\()p Fq(H)2204 3142 y Fm(")2263 3128 y 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b(norm)g(less)h(than)f Fq(C)7 b Fp(j)p Fq(")p Fp(j)997 1240 y Fz(\000)p Fl(1)p Fm(=)p Fl(2)1162 1273 y Fr(.)47 b(T)-8 b(aking)33 b(adjoin)m(ts)g(w)m (e)g(see)g(that)g Fq(\036)2423 1240 y Fz(?)2482 1273 y Fp(h)p Fq(H)7 b Fp(i)2635 1240 y Fl(1)p Fm(=)p Fl(2)2746 1273 y Fq(R)2815 1287 y Fm(")2880 1273 y Fp(2)29 b Fq(B)5 b Fr(\()p Fp(G)3138 1240 y Fz(\003)3177 1273 y Fq(;)15 b Fp(H)q Fr(\))33 b(with)f(norm)0 1386 y(less)f(than)f Fq(C)7 b Fp(j)p Fq(")p Fp(j)544 1353 y Fz(\000)p Fl(1)p Fm(=)p Fl(2)709 1386 y Fr(.)41 b(In)29 b(particular)1071 1552 y Fp(k)p Fq(\036)1170 1515 y Fz(?)1229 1552 y Fp(h)p Fq(H)7 b Fp(i)1382 1515 y Fl(1)p Fm(=)p Fl(2)1493 1552 y Fq(R)1562 1566 y Fm(")1599 1552 y Fq(f)j Fp(k)25 b(\024)g Fq(C)7 b Fp(j)p Fq(")p Fp(j)1984 1515 y Fz(\000)p Fl(1)p Fm(=)p Fl(2)2149 1552 y Fp(k)p Fq(f)j Fp(k)2294 1566 y Fz(G)2340 1548 y Fo(\003)2380 1552 y Fq(;)36 b(f)e Fp(2)25 b(H)q Fq(:)0 1719 y Fr(Finally)-8 b(,)32 b(w)m(e)f(use)f(this)g (estimate)i(in)e(Lemma)h(3.9)g(with)f Fq(u)c Fr(=)f Fq(R)2186 1733 y Fm(")2222 1719 y Fq(f)10 b Fr(,)30 b Fq(f)35 b Fp(2)25 b(H)q Fr(,)30 b(and)g(obtain:)525 1881 y Fp(j)p Fq(")p Fp(jk)p Fq(R)731 1895 y Fm(")769 1881 y Fq(f)10 b Fp(k)869 1848 y Fl(2)869 1907 y Fz(G)939 1881 y Fr(+)20 b Fp(j)p Fq(\026)p Fp(jk)p Fq(R)1249 1895 y Fm(")1286 1881 y Fq(f)10 b Fp(k)1386 1848 y Fl(2)1509 1881 y Fp(\024)25 b Fq(C)7 b Fp(j=)p Fr(\()p Fq(f)e(;)15 b(R)1962 1895 y Fm(")1998 1881 y Fq(f)10 b Fr(\))p Fp(j)20 b Fr(+)g Fq(C)7 b Fp(j)p Fq(")p Fp(jk)p Fr(1)-20 b(l)2484 1895 y Fm(J)2533 1881 y Fr(\()p Fq(H)7 b Fr(\))2686 1848 y Fz(?)2746 1881 y Fp(h)p Fq(H)g Fp(i)2899 1848 y Fl(1)p Fm(=)p Fl(2)3009 1881 y Fq(R)3078 1895 y Fm(")3115 1881 y Fq(f)j Fp(k)3215 1848 y Fl(2)1509 1994 y Fp(\024)25 b Fq(C)7 b Fp(j=)p Fr(\()p Fq(f)e(;)15 b(R)1962 2008 y Fm(")1998 1994 y Fq(f)10 b Fr(\))p Fp(j)20 b Fr(+)g Fq(C)7 b Fp(k)p Fq(f)j Fp(k)2441 1961 y Fl(2)2441 2019 y Fz(G)2487 2001 y Fo(\003)0 1936 y Fr(\(3.20\))0 2158 y(whic)m(h)39 b(implies)h(\(3.15\).)71 b(This)39 b(estimate)i(implies)f (also)h(that)f Fq(R)2288 2172 y Fm(")2365 2158 y Fp(2)g Fq(B)5 b Fr(\()p Fp(G)2634 2125 y Fz(\003)2674 2158 y Fq(;)15 b Fp(G)5 b Fr(\))41 b(b)s(ecause)f(if)f(follo)m(ws)i(from)0 2270 y(\(3.20\))33 b(that)913 2431 y Fp(j)p Fq(")p Fp(jk)p Fq(R)1119 2445 y Fm(")1157 2431 y Fq(f)10 b Fp(k)1257 2394 y Fl(2)1257 2454 y Fz(G)1332 2431 y Fp(\024)1438 2370 y(j)p Fq(")p Fp(j)p 1438 