Content-Type: multipart/mixed; boundary="-------------0408172206176" This is a multi-part message in MIME format. ---------------0408172206176 Content-Type: text/plain; name="04-254.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-254.keywords" Trotter product formula in norm, unitary group, Dirac operator, relativistic Schr\"odinger operator. ---------------0408172206176 Content-Type: application/postscript; name="NormUniTro_IT.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="NormUniTro_IT.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.78 p1.4 Copyright 1996-98 ASCII Corp.(www-ptex@ascii.co.jp) %%based on dvipsk 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: NormUniTro_IT.dvi %%Pages: 16 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMR10 CMR8 CMBX10 Ryumin-Light-H CMBX12 %%+ CMMI12 CMSY10 CMMI8 CMSY8 CMSL12 CMTI12 CMEX10 CMMI6 CMR6 %%EndComments %DVIPSCommandLine: dvipsk -D600 -t a4size -P dl NormUniTro_IT.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.08.18:1116 %%BeginProcSet: texc.pro %! 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%!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523de97a57cbed59a39 c235a135d115ebd4abbd5c9615ae06b3a137bd5ee4181428352e4ac5a2711b30 6772a97888d406f3e2c874ec8fdad2fe950aea02869a0272574daa4451cf537b 7e4309bfd807ea34c2e6913bd02662ff2c1bdac64da947e4dcf6894c3df41ba6 58257473f2aa05c0c5584e7fd244c8382fc89050897673bc721ad94f71400579 256f659bd09afd2a6f90e291dabacf9fa81dffd96d3d140248f636f02cdd9af1 f810c49850024f9577269e0ee75ef54c772eb52c8148650d1a9572dd87da41c7 1cc8ac203b22158a3e79808af8ab001964958eea7b051201d587a6174787221d 62f9babf8458a7a21b79db22c0fdd72bdd59b74d32d9917f1b5458178ab8ebee fa90e161c182cfda8f9b74fbfa1f3aa7f842365fc6ee4fab989c985d01256134 61d375107a61abd6896835f39c5da0222b1bcbc25188f3f008197e473223803a 2f0264c377d3c5c749d3bd3312ce1e2f1b825f5d4d5750026201cc2f9e51a9fe 1e3e934ab75cae831777d7cf70c8020a377a23be8104a7bc76f8a6ce235fcb35 ccf828bad131e2e85545467be70b23ec91974e8814583546c7e023ca1694931c b5f8efe6236dd16228d9847251ffe9ec0d617a54e4350bde36af3d185107 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 34 /epsilon put dup 106 /j put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425 5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f bcea9907a04cf93c12727ec40db3f2f77596dca477862747435bdedacd9b2311 6cc97fa47ffdd7d897fb6bdd5572e35d34e7e1cb5e7273a4ffd86525323ace4a 84e1297028c2bd5469baa2e75d19360c2c9042139d5e7dd4390a6a3935424711 de21910126d750ae279916ceb71da3591d60dc62db333c5021e2c1cd61ade51e 9390b8b2d3a0204a6fec9e5a25a634ca16bc351f11886c4c12d0a198f515cbdd 1c2d1749fc1dae6df5191778edc9daeda079a7be2ff7978d1747d79d59a62555 46ccfb992dbb1ebfe708035ed419b1b069c3779c6c7ff3337b29337d43b05e22 353467689d1c69188c873592da26abcdf18ce896a9618d235495935e64d664dd 7ff1ca8324170a3e6cdb1413957f66f9a0cab3cef46396060c72eb273a948ead 353375a9bad639fff4d2e0de8907a7e2c4b85bbe1eae1bec40a3a09b5ea2e7aa 322d2b0c2ab5e9de9e2b701d7455b21cd3b46847ccb9beea8c2002c5ac96c0ef b385c4fe0df4fe6bddb51f56607d1c3e666ca2e378b48f4650fade6ed8c5f246 d605842de26cd8ce9495dd5632012ac5b1ab27676d21df17e00fbca690cc3852 23222481dd8a47a67c0f531dbb2be8c8af31256098281f01a6770ab2088f3e91 5e4213655e8547211a53312a61a3e8d28f5d607278540c7f9fb2dcc16a1c6297 8e3bc76d1e4ca09bf558159bae6e61b0e19a229cb9b22deb4676cbf358c80716 12d1f6c20f50170478c4a80aa24ce407ee23b15083295833bd66fa71db55bd49 842b822060f3311d90aa0a946f8894380889164ea304ad2ecddcc2fc68b9e0cf 6c6fb6f7cc898ff3136cdf28d3dc61ab900af05ef20a8ef36bdf41e348c489e9 648d5ea0cf15acd0effcb85cd0fd1221ad2ede86b09145fcfd3c2baeefe30973 79d7f27fffee7b6a6d53554282785b359fe17e0c565b6ec1f51dc452f2788132 0900450f896668958092a3bc657311c485eba8fc0dd92a4d 