2410 93 4 v 1462 2494 a Fr(2)1541 2431 y Fp(k)p Fq(R)1655 2445 y Fm(")1692 2431 y Fq(f)g Fp(k)1792 2394 y Fl(2)1792 2454 y Fz(G)1862 2431 y Fr(+)2009 2370 y(1)p 1963 2410 139 4 v 1963 2494 a(2)p Fp(j)p Fq(")p Fp(j)2111 2431 y Fq(C)2183 2394 y Fl(2)2222 2431 y Fp(k)p Fq(f)g Fp(k)2367 2394 y Fl(2)2367 2454 y Fz(G)2413 2435 y Fo(\003)2473 2431 y Fr(+)20 b Fq(C)7 b Fp(k)p Fq(f)j Fp(k)2781 2394 y Fl(2)2781 2454 y Fz(G)2827 2435 y Fo(\003)0 2635 y Fr(hence)31 b Fp(j)p Fq(")p Fp(jk)p Fq(R)459 2649 y Fm(")497 2635 y Fq(f)10 b Fp(k)597 2602 y Fl(2)597 2661 y Fz(G)672 2635 y Fp(\024)24 b 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Fk(is)33 b(the)g(inverse)f(of)h Fr(\()p Fq(H)2043 3533 y Fm(\017)2096 3519 y Fp(\000)20 b Fq(z)t Fr(\))26 b(:)f Fp(G)31 b(!)25 b(G)2604 3486 y Fz(\003)2644 3519 y Fk(,)0 3631 y Fr(\(ii\))34 b Fk(for)f Fr(0)26 b Fq(<)f Fp(j)p Fq(\017)p Fp(j)g Fq(<)g(\017)711 3645 y Fl(0)751 3631 y Fk(,)32 b(the)h(map)h Fq(z)29 b Fp(7!)c Fq(R)1418 3645 y Fm(\017)1451 3631 y Fr(\()p Fq(z)t Fr(\))h Fp(2)f Fq(B)5 b Fr(\()p Fp(G)1847 3598 y Fz(\003)1887 3631 y Fq(;)15 b Fp(G)5 b Fr(\))34 b Fk(is)e (holomorphic)k(in)d(a)g(neighb)-5 b(orho)g(o)g(d)36 b(of)d Fq(I)3554 3598 y Fl(+)3613 3631 y Fk(,)0 3744 y Fr(\(iii\))h(s-)15 b(lim)387 3764 y Fm(\017)p Fz(!)p Fl(0)522 3745 y Fo(\006)592 3744 y Fq(R)661 3758 y Fm(\017)694 3744 y Fr(\()p Fq(z)t Fr(\))26 b(=)f(\()p Fq(H)j Fp(\000)20 b Fq(z)t Fr(\))1243 3711 y Fz(\000)p Fl(1)1370 3744 y Fk(in)33 b Fq(B)5 b Fr(\()p Fp(H)q Fr(\))32 b Fk(for)h Fp(\006=)p Fq(z)c(>)c Fr(0)p Fk(.)0 3919 y Fh(Pro)s(of.)65 b Fr(W)-8 b(e)36 b(ha)m(v)m(e)h(\()p Fq(H)834 3933 y Fm(\017)890 3919 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b Fr(\(3.29\))0 1414 y(Finally)-8 b(,)30 b(w)m(e)f(also)g(ha)m(v)m(e)h(the)e(easy)h(estimate)h Fp(j)1612 1378 y Fl(d)p 1594 1393 75 4 v 1594 1446 a(d)p Fm(z)1679 1414 y Fq(\036)p Fr(\()p Fq(z)t(;)15 b(")1896 1428 y Fl(0)1937 1414 y Fr(\))p Fp(j)26 b Fr(=)f Fp(j)p Fr(\()p Fq(u;)15 b(R)2340 1428 y Fm(")2373 1437 y Fi(0)2412 1414 y Fr(\()p Fq(z)t Fr(\))2528 1381 y Fl(2)2568 1414 y Fq(u)p Fr(\))p Fp(j)26 b(\024)f Fq(C)7 b Fr([)p Fq(u)p Fr(])2976 1381 y Fl(2)3016 1414 y Fr(.)40 b(Th)m(us,)27 b(from)h(\(3.28\))0 1527 y(and)h(\(3.29\))j(w)m(e)e(see)g(that)g(the)g (conditions)g(of)f(Lemma)h(A.2)g(are)g(satis\014ed)g(with)f Fq(\033)g Fr(=)c(1)p Fq(=)p Fr(2)31 b(and)d Fq(M)36 b Fr(=)25 b Fq(C)7 b Fr([)p Fq(u)p Fr(])3715 1494 y Fl(2)3754 1527 y Fr(.)0 1640 y(As)30 b(a)h(consequence,)g(since)g Fq(\036)p Fr(\()p Fq(z)t(;)15 b Fr(+0\))27 b(=)e(\()p Fq(u;)15 b(R)q Fr(\()p Fq(z)t Fr(\))p Fq(u)p Fr(\),)33 b(w)m(e)d(see)h(that)987 1844 y Fp(j)p Fr(\()p Fq(u;)15 b(R)q Fr(\()p Fq(z)1286 1858 y Fl(1)1327 1844 y Fr(\))p Fq(u)p Fr(\))21 b Fp(\000)e Fr(\()p Fq(u;)c(R)q Fr(\()p Fq(z)1834 1858 y Fl(2)1875 1844 y Fr(\))p Fq(u)p Fr(\))p Fp(j)26 b(\024)f Fq(C)7 b Fr([)p Fq(u)p Fr(])2318 1806 y Fl(2)2358 1844 y Fp(j)p Fq(z)2425 1858 y Fl(1)2485 1844 y Fp(\000)20 b Fq(z)2618 1858 y Fl(2)2658 1844 y Fp(j)2683 1806 y Fl(1)p Fm(=)p Fl(2)0 2047 y Fr(for)25 b(some)h(n)m(um)m(b)s(er)e Fq(C)32 b Fr(indep)s(enden)m(t)24 b(of)i Fq(u)f Fr(and)g Fq(z)1680 2061 y Fl(1)1720 2047 y Fq(;)15 b(z)1802 2061 y Fl(2)1867 2047 y Fp(2)25 b Fq(U)10 b Fr(.)39 b(Since)25 b Fq(I)2361 2061 y Fl(0)2426 2047 y Fr(and)g Fq(I)32 b Fr(are)26 b(arbitrary)-8 b(,)27 b(this)e(completes)0 2160 y(the)31 b(pro)s(of)e(of)i(the)f(theorem.)41 b Fb(2)141 2372 y Fh(Pro)s(of)36 b(of)f(Theorem)g(3.5.)41 b Fr(Let)31 b Fq(f)j Fp(2)25 b(E)39 b Fr(and)29 b(let)j(us)d(consider)i (the)f(v)m(ectors)1311 2609 y Fq(f)1356 2623 y Fm(")1417 2609 y Fr(=)1523 2548 y(1)p 1523 2588 46 4 v 1525 2671 a Fq(")1594 2494 y Ff(Z)1677 2520 y Fm(")1640 2683 y 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3090 V 2225 3173 a Fq(")2293 2996 y Ff(Z)2376 3022 y Fl(1)2340 3184 y(0)2416 3111 y Fr(\(1)21 b Fp(\000)f Fq(W)2694 3125 y Fm("s)2763 3111 y Fr(\))p Fq(f)10 b Fr(d)p Fq(s:)0 3353 y Fr(Let)31 b(us)f(abbreviate)h Fq(l)r Fr(\()p Fq(")p Fr(\))26 b(=)f Fp(k)p Fq(Af)1148 3367 y Fm(")1185 3353 y Fp(k)1230 3367 y Fz(G)1276 3348 y Fo(\003)1336 3353 y Fr(+)20 b Fp(k)p Fq(f)1527 3320 y Fz(0)1517 3376 y Fm(")1554 3353 y Fp(k)1599 3367 y Fz(G)1645 3348 y Fo(\003)1685 3353 y Fq(:)31 b Fr(Then)904 3607 y Fq(l)r Fr(\()p Fq(")p Fr(\))c Fp(\024)1178 3545 y Fr(2)p 1178 3585 V 1180 3669 a Fq(")1233 3607 y Fp(k)p Fr(\()p Fq(W)1399 3621 y Fm(")1457 3607 y Fp(\000)20 b Fr(1\))p Fq(f)10 b Fp(k)1728 3621 y Fz(G)1774 3602 y Fo(\003)1834 3607 y Fr(+)1935 3545 y(1)p 1935 3585 V 1937 3669 a Fq(")2006 3492 y Ff(Z)2089 3518 y Fl(1)2052 3680 y(0)2143 3607 y Fp(k)p Fr(\()p Fq(W)2309 3621 y Fm("s)2399 3607 y Fp(\000)20 b Fr(1\))p Fq(f)10 b Fp(k)2670 3621 y Fz(G)2716 3602 y Fo(\003)2757 3607 y Fr(d)p Fq(s:)-2876 b Fr(\(3.31\))0 3847 y(It)30 b(follo)m(ws)i(b)m(y)e(a)h(c)m(hange)g(of) g(v)-5 b(ariables)31 b(and)f([ABG)q(,)h(Prop)s(osition)f(2.7.3])i(that) 907 3979 y Ff(Z)990 4005 y Fz(1)953 4167 y Fl(0)1080 4094 y Fq(l)r Fr(\()p Fq(")p Fr(\))1244 