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /vextendsingle put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 40 /braceleftBigg put dup 80 /summationtext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fd06d0923a82021d8d64a54500a7f802bcde0cdaf62e888f7da0ff6f8a0b18 ab840fe6d58d89506ccbc5b8566b1357eac1baeb02823d4fe1befa9d25755d21 7a66022b687e328bdd0e161dedc6fa5d527bfa21ba4f4f756320d7cddd205301 174c835e064e31ef1cb70199a90222d37e81c23282ef9bfa68d8aff6eb56be62 6278801051ac1ed60e1c3900cd5d18b949a2e278e80121e9c45d91cfcd33e33e d1fbb205f3cf85deddca3590f1f2340027274e529e5191fc988e2d1f88be1aee 96770ed796fa1e89904774d3fb443523681aa0f7617d76a92aaf77810e82a0ad e87d78dae5dacf4dcb82268b1ab31bfec386573c875ae44c9534d6fcc8af0752 3d8421ad129a766db24aea1888f3464d00107d2c00210cfb1ba23369af4f1d65 4e7a5efa78f7fbca7a020b6bf0b421720594129569b27f6053ecd14c961b5e3d 297f291dc2e773f36bb1c2d7a8dfa4c626f7ae0e267ebb44d5fa3d5422547885 147800aa0fdec57b1f490ff6f07a51b6617fbb69b606fd2ada6908a1c12c6251 13ffc1fc80242f87668cc2f01d53d3963b04786ce1daac600f2b95ad558f3942 018708a42e32fc1915ea49ce1cda967f06598d4cd039d28474a52531ab793854 bcc9db49a5ac6fc777f492a9e582d2a6d6f2e58cb7bc068f8fbcf43c2fa4b01f 3e4cfe3b78df25e73b2494eb7f081d7da3baa927cdf1204b586401a5507f7b1d e24e23bd570b7245a6932ce7baa70e733a9b090a0d3facde626ac3b0d46ba857 d5011cb6f31c75510e16d273e742a562043926dbb5b9c0470be34b78a02b0ec6 d02cc7105830c8e363126db65fec920b662e837e686bd43d83ecc62d07d16f29 6ec01c41c3c1825e08936695067df0832f18e3b378087d2956b37a4e10eb5955 556113509696925cbd20f0cb395deaeb66e1af946c2173196c80d36d12c9c4a7 f24dcbc4c59a1e6360fabcb40c43918e88eea0a5dc6c94741b7e809dd2186d41 ccb1302a7f3c8935f1433fd3562aee932bcd8923f1174eee966a71a727c95fd0 3515a278141dab6a485e1a7fd81fa4d93d5b1cc4d8b8c3e4a4dd628b604ab624 ef3775477d85d0ced114f6e23d21691e079c4530b5f1522684e9a1711cf1ee9c e16b787a09c85efa9b20696bf1804bb689b4b43439334aeb1c9d4b3bfc3800fe 6b1449372f3ac75791fe458337095848db2640b9e75f2e76fc214edeab916c24 c774d1c4a23294f8c01d6c0777081c5e28c9187ebf6722020ffb3f790198c109 6351bede7b7fc94755f854aa1cc41f05d2e65976a69f79fd5fcffcd2f120ce73 68291007e6b098486217f348b8a55b96853f08d1780bc2ee385d630911ab1b59 ec4d775e006087248691dd8c2b933c44310dc2adf8abf822c1945fadf0288705 34cd0792fc8f4d8887b89b5d98a31d232c6e600ddeab1e1e925ffaad8be92fda 513bc8eeaaca4ace7fd08748bdeced9184ea0c8b3187911d006898a7050b0511 24c2df9acf38e81f940c2c943e19f4e33d80e23cc91396bf29edc92e5a1b73e8 7e663605b1eb9d05cedcd73d0dc1a0566c0978c3859a85c464d91a3527755947 4f286e79e45d0d57b25c3639f45f377becbb267f9335e2c22d3bda9574a674d0 a944b212108ba96168da373d85f490a3c1f3e63389870b5e868885fba76648ae 6e89193192d098f99b8c6893b269e2b50c84eb8e63547036fad0b5321914f8cb dc0e3ab3f2d68e9bb5ebf0b44d0b9972f6199817379d7f9008654092ceeb6651 d39a232f4dfc0f942c37f0a0ff1fdc020d5ff30611f8bbc4d6622272eab35a86 f0437f575f5b381f6cb06884f01e4aac4c77926f487087255b6f6e79e3061dde dfea6c7bcfda81a7c483b2ff0bba7d6898122560f6cba08d4ebd0547edc555bb e4aed84561c3eab2a1f6fb157fa249e1c8b165c11696d8dc8314a426e722f293 5b67148815ec607a431ea18613c192ca441e078ea98459de2bbe52b47d71aadb 0254502dee68f6cb1069a1cf1c3b92030d2e0b5328406af7109dce76d941345b dc02df2d8c0671b0c7292bd377811a49c226970cd7da5fafc0478e2e3267398a 33341c04f3beb37695f6acf215892f3401fc65f7d1d05cd1be9aac047aa7f92f add5c00508ce597891ee0516a95edda4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 58 /colon 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 74 /J put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 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 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 100 /d put readonly def /FontBBox{-56 -251 1102 750}readonly def /UniqueID 5000799 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 