4032 y(d)p Fq(")p 1231 4073 119 4 v 1231 4091 a Fp(p)p 1307 4091 43 4 v 65 x Fq(")1385 4094 y Fp(\024)1491 4032 y Fr(8)p 1491 4073 46 4 v 1491 4156 a(3)1562 3979 y Ff(Z)1645 4005 y Fz(1)1608 4167 y Fl(0)1734 4094 y Fp(k)p Fr(\()p Fq(W)1900 4108 y Fm(")1958 4094 y Fp(\000)20 b Fr(1\))p Fq(f)10 b Fp(k)2229 4108 y Fz(G)2275 4089 y Fo(\003)2355 4032 y Fr(d)p Fq(")p 2325 4073 153 4 v 2325 4159 a(")2367 4132 y Fl(3)p Fm(=)p Fl(2)2513 4094 y Fp(\024)25 b Fq(C)7 b Fp(k)p Fq(f)j Fp(k)2826 4108 y Fz(E)0 4094 y Fr(\(3.32\))0 4340 y(where)30 b Fq(C)37 b Fr(is)30 b(a)h(constan)m(t)g(indep)s(enden) m(t)f(of)g Fq(f)10 b Fr(.)141 4453 y(Observ)m(e)30 b(no)m(w)h(that)g (for)f(eac)m(h)h Fq(u)26 b Fp(2)f(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)1659 4420 y Fz(\003)1699 4453 y Fr(\))31 b(one)f(has)830 4638 y(d)p 809 4678 93 4 v 809 4762 a(d)p Fq(")912 4700 y Fr(\()p Fq(u;)15 b(R)1108 4714 y Fm(")1145 4700 y Fq(u)p Fr(\))26 b(=)f(\()p Fq(R)1459 4662 y Fz(\003)1458 4722 y Fm(")1498 4700 y Fq(u;)15 b(Au)p Fr(\))21 b Fp(\000)f Fr(\()p Fq(Au;)15 b(R)2121 4714 y Fm(")2159 4700 y Fq(u)p Fr(\))21 b Fp(\000)f Fq(")p Fr(\()p Fq(R)2505 4662 y Fz(\003)2504 4722 y Fm(")2545 4700 y Fq(u;)15 b(H)2720 4662 y Fz(00)2762 4700 y Fq(R)2831 4714 y Fm(")2868 4700 y Fq(u)p Fr(\))p Fq(:)-2980 b Fr(\(3.33\))0 4929 y(Indeed,)35 b(if)g Fq(u)d Fp(2)g(D)s Fr(\()p Fq(A)p Fr(\))j(then)f(this)h(follo)m (ws)g(from)g(\(3.25\))h(and)e(the)h(symmetry)g(of)f Fq(A)p Fr(.)54 b(No)m(w)35 b(arguing)g(as)g(in)0 5042 y(the)30 b(pro)s(of)e(of)i(Lemma)f(3.13)i(w)m(e)f(see)g(that)g Fq(")c Fp(7!)f Fq(R)1737 5056 y Fm(")1799 5042 y Fp(2)g Fq(B)5 b Fr(\()p Fp(G)2053 5009 y Fz(\003)2093 5042 y Fq(;)15 b Fp(G)5 b Fr(\))30 b(is)g(of)f(class)h Fq(C)2734 5009 y Fl(1)2803 5042 y Fr(on)f(]0)p Fq(;)15 b(")3080 5056 y Fl(0)3121 5042 y Fr([)29 b(and)g(that)h(\(3.24\))0 5155 y(holds)35 b(in)g Fq(B)5 b Fr(\()p Fp(G)522 5122 y Fz(\003)562 5155 y Fq(;)15 b Fp(G)5 b Fr(\).)57 b(Th)m(us)34 b(the)i(left)g(hand)e(side)h(in)g(\(3.33\))j(is)d(a)h(con)m(tin)m(uous) g(function)f(of)h Fq(u)e Fp(2)f(D)s Fr(\()p Fq(A)p Fr(\))j(for)0 5268 y(the)31 b(top)s(ology)i(induced)d(b)m(y)i Fp(G)1058 5235 y Fz(\003)1098 5268 y Fr(.)43 b(The)31 b(same)g(is)h(true)f(for)g (the)g(last)i(term)e(in)g(\(3.33\),)j(thanks)d(to)h(h)m(yp)s(othesis) 1844 5517 y(34)p eop end %%Page: 35 35 TeXDict begin 35 34 bop 0 162 a Fh(\(M5\))p Fr(,)25 b(while)f(the)f(t)m (w)m(o)i(remaining)f(terms)g(are)g(con)m(tin)m(uous)g(for)f(the)h(top)s (ology)h(induced)e(b)m(y)g Fp(D)s Fr(\()p Fq(A)p Fr(;)15 b Fp(G)3461 129 y Fz(\003)3502 162 y Fr(\),)25 b(since)0 275 y Fq(R)69 289 y Fm(\017)127 275 y Fr(:)g Fp(G)5 b(\003)27 b(!)e(G)5 b Fr(.)39 b(Since)25 b(b)m(y)g(Lemma)g(3.4,)i Fp(D)s Fr(\()p Fq(A)p Fr(\))f(is)f(dense)f(in)h Fp(D)s Fr(\()p Fq(A)p 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b(treat)h(the)f(in)m(tegral) h(term)f(in)g(\(3.39\).)50 b(F)-8 b(or)33 b(eac)m(h)h Fq(")29 b(>)g Fr(0)k(the)g(limit)h(lim)2590 1311 y Fm(\026)p Fz(!)p Fl(0)2738 1292 y Fi(+)2808 1291 y Fq(F)2879 1258 y Fz(0)2866 1314 y Fm(")2904 1291 y Fr(\()p Fq(\025)22 b Fr(+)f(i)p Fq(\026)p Fr(\))30 b(=:)f Fq(F)3447 1258 y Fz(0)3434 1314 y Fm(")3471 1291 y Fr(\()p Fq(\025)22 b Fr(+)f(i0\))0 1404 y(exists)33 b(uniformly)f(in)g Fq(\025)d Fp(2)g Fq(I)7 b Fr(,)34 b(the)f(function)f Fq(F)1644 1371 y Fz(0)1631 1427 y Fm(")1701 1404 y Fr(b)s(eing)g(holomorphic)h (on)f(a)h(neigh)m(b)s(orho)s(o)s(d)f(of)g Fq(I)3396 1418 y Fl(+)3455 1404 y Fr(.)48 b(Let)33 b(us)0 1517 y(set)k Fq(\036)202 1531 y Fm(")239 1517 y Fr(\()p Fq(\026)p Fr(\))e(=)f(sup)641 1539 y Fm(\025)p Fz(2)p Fm(I)784 1517 y Fp(j)p Fq(F)880 1484 y Fz(0)867 1540 y Fm(")905 1517 y Fr(\()p Fq(\025)24 b Fr(+)g(i)p Fq(\026)p Fr(\))g Fp(\000)g Fq(F)1417 1484 y Fz(0)1404 1540 y Fm(")1441 1517 y Fr(\()p Fq(\025)h Fr(+)e(i0\))p Fp(j)p Fr(.)59 b(Th)m(us)35 b Fq(\036)2152 1531 y Fm(")2189 1517 y Fr(\()p Fq(\026)p Fr(\))g Fp(!)g Fr(0)h(when)f Fq(\026)g Fp(!)g Fr(0)3060 1484 y Fl(+)3155 1517 y Fr(and,)i(b)s(ecause)f(of)0 1630 y(\(3.38\),)41 b(w)m(e)c(ha)m(v)m(e)g Fq(\036)705 1644 y Fm(")742 1630 y Fr(\()p Fq(\026)p Fr(\))f Fp(\024)f Fq(\022)s Fr(\()p Fq(\017)p Fr(\))i(for)f(some)h(in)m(tegrable)h (function)e Fq(\022)s Fr(.)59 b(Hence)2774 1561 y Ff(R)2829 1588 y Fm(")2862 1597 y Fi(0)2813 1658 y Fl(0)2916 1630 y Fq(\036)2970 1644 y Fm(")3007 1630 y Fr(d)p Fq(")35 b Fp(!)h Fr(0)h(if)f Fq(\026)f Fp(!)h Fr(0)3695 1597 y Fl(+)3754 1630 y Fr(,)0 1743 y(whic)m(h)30 b(is)h(more)f(than)g (required.)40 b Fb(2)141 1943 y Fh(Pro)s(of)33 b(of)g(Theorem)g(3.7.)40 b Fr(W)-8 b(e)29 b(shall)g(pro)s(ceed)f(as)g(in)g(the)h(pro)s(of)e(of)i (the)f(corresp)s(onding)f(assertion)i(of)0 2055 y(Theorem)34 b(3.3.)52 b(Let)34 b Fq(U)44 b Fr(b)s(e)33 b(as)h(in)f(that)i(pro)s(of) e(and)g(let)i Fq(\036)p Fr(\()p Fq(z)t(;)15 b(\017)p Fr(\))32 b(=)f Fq(F)2399 2069 y Fm(")2436 2055 y Fr(\()p Fq(z)t Fr(\))h(=)f(\()p Fq(f)2766 2069 y Fm(")2802 2055 y Fq(;)15 b(R)2911 2069 y Fm(")2949 2055 y Fr(\()p Fq(z)t Fr(\))p Fq(f)3110 