806eb7b8c434269c8a30d52dd3a6e85ebcf727aecf5607b54ac3942d00365274 9fef6277965f241846e12c5fc12f452046f9c7df8d1d31e228d6011de7485f19 4de778c725bd819dd7c91f2cfd0a9994b0ccdf95f200c0247f2c39f74a6ec77a c20f4789830ad04647b0784bd6740b2c56e2e41da705d1f709b16b92abcf7e4b aa92321eb28f528123e04dd7a74742e176a447a518a4aaeb0a4d3d5c23003c2f 98ac15a3b49f60efe1fd02bfa0c4344ea0300cf33a57ae113a16baf4bc852b2c 0ae48195b9930218490abd06f6102cd3314b61286d6cf26ab735e56cd7cb2cc5 07dfa75f1b0eb40953064e80654dd9ba6aadbc499f64d92fa58245e6b42337b8 95ee240599a523542c9b75d02457f4206181f124211d7785b665c338cbf95a83 20beecde03ebc387ff69b8ea66cb977fc926cb9ccba1125834e9b45e838a9509 28da66519e8782afddd42da1a6fec0293d2c54bf37ee6f265ba589094d3170f4 74264806cb095940e14f8573c66f3695bfece5550daf89b3584c412fc8bc3666 48e689c3af3cc9671a951f0281aa81dce103dc01d718e2982306e185ffc8abef ec62b3cddd662b7ed2233dc6c11acff1dd39c8674eb818de0da9ade582824bf4 0a475de261046f32f0a1db2ba342df06062584ece7fdebf26e73d5a70c65a7ef 509eba5ba5fbc2d1c68161a01e13666ac624253e70fc8835bca2263da9a43277 bc7e6b1a6cfbd3f82e55d79cef1d4cc4744fdcc97d0e7453f9314af146e6642e 9645821305f50fe0e4f0f6085888adc6007d613f23e810e65fb05b53e1b98cb8 1ff9ef4b3af7b19f702447cc8270163f642f3ef1e195de5713b8cd78ceb42c76 b1df6f96e8a4d5473bee5c79a73bed49e17151208b7cc685fa171362b31739db 08fea3c5558a1da16b764282a560423fc09d679275514c3c63d7851d7de368a6 f3c91ac9ffde78ba1ed81fb11d4d3ee7d423ab0945d9d6564d40a3c500aff634 3936f9a09a27f0abeee405850553a9f78922a299715b3ebc3ae918bdbcbb0cc7 5f72ee874ebcdb0c3324d4e0e31568152b16603e6e3054cef21387b43cdb4b79 7a36fdb499e9f9f9559c01238e23e17d8dabc1b26495ba47a5c467f51cecc7a0 1d216187ea6acae09b09ec258e98c133fd16b999a75d9f0b0011bf52492eba1e 859f47791ce6f1a6ccd6fd6a79422983f4fa7b8e0bea9dd40e392f561c84dc7d 88c8a6883a6579714d1e807fe2720a0ecc75cc44a74061d60813ac5e8c98e9b0 68f7e7ab46c438d13a9c032b30f50fa934260e2ac4da434f7056dcfc39162228 5a865c67282942188718250a5ce7bcb67fa1a320a7112a6a241d 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a4261be7bd48981fe5d74f36597276d570bdc1ca4d7a29ec280a13e7 cf740be69a5d79aff1ac325360e35ace9b7338a0d639d1a12ea484c43a1ae98c 3b6388532dbf33a3d9d0269db68b7a40451f68e14ea905164d8cfdf7e0108bfc 5dc1e3a19c19ac31c8584efec4c0a7e569d1a1d4a1fc1e218530f9967984aafe 4883fdd97f9b6f8ad4d64cebadd6feb049fee2f66a633d5f58bf122db477b7b2 551b8dc3ab3578b9e5f8eaf8490926b8a961675794450f40190422e0eab2e48b 75e35ce2164f3c60b2e30c689f449cdea67b0eb8ef87551dc8c1295741cdc9ce 5921db095b7f0ad149b179146d1853d6928773ec136cafeedcd23c9ecdd69d13 636f8145c1caf1db1fd83f2b8a68919699831dd1efb2cf6ca4747d5831f39f0a 679f6a43a90e3fd2d0a3d3f6cb9aaab30725038960ccd7dd11d88150d0499a89 8d7b5d1a23ccbb588221820e9e3cdb2303d2fb9916e1e37c7941c1cb3f56d60f 6d413e34aeb8964dd8e8e2bf209668c25312c8b6996d1906357541d1d004e187 691fdf9828012d6885279a24c2abe5e35b2b43c420a52a6f4f049c98b147ef93 8ecf772cb574012cfb4d5404c09bbf3597ba31630330600c90741ddc7dea8850 871b7efe4a9eae095a68f45073dc126e181ddfb293566bc4e1b2f2e66033845c 08c8d1c7cfa92904b3c386f6e5a8d9623066954984ef1fc2666979f16f098d63 6c3b13e49c8f9aaac6188ddc120012f195d14c73d09dbe7a0bfecd98fcc53832 4ded1b8ae0e23674606f229d438f156295822a90fd4c157f5be9f695996a75d8 26beac63eb9e06ef2d65cca8c8996fab2cdaa6b3da536b0c267a02f7eba7e8e8 5552ce1003260e157b8bee34d1c55044463490895c7c25e7c11b3e537a8629de 13dce86342b691cbbf420fc24a52a6c2c84ca9032b879ce0bd2208105db86481 947f6aa51005282b676a3cb028ae9a507f58be77f0151445216c6202055f9da7 8d6e966ea523e20be37277e15000685e61ed90e90c49a8066593f1b1ea0992b6 d61244c74e8f6db07a65074852cf86bb46defddad1222ba502dbc266bde97dbf fce6c457871e70aed258b3f835ca549db049ffa51a31f758356815185eae177b 2ea8354eacf3a6ec19aeb99dbaeeab1ca17cf3149bfeeca6fa7b7037dec21dc6 a304d5e38724f3baf98a9fd4fc654304a108373a37cb60356dd4cbb0b758d18f 1661e8fe03d68b693ca59ca9d6808d633343e506c12120060c3934520fcb2abb 8a439f9843553d529b0703f0dda5d228e598290563c1d39497c1c8c60606abbf 118c97ac7e34edd294572364f127fa3281d1b2cc5b1c859ff6e0f90c03ceda58 439f3cf3acb234dbd8e3fc95fcc29255880a60955472418fb6e92b095c77d2f6 3a198255a4c9b127dd455643528c2a60f65966d1a34882bc2da090fef6a512ab 7e5f1e68dc8be6791897402ee2fc1711bfdeadd6fbfce95cfbe2c1d69f915693 e2dfb1c1d36d9f754796e19787cb31ab31deb38904cf6c38b77f16405fd15505 e727c209a12ea22d553a3c684383f68a384936dff04d6feedaf6f8bd15f5e262 4946ae171df0ca10b088183364e075d014fc26ac0dcd9fa29c8d1288bd270bc5 e0c7834492e1f5d16a50b81526cc1ec73a951d99890e6b33fe54d5763afcb8ba 87f523f1a17f89a234278ee79f6ea69397fa8c67ec53dc91a5369dadb431917e 347620300543c3602c5d644e0c491a55d84a5276d35739167f0140e674dda47d dde66f4ce88077af4bc8bfb07ac716aebe0bbeef4c14422dd5b36916e1f54692 7b800e198bded537ab4213b4b424a0f3d73c38e39bc77cef39d2b6b2660eaa85 ae07bda7816da4e080b30eeafe93a9a24ef522e24ffe3b6c58b0a6f5bd2b1670 0066d2aa07603fd06dd9bd0becc0840ec6dff7cd6315663839696448c11ee2f4 8f13d6207994bde6acf913bef3e654f15c337f5c9d40d8e462f953f35ac1a22f 1a8b33f5cc32a4c71abd0e80c99f8fef77d627b54c6d653bed6ae310789af14e 8908e0806b27f079f75ed21153fcb61b8ed196736335f6fc4712e911aa5754c9 b31ff89348129168eeb3caa0fa9805d706000a67979a9676f6a9fc7fb39cd246 7a6b16013df1ead89cb4963ee693a3256b738b5601ffdc8fc13e72ef7300fd62 c2ef2ca988da5ef626d5b5b628b1ee7533dbd1d19abd0c4745 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 20 /kappa put dup 23 /nu put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 34 /epsilon 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 68 /D put dup 72 /H put dup 76 /L put dup 86 /V put dup 88 /X put dup 99 /c put dup 100 /d put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 115 /s put dup 116 /t put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 68 /D put dup 72 /H put dup 83 /S 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 readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 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521244dc2f9b394ee298535dad9fbbc9a7382e6ba946854e410b30661fa5f605 ab0bce6c0afa751ee7770a8b51d5253dfd70214ae09517c5bea159cbb5116c8a 1ec7413c8f86a222482e3af96cb44612432ba0627e9fc8bb31b1614fcc8f6fbc bb254b84f11b5da124ae188764b31916bafbe888189844c31f6e0ce746bd31d3 28a712fafdeba20b016f0e7df9075297f7838cdd81263836354956ba068e9968 cce701aa0b4299acce 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 18 /theta put dup 20 /kappa put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 27 /sigma put dup 28 /tau put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 79 /O put dup 82 /R put dup 86 /V put dup 88 /X put dup 89 /Y put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 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{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7bcb09b7064e91fa0ded228e42 09aae407a7aaca60b1076299ac4abd23ef02f108765f0e3d91f92f3afbfded37 2fcf6e4b1416901517da8f2fb3c9fe7a87bcbe6fd36cd5b5823fdb74229036a6 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97505648ae46ae64f6eb6248bcbb09402431f8430b3d17abf939bb2e6b5be93c ccdacafc891afbd6208915f699718f9f28dd7fd8ffb970ae730068cdfd55d9c1 484def27dcf80a781dea533075699686a3c973612833a674358b7cb602283520 42c9a67d4b2bdd8a1919cc39a22a8b4efae8043e 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 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86056a19e41ea8c494dc11443052ebbbf183261e04463dd03431c12fb6a313c7 11d94b5be166c78e696b1b02d66023ebe5d77af96affac7ec1a7828551d6b2e0 55dc51d5e94c04d2329deb52d5bc26285bb6a472bf3a472151841fbf9ba3b283 1eed08c251a4f5c0b2c74c8d0a2c9259685abca76d1f57b8d461781278a7fdd2 45be8413d35546bf74809dc7adf8432fd22e20e0dc4da429f6cb1b2a1f32cc4d