2069 y Fm(")3147 2055 y Fr(\))34 b(for)f Fq(z)j Fp(2)30 b Fq(U)44 b Fr(and)0 2168 y(0)26 b Fq(<)f(")g(<)g(")372 2182 y Fl(0)412 2168 y Fr(.)41 b(By)30 b(\(3.38\),)j(there)e(is)f (constan)m(t)i Fq(C)37 b Fr(suc)m(h)30 b(that)1088 2396 y Fp(j)1144 2334 y Fr(d)p 1123 2375 93 4 v 1123 2458 a(d)p Fq(")1226 2396 y(\036)p Fr(\()p Fq(z)t(;)15 b(\017)p Fr(\))p Fp(j)27 b(\024)e Fq(C)7 b Fp(k)p Fq(f)j Fp(k)1838 2410 y Fz(E)1900 2302 y Ff(\020)1949 2396 y Fq(l)r Fr(\()p Fq(")p Fr(\))p Fq(")2132 2358 y Fz(\000)p Fl(1)p Fm(=)p Fl(2)2319 2396 y Fr(+)20 b Fp(k)p Fq(f)10 b Fp(k)2555 2410 y Fz(E)2602 2302 y Ff(\021)2667 2396 y Fq(:)-2692 b Fr(\(3.40\))0 2607 y(Then)29 b(from)h(\(3.34\))j(w)m(e)e(get)118 2773 y(d)p 97 2813 V 97 2896 a(d)p Fq(")233 2773 y Fr(d)p 210 2813 97 4 v 210 2896 a(d)p Fq(z)316 2834 y(\036)p Fr(\()p Fq(z)t(;)15 b(\017)p 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Fo(\003)2412 4290 y Fp(\024)25 b Fq(C)2580 4253 y Fz(0)2603 4290 y Fp(k)p Fq(f)10 b Fp(k)2748 4304 y Fz(E)2795 4290 y Fq(:)0 4475 y Fr(Inserting)30 b(this)g(in)m(to)i(the)e(preceding)h(inequalit)m(y)g(w)m(e)g(\014nally) f(see)h(that)g(there)g(is)f Fq(C)37 b Fr(suc)m(h)30 b(that)961 4697 y Fp(j)1017 4636 y Fr(d)p 996 4676 93 4 v 996 4760 a(d)p Fq(")1132 4636 y Fr(d)p 1109 4676 97 4 v 1109 4760 a(d)p Fq(z)1216 4697 y(\036)p Fr(\()p Fq(z)t(;)15 b(\017)p Fr(\))p Fp(j)27 b(\024)e Fq(C)7 b(")1725 4660 y Fz(\000)p Fl(1)1819 4697 y Fp(k)p Fq(f)j Fp(k)1964 4711 y Fz(E)2026 4603 y Ff(\020)2076 4697 y Fq(l)r Fr(\()p Fq(")p Fr(\))p Fq(")2259 4660 y Fz(\000)p Fl(1)p Fm(=)p Fl(2)2445 4697 y Fr(+)20 b Fp(k)p Fq(f)10 b Fp(k)2681 4711 y Fz(E)2729 4603 y Ff(\021)2793 4697 y Fq(:)-2818 b Fr(\(3.41\))141 4908 y(Un)m(til)36 b(no)m(w)f(there)g(w)m(as)h(no)e(assumption)h(on)g Fq(f)44 b Fr(b)s(esides)34 b Fq(f)42 b Fp(2)33 b(E)8 b Fr(.)54 b(No)m(w)36 b(w)m(e)g(c)m(ho)s(ose)g(1)p Fq(=)p Fr(2)e Fq(<)f(s)f 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y Fm(t)2391 1849 y Fq(C)2463 1816 y Fl(1)2456 1872 y(0)2502 1849 y Fr(\(\012\))c Fp(\032)g Fq(C)2835 1816 y Fl(1)2828 1872 y(0)2874 1849 y Fr(\(\012)2975 1863 y Fz(\000)p Fm(t)3060 1849 y Fr(\))g Fp(\032)g Fq(C)3292 1816 y Fl(1)3285 1872 y(0)3330 1849 y Fr(\(\012\))32 b(and)f(w)m(e)0 1962 y(can)k(apply)g(Nelson's)g(lemma)h(\(see)f(Remark)g(2.35\))i(to)f (obtain)f(that)2478 1935 y Ff(b)2454 1962 y Fq(A)g Fr(is)g(the)g (generator)h(of)f Fp(f)3384 1935 y Ff(c)3376 1962 y Fq(W)3462 1976 y Fm(t)3492 1962 y Fp(g)g Fr(\(note)0 2074 y(that)27 b