bf9bba4f0275cb7ba9e90e9f3d24c45898afb6d8c8cbe5bf1664e53f26e000cd b6feaec3c46a21cacea3439a79f6e69f4c85c95befe0dc31209c07acef972805 5ac83a7edff6e33ea690f0858381548ca25a23dd19e90ec53b8aee1f21505d7f 6e9a3cb9b28504b99ff0e78683ee462af35f7bea6b61a341575e14411d8ee136 fa63b2fc16bf86426fc6b8b9249902c3843460fcf97d53b175b0920c361a742b 82ddec08093b280e05f682cd22c4ebbb11e0dfbf823454d260da27ea3d767051 bc013b0d8a6b47482dd5adfb62b870c7b86ddb9b4e9e921ca7978ef738c5f7cd 42d15347de510caad74734e2c15805718c7171abbca95e1578c495e7b801745c 782aa53deaec049ac8182794fe76839a91ffaf28863db01a405619263ed79ab7 e84c38c5d966af9c94b93f952c6ed86adb5ee9a9f9525f8284c27a105c72844a a5d422755354761cd9d2306d199dfc201d14ffb7e3d37ba387fa1e39aecac59d e59b738ba193f0686cafa9e1e66f65362097dab2b33cb202e6773dcde18e871c 18e4cae958ebfad534b835a4caa30dbdec6f7e078d7df0090e86e4e31aa5d559 16b8c6dc5c95dede458bb26486bbed062c58311443001cf21305c0bf8d7401a3 f790369f170f619c1296fd00cecf91872d763c7407521cb5856d570ab49e07c2 4ad0544c7ef733680a28c37a2b46f7b9441ad359e992d8113bdd46337d1e5bce a734b97bed3249f334e8eedcd9b0afcc0fabcabaec5fa52b8231cbedfac4503c 3dfe46cc8f7c2088686a6a0e46aed04e0cb8702b3bad1abcb645a80c7216200b ca9b6d193a9c39e6c7a2a314cf76f1ab164719f7a8a06dd5284cf2c5037cd308 c79a22c33818eeb3d7eea0165460a0ef01cbac2aec5bbe488444ea1c02a9dca2 dbe3ce29aec9a33e111c946bfdb1606c3ee2837234223203c05207f002625a75 f9cc885f43903d68167b31bc5d2cf49f613c3549b759177661cb578bc6e47cd4 66d322b84a42f9236f20b6bf30f1b51cb07c057dadbcae0fdab5aed439ee84cb 064431325842e373540033e934a26cd4d3c802f24cb985e514aaddec6434054f b2fcd84570783f8b960eb57d9043a7b494daf0221a2ebd2ead945ff65b38d8e6 2690b7f91687fc2210c8989e123fdf5c0ccdf1bbd5623903ee25359886b3a769 ff14502515e421c526e0a85f3b55a9d210c803cf488424ea79c029218c6df9fb 710965ae27d7df397fa4f2c67e23330e871f75360e5693c16cc9309d15fd971b 338ea0c64a11f7e8ccd2d329b4427933750b1b240f065263469d803b174b03f9 1283d02411063d2849a7426b4ea36b41feca0d60d70ead5a3d7aac22c7560bab 3534a86e23d4c579084a5389d01036d9d254a4b3967bc1e5e7df42eef187e9b5 d522a9e7bf2219cb336d7c4ead31dbdf01f94e54ffb880193613c4dc62d43cad 72923b2d672a6205e3da2a6876dd7b3981acdf90f5ed59b7963d3f430b9f1c30 d13bd4a12f4b1f9ab9f87556f17c1c829a693cb1346541011e243305eb5f1c66 542c68cffc1dd0b4cc0c22f0c21c50fdb13222d37b8bb859dce0d9f599ff5097 d884cd944c9adf50bf1f75f4418104c53cc55f4bc95089b9454a4776eddc7176 9c4a171acab83513b92f86a94d41918dbc4d8704cfbf89c4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306462c563d51ece66fcc9c831843ecae 1fefc1a232e2724f7baee428ae03aadb95c3035345c15e9922fe49e1f2cfc980 237316572dbc57064edac9b0db8913a5e2d45e97e19a91435ccf8adfc835b585 48e74b291446d689c7f2f8c4325e8356e974ae30c3e2977477baeaa33d141fb7 80f59351e84bfc88c87b3a4a1d25e168b9d134554f6a581378c7d2d6eca8ac09 045cc3a5e0ed86f147133f094029e3483bebc81cfde69942cf645ea20d0a2b64 5140ccc2f9cb4a3d969f4b0a79cd3329b440dfcff5285494406f3dd08d804c86 df191e57232f6f1f83df6430f214e03fa5412b1e13d83c60c52a698bc9a38159 19a64162af7b83a9468fae9507c6cb55ea80df8c696dfbc3296c663902d77e89 a181502627281181ac8624f65be9de5fb32f056cc7dd7cbc7366a91717b5892a 34ef6b441871c6993da3a81afc9bf70ff3842a21a29c0e49da1ccba37dd6b920 2702db510b8b1109acf4c27ee8d676bdbd16abe189f34a9b61532eb777457698 cee0561838eaab2d3939c5093afbb215bac433d1918c739b62566906bb2187f3 378521fb52e70c18886e1aa15f53a1f8a169528cf2ddd54c203613ff88e619f2 6c9c50c2c3b8b8c868a88afab1dc8472e7b6f3f992a161723a3c0904865a7c42 3281601eee91f35222c4a71f343739f102eb43145a47e4fac3bd666e4c114a90 5950618ecb1bdc29f90f6ebed1d8325fe6b52e14a8870e9b4bb088e585c71b91 493c12845a101937e3473ac5e9ae24f7c358f06c8b42dee8ef2a1a7a9f536037 57517f2fb6da0ea305d9d20cc74d922ec4b95b8b299459b71825f6f67abee3a6 f5267c6283c7c62aa8d36663071f18e1a3f0b35dcd88d739caf8dbc344630a28 7f583f037768d861f37d7929f248146b5f31ed9f61ef0a9659b50f47ec328516 9fd999b19687e50303557945476fe9845e5c4780045d84d7df253fe61bf69607 fd277a265296b02b4e4b35884f985d29521ee7327887d983bb92dd84ff646661 2b348b5e558d3bc65047afcb202750ea6e9c18a769a4e945e0954787ee65948e 7e8e443a9f2b9f5408e0febf523423b2200166ade223570bd17a6f7dd0386f3d 2246ebb40648548e0a3ff7bab6637a16137c24b042010a3cce2ba9afb9317fcf 4a5b893c4915859ff2b53a77ff0334966f7a234ea8a4349c3e048acd6876f5f3 17b9c238f37ed4231b5e8b661ba52c32821de47f7a0f6fa9c7e0f4bf09bf98a1 8008087aa44eaf37894e83891f552626f1f46563b5188ad949521e1a398eeba3 b9b8f4ac3c24785d50bdf01e5c9b7e4ea1d6b7b6c8019d2d5f353cacf216e30b 71f09d9b95805210964ccbf8f2e30aa04ac3a3a57bde635c9d2be1f5c8f64ad6 19764c72aca8152a51003bc396bce21a56c29306bccc36a37d816de2568e7794 a8f80d857132a3dbaf3ef75409cace85e1b85a8233ef2757a507158bbba8f5f6 d9c08ab4ee39f33a1c1a41ff2b8e81320050b6c4c167596b93918824a65fe1b0 6e7dcf5d7e128a77e5509f3a3a2af6f71de243cccfa5788088d277175e59bd61 a3b5cdc10cfd232cc14682d3b37d3aca68df524af6f38511e5627286034a7c08 1c7596bfc3adecc7d1868cb9d645f8cb61041bccad92249142542934977000c1 bfbbaf570bf1a3fad2368d1e6480ed485642acd1d44258a885562397035dc979 b08877eadba7c99963e7d866be89270b10629964b5c88439c08a7721e2fd6a7d 2a03d9cf2d7fa713411824db51a9141a7c3ca37feeb758ab37376d75b9ad8534 6fe75968a1e7f6b9b549b7bbef5da78116a7d029e6e95db78593abf789ab985e 301f5945c1628f591b4867079526cd9c779b05cd30de4d9dbb820ce964cb3acf cf693b39b15335996a208373a9a1cd362e93d740535d4fe06aaef81a77034010 883c098f8fe19617d6a3cc3ccaa63742d3b251b8baa94aba7ebb7f3cad53c3c5 2c626e3918191af1e343757e0fc5f9fa620ce7e655482aaab7303710167e3041 148e3e6aae44ebe904d96a7dea9281fdbdf93b03ccd08a315df83531214f1726 dd6eff4d5f494262983201ee2afd6cc77eac76155fc59d9e42a5c45735a37af6 c3c9c4aa7c535717838a1ce8ca3424188a3ddc2bb7f58483ef08fe9b6ea090c8 bd5a639bb56a54bed34a443f0f1624f13fffd6b4f24024573a6cdc110f2a85b3 f669c706b0bcf205ee9ff8342b38525e9cbf1f1b772a71c7718b30bd59f46490 dd92c121c9fd0b99edf33c57611ce19ca35fe17079c90ce99afdfd9227184562 f4e2dc14aea6d0989a8f01f17c0983ae121614d8f578d34ead9c05a88007bc4f 90e135d97abf57c1e32fd94ed63ceeddab6c1d42f3238e6cf85a063d1239a1d9 c5de6f9e7954b873ccef98d8b44f1761e66da28b9759a24f181c9f7ca8ca190d 4d5a52b1286ad43b5f8caebe64283da13e6a9e66536a821ebc1b50e98073d79e 335c244c2b8efcd7c0b223983db1608d6f1837ae6f73d970e567960e7e03d1a6 5f7dcaeecd4f9afd0266592ed051f800ee3d5a8954460f3f57a9fb9716f4dca2 616d5e77e19918f2b1c290fa9d049267df21a4b33a06e29c758e0ecac9746be0 b7988da1634f2e7162c2c483f1c8d78eaefc94e907d3bcc79cc389979ab0dc15 bf1b2371fe907e9c6f46e26260566e38ed55175ce116e4da7024db03b6657b44 1543e575e850440d7613b96baa8320e2cde5ab834d1f333a9a749c3ab079546c 3429c90c61bfda4b758861c2e351866a18c4d14d3bee4d863edce298231a71dc 9e4c701ac2d01fead65c2244a81865874b1c22125e9f11720450c10366eb6eec 694ba3acd45ea6f9cda354cc938222a523494fa570ba76d359afd28f6ca82c35 dc9890f6e09346d93734ef8c82d7b62344fb8103a1fe6f84fb56f55e1969c4bb f61c916f5fc7aaf919d620ed2c25d2bac648ede51f981afe1d4ecf8263830258 75069803a3032b0fba0522 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 64 /at put dup 68 /D put dup 70 /F put dup 74 /J put dup 75 /K put dup 77 /M put dup 79 /O put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put 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 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5 2d2e7bb57142033993f9c08c315abade8dbc4a732e84e142d3bee51557910e12 cd8aa37c459a5e6b7f5269f59078aba3be4641a11ac48d0b625c8325b38ec08e 4c9e5e7fed976a5650d99d82114f449b9ca14c4ec957702295a39a93ef93f618 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175f591349d64cc327d1c4a4d3a0c218980db66e6cad2e995afcdd326ea708fb c21e14d8b3ba1ae1f35c55569f6b7a8dac74a517aa63e872bac0d5d6306a7a42 