Fq(C)265 2042 y Fl(1)258 2098 y(0)304 2074 y Fr(\(\012\))f(is)h(a)f (dense)g(subspace)g(of)h Fq(L)1407 2042 y Fl(2)1446 2074 y Fr(\(I)-15 b(R)1566 2039 y Fm(n)1613 2074 y Fr(\)\).)40 b(Th)m(us,)26 b(the)h(closure)2476 2048 y Ff(b)2452 2074 y Fq(A)g Fr(of)f Fp(\000)2727 2039 y Fl(1)p 2727 2054 36 4 v 2727 2106 a(2)2772 2074 y Fr(\()p Fq(F)13 b Fr(\()p Fq(Q)p Fr(\))p Fq(P)26 b Fr(+)12 b Fq(P)h(F)g Fr(\()p Fq(Q)p Fr(\)\))p Fp(j)p Fq(C)3603 2042 y Fl(1)3596 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4945 a Fq(")2233 4883 y Fp(r)p Fq(\022)s Fr(\()p Fq(y)s Fr(\))g(+)g Fq(f)10 b Fr(\()p Fq(x)20 b Fp(\000)g Fq("y)s Fr(\))p Fq(\022)s Fr(\()p Fq(y)s Fr(\))3126 4764 y Ff(\023)3202 4883 y Fq(u)p Fr(\()p Fq(x)h Fp(\000)f Fq("y)s Fr(\)d)p Fq(y)s(:)0 5128 y Fr(But)31 b(this)f(clearly)h(con)m(v)m(erges)i(uniformly)c(to)1581 5059 y Ff(R)1637 5128 y Fr(\()p Fq(y)s Fp(r)p Fr(\))p Fq(F)13 b Fr(\()p Fq(x)p Fr(\))p Fp(r)p Fq(\022)s Fr(\()p Fq(y)s Fr(\)d)p Fq(y)23 b Fr(+)d Fq(f)10 b Fr(\()p Fq(x)p Fr(\))p Fq(u)p Fr(\()p Fq(x)p Fr(\))26 b(=)f(0)p Fq(:)p Fb(2)1844 5517 y Fr(44)p eop end %%Page: 45 45 TeXDict begin 45 44 bop 0 162 a Fs(References)0 365 y Fr([Am])128 b(Ammari,)33 b(Z.:)45 b(Asymptotic)34 b(completeness)f(for) f(a)h(renormalized)g(non-relativistic)i(Hamiltonian)322 478 y(in)23 b(quan)m(tum)g(\014eld)g(theory:)38 b(the)23 b(Nelson)h(mo)s(del.)g(Math.)g(Ph)m(ys.)f(Anal.)h(Geom.)h Fh(3)f Fr(\(2000\),)j(217{285.)0 660 y([ABG])69 b(Amrein,)40 b(W.,)g(Boutet)g(de)d(Mon)m(v)m(el,)42 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(theory)e(of)g(massless)h(Nelson)g(mo)s(dels,)f(Rev.)h(Math.)g(Ph)m (ys.)f Fh(14)322 5268 y Fr(\(2002\))h(1165{1280.)1844 5517 y(45)p eop end %%Page: 46 46 TeXDict begin 46 45 bop 0 162 a Fr([Ha])159 b(Hartman,)31 b(Ph.:)40 b Fk(Or)-5 b(dinary)34 b(di\013er)-5 b(ential)34 b(e)-5 b(quations)p Fr(,)32 b(Birkh\177)-45 b(auser,)30 b(1982.)0 344 y([HeS])113 b(Hel\013er,)30 b(B.,)h(Sj\177)-45 b(ostrand,)28 b(J.:)40 b(Equation)30 b(de)f(Sc)m(hr\177)-45 b(odinger)28 b(a)m(v)m(ec)k(c)m(hamp)d(magn)m(\023)-43 b(etique)31 b(et)f(equation)322 457 y(de)g(Harp)s(er,)g(Springer)f (Lecture)i(Notes)h(in)e(Ph)m(ysics)g Fh(345)h Fr(\(1989\))i(118{197.)0 638 y([HP])142 b(Hille,)35 b(E.,)f(Phillips,)f(R.)g(S.:)46 b Fk(F)-7 b(unctional)36 b(analysis)h(and)f(semigr)-5 b(oups)p Fr(,)35 b(American)f(Mathematical)322 751 y(So)s(ciet)m(y)-8 b(,)32 b(Pro)m(vidence,)g(Rho)s(de)d(Island,)h(1957.)0 933 y([Hor])123 b(H\177)-45 b(ormander,)41 b(L.:)59 b Fk(The)41 b(analysis)i(of)e(line)-5 b(ar)42 b(p)-5 b(artial)43 b(di\013er)-5 b(ential)42 b(op)-5 b(er)g(ators)p Fr(,)45 b(v)m(ol.)c(2,)h(Springer-)322 1046 y(V)-8 b(erlag,)32 b(1983.)0 1227 y([Hos])123 b(Hoshiro,)25 b(T.:)37 b(Mourre's)24 b(metho)s(d)f(and)g(smo)s(othing)g(prop)s(erties)g(of)h(disp)s(ersiv)m (e)f(equations,)j(Comm.)322 1340 y(Math.)31 b(Ph)m(ys.)f Fh(202)i Fr(\(1999\))g(255{265.)0 1522 y([HuS])102 b(H)s(\177)-48 b(ubner,)32 b(M.,)i(Sp)s(ohn,)d(H.:)45 b(Sp)s(ectral)33 b(prop)s(erties)f(of)g(the)h(spin-b)s(oson)e(Hamiltonian,)k(Ann.)d (Inst.)322 1635 y(Henri)e(P)m(oincar)m(\023)-43 b(e)33 b Fh(62)e Fr(\(1995\))i(289{323.)0 1816 y([Je])185 b(Jensen,)30 b(A.:)40 b(Propagation)32 b(estimates)f(for)f(Sc)m(hr\177)-45 b(odinger)29 b(t)m(yp)s(e)i(op)s(erators,)f(T)-8 b(rans.)30 b(Amer.)g(Math.)322 1929 y(So)s(c.)g Fh(291)i Fr(\(1985\))g(129{144.)0 2111 y([Me])149 b(Merkli,)43 b(M.:)60 b(P)m(ositiv)m(e)42 b(comm)m(utators)f(in)f(non-equilibrium)e(quan)m(tum)i(statistical)i (mec)m(hanics,)322 2224 y(Comm.)30 b(Math.)h(Ph)m(ys.)g Fh(223)g 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b(On)24 b(comm)m(utators)j(and)d(Jacobi)i(matrices,)h (Pro)s(c.)e(Amer.)h(Math.)g(So)s(c.)f Fh(7)g Fr(\(1956\))322 3696 y(1026{1030.)0 3878 y([P2])165 b(Putnam,)35 b(C.)g(R.:)50 b Fk(Commutation)38 b(pr)-5 b(op)g(erties)40 b(of)c(Hilb)-5 b(ert)37 b(sp)-5 b(ac)g(e)38 b(op)-5 b(er)g(ators)40 b(and)e(r)-5 b(elate)g(d)38 b(topics)p Fr(,)322 3991 y(Springer-V)-8 b(erlag,)31 b(1967.)0 4172 y([RS])154 b(Reed,)46 b(M.,)h(Simon,)f(B.:)66 b Fk(Metho)-5 b(ds)45 b(of)g(mo)-5 b(dern)45 b(mathematic)-5 b(al)47 b(physics)p Fr(,)h(v)m(ol.)c(1-4,)j(Academic)322 4285 y(Press,)30 b(1972-1980.)0 4467 y([Sk1])128 b(Skibsted,)29 b(E.:)41 b(Smo)s(othness)28 b(of)i Fq(N)10 b Fr(-b)s(o)s(dy)28 b(scattering)k(amplitudes,)d(Rev.)h(Math.)h(Ph)m(ys.)e Fh(4)h Fr(\(1992\))322 4580 y(619{658.)0 4761 y([Sk2])128 b(Skibsted,)37 b(E.:)52 b(Sp)s(ectral)36 b(analysis)h(of)f Fq(N)10 b Fr(-b)s(o)s(dy)35 b(systems)h(coupled)g(to)h(a)f(b)s(osonic)g (system,)i(Rev.)322 4874 y(Math.)31 b(Ph)m(ys.)f Fh(10)h Fr(\(1998\))i(989{1026.)0 5056 y([T)-8 b(r])178 b(T)-8 b(rieb)s(el,)26 b(H.:)39 b Fk(Interp)-5 b(olation)31 b(the)-5 b(ory,)30 b(function)e(sp)-5 b(ac)g(es,)30 b(di\013er)-5 b(ential)29 b(op)-5 b(er)g(ators)p Fr(,)30 b(VEB)c(Deutsc)m(her)322 5169 y(V)-8 b(erlag)32 b(der)e(Wissensc)m(haften,)h(Berlin,)g(1978.) 1844 5517 y(46)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0304270344917--