b947ded05bfd85cc8004ac8ecaa90f50b38e85c19a13cadf4f1f7ee55c1de9e7 867d8911d394a60b2f2309847d3d63939dd38355fee3ed2b9534a14adc626bf5 4c6c615f35b23a13fc86df13ef8458beddc17f95d49633d714f6012b970c736b aa9e805328caa009c74f32171a4514d5579c967fdd443d99838597772b085ddc 1d00472ffecfda72de6142dab03b70402ff223fdd28c3819d86a89c477c2b858 3ed8548db4aa2714f105457d6ee07bfb2b5cabd472899165b24ad4066eeec08c 8a243f2da4c26c0e1680b7f9b71245797ea2676edbab4bdf4d55c676c659a9ce e79568566669e88b8d0266b89851c28b87fc5c2ac6dbf932415bf6bc56314ebf 73d1772f7cea6e7311f6dc0d7951401f78710464fce5bf374121846bc35a03c9 5f7438484be6436d488f011af2f9533a8c14d78d293a110c007a8ca5663718ca 73e90c0e6b8aba51a4c374248e80a38b10b0a28f19b547c53b98fa0f1a1ca33f 5d687e227ade04ce4c68cd1ca9d564d1a5f3431a313e7ff7e309f6f0229e5409 3a9f0eb906b1cf1641775d21f0441d5bf322df0bd084ce01fb3fe2bcc34389f4 8d08b277d894239c260dc8b8d1c0c7d3232cbd7c0862bb47588d7c92bfdf14e0 3c2bbcea7145bec1fcce53fad8d0c16a8eb08898cdbd69b5c31220b4950e5171 c5a6812811764e6b58e7c1c095c48a66dae0e6534c5ec8e3ebb9c07fdd7f4a69 a1b3234d9a13b44a9e66c4d312080783ac07581c4a6947d00d3d485680d55b0e b19aeb260d3e115882016612f984aeafc461a81eaeec7810247717aae2718083 3fa58ae704e9ddbdb5e40964629f6ac302f6f22035f98172bc1d18731d33cbf6 1df87ac0feeb3b5806d29ca829a964c792fc326f58c35ba69ea992a6c709c389 f6add6161bddcd8fdc7b5d1ae465cf8c43ae3516590bac9102063ee71c91e7dc 4a38af748170fba1ca367a1e3f6b5488445654a54838a280d74cfc2fb60166cc a89c586ed9dfb65fe02b5122184ea9133babed72eec62b035cfd92680e1bb332 8cc64a76b5964514de398b7f14a7f7469c10c2fcd5967267cff407537d84695a 376eb58a392bc3c7ca03bfc2ed01f9cbd3ae0d22e86ca8c55bd2b367e785f56c 4f5ca1acfd2b26195dc4c06d96c4b09f22c8438b01e139153645917c7f378610 60da19102926eab32b7159671631c19e128dc4b388e5eb4a865261623d25fc23 41d86d3398c4e131be1b1c7cc6b558939895a7d0cf00d5d1f4cf7cf0675e92f8 92ceb1a489746159cc3294e542494ae937371e1bbde1820735dfc6e5962445df ecc520d2c96823d52e6d2b1557d418be3ef313bc6f005250845654f7b2f87e84 37f341f876f821ea5a8a7e4fca9c8c0f823508c54adfa63bd3a07134a147e1df c6df9ca58ea0d7e42cae4156e4868313b064362520f4893e99e400bfbf74adcd 13cc86c383f3b9b6fbe14e7f83585c54cc107362507d317b6ce2873a8440b169 c9e68aa07eb268804c8a6386c3de174ca697e572deed64c35f86d38cd9cf6b4d 97fd647e6d32d727856801f25f6f90990d1dfb6b091fe428e643f99ee2c9a5ca 20bf1c9857a34a81f046e84cbc02be6efd9b8188298c2ac2ea40ffb08a68b29b 5b70644ed3cdb9c66e76fda2ccd600b989bdcb9135dc3c5feb4385d9bf5fa2ec b261e9856dc0c06d1bd1b20c2c59795264db836404391605e6541dc8fc28a65e 4a3cc2a25eabd50d487af4a9adf2383dcb5e33f609fe0f76497624e380032e8b d4f6bf246beca6a5d8ee65b5f417001bc0f4e18f93b4ff555db31724f469092d e57d6d35ec3c581f98ab6166bc1664563a89590e1aa5f86243e7d1dcb3cf7482 cddc576d86590e442e32456189dc976bc6aba8e45507fdd47191439ffcc64633 bb2fdcc77bd91074d7eda22cc7ae409155c9ca33ac034183d66be72bb81ee85c 4e60d3fff8491ee6ad2ff1547b7cb74af296b1afa01f45707f712f9506a9abf6 7420ec64fa73e298bbc4f46b6df198f8d10a80842d099413d28c02de001a6d37 2044dec5bff67ad092cd37b1c8bd545b65f6046d2181fce64ef586d694682c34 1324b8e0912cb6e8c99a23fad740b14528f6a7877bb6b59ae2dac8e24c94271f 6d0b104632046eb8e836b73d0375d8f5754a30551ccc8beee580bb7dd09251f4 f6a4a4ae3a3c40db1d627d4ac57ef980b6ddb4d420f819d181588982491f6463 131b791d6c7f6e01fa33e299b87c75ffb370647cd901eb33527afb3564090ae5 1d77101c22a8352ee1b7ba5ccad1216a35a1aba82ecd1a0b489816d1347b27b9 66466f2fe158fbffefbe0f993dbe7512819b312015cae22f0001803e617891c1 bd06ea279a591efa6cd7200979bddb4015d24a2084078d6f7375f3ab1b895fd1 ca291c9fe16f6687e3a90c88b7acaf13273779b83178aa8c4b4d09e6d33a4a5f c3c607cc6bd9134ffb86064858f6d10e7247c36ddbbd99304f8dabfececa50ff 70f9ce33dcac34779710ceebe06954e12c19717eb1df77ad64a5de966bfe7d9c 36a1b8513265db 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 59 /semicolon put dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e50e42374ab0a611be 7cf8003531f4120ca0b862a73354c6ce6be74188ed6f51ace718440ffb32dabb e4026cba59d2d22ac89be63c49fbc87c5cbbdf8aa68f13753f59578149ba446d 745801a8d99ea744e1413fcb2f4c3295d16d2aa16f044ebe774ab57d42ce7236 85f2579bc22a510175710e7e7f3a65022809cfd15f9debd87158a5d2fb370e98 edafa99af65878536a75985bc70cd35e823627c8d92ba9953c7356d1561e275e afcb9bb730a43692e3c2bf0738eca8d3a77c3568c0a86fa32b214dc86c9d363d 778492033829bdc00c8ede8127fa3ce157c203d709f1f36190092eeb9082de23 41b3df9b7935b138d8fb22da63989c48b92b9e6adae45b58925336f96b831605 c3c2944c64492bdb7b2f67089209ed3825b5b0a933a032606d101b4e3154bc16 80df6488ddea2a0cd4fe694a84fd4e4e434f70a0bca1cf6fd2ca595a59e8881c 056346f88c2fbcbcd8c57c9d7e7b50385ae33ebd87bb3120a271d3b2402ffc38 527e73367af2063720a1cc836e1a9ec07090736eaf1053771d863750623824c2 ff00bc502029994effb1350ce3b19d1893d1050437ca82bb29b4dd24026d05f0 6644437be6fd8073bc1573ef03c82ccc34b72f820deeef4801fbd9e5b105ddad 6f1dc07c47af2fcc3dce75f9480cda66f59a541461178534df4e8566249a8cc4 2301fd9329735522bcae89af98ab9df4bfa56562931ba08edf41f4050b446f24 3a661fae8db1f017db2a92415039cab4a4f03ccc7fd17d56a11c2e42104fd2be a9bc9c900e41357ef62026e862f58841c8d910ee7e574be3db640d0454c05578 2522fc3b1559eda2fae74d98b9d30d523c6e49ca4abc971d7fdca973fb34d44a 3a8ed082d728cc4b2248c3bd049d0707e8e6fdc2598ef2dcc4843dfa28383298 fdd106724a93a9f676529c579093b302767168b71ea6b17d6cabf53b99f363ec eb61cf59dc989641d8862c229a44ccbd7059e892aa55e04d5c70424d6a834fa5 6b0f9d4e4517ced8c57271c64f28ca3061c62f5ee4183895c033fdbff6ef6052 19ae98bbaa399b6b3c32878603998a1e580a7fdfa870a6803787fde6456103cb 7f1fe2c78564ddd4a019cfed9354065ffd4bd5246278cf1c43a07cad7cb4d685 bce090fdbd11e7c5c54ff476d9a2dea087376ae355a4e820216f11b427669965 93c325c3eb09ead4ccd131b61da6887e982b4a8ccdffefbe463cc7386a0d9368 b3b3ca4399758a7cf8f23dce6fe3e6255a86b0886f6c752c7247da927085bb84 e4181653b1603ed93e39041909ff065852c0d19581b331745130779e97ca47dd 97f91696761966f5817fd7e2acb1784fb51d040bb2c2b8edc5cbf0f2a69b396c 84de7bfe603cd145605416deeed36f3d12fc82a69515553925163d5de36949da 165d84229472763995f4efefdc19a4cb07ba863b3abe04470d7d40bc8ac82cda c1dc28fe4ec5868c47858ff81d98517c13f39e190f916855514e627610466047 cd86d2befb8afc1c7e28a341b1f2da9a6af65618d1478b0c452c207d45aa6362 69436acb6e9db1fc2f7dcccb2c58db3ef32998e30025f2d483f889ed826d6bae 5c5fe356755475c6bae797a3258263e59c3a564781d6bf9a91274ba6205b3ec8 2f4f281bd923ed4a92b1b9adf1577820ac8efe1c242fba9aa970dbc02ddb9e8e 6cfd8ee6fe1fd18591ede212555a31fe6b2f4c5960d3a7f22e67e69524067e48 0805d4a95972ae3aa68f45ca70a1a225e1e41075d63a94798ba43441fc1637ea a275dc240aa2475bbd7c231a80c7e267b5477f69233ba9dac84d33004f44e33b 0489fdf4d6652844c022bd7430e271d5546906d3b8334cdb8613314aaacd85c5 6de52251668d879493b69465de7493641f4bb7b252c0196fc02db53967a291ad 003a4924bd3eca831ac561883a5968c5a8c79451bc5d3ffd8931756fdd1194a1 a32297cbc6291f85c5da8be080e5fe0939007ce515a8a86920ea51086a49c290 9825f27e0953f309911a2207e8c66b29e9e142b86fd5f2d9c22116eccd48a21d bbff41fdeb760c24727ea2e7296723c9ca33221e8a43479887c447c9f443d0e2 be3fdab29faf418a23015bf983222dfd06a4ede3e05ba05e00bd 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 84 /T put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be356c29c3aec91ef17f5d31183b1e489f1fa 559a6693fbdd04d4f7e99886d8cb7cca13d4aa9ceb34a708af22e69ccef0e504 c3997075243585edf60b6447c8d01cffb04b6e3ddbaa7da5891286861322a795 e9d990fd56af2f5c2b35801a0b07874e4ac3170481d232e150443253c92a8b05 513d4a4154a99d91f629ccd30376500f5d16aaa9b203bad6350e4b19424c0e33 75f2949bc1927a6f6221252f8a96618e646aa1b0810753c98becc26b37837775 24bca72b818d314074c1c91f4e1f4148d3d703d12d179ee6970bd55d04aa9a9d 97f63f2c7dbd129ec2ed3ba5f8080270ea5854ea165dbcc061e2f47f1aaf0997 2ac9a689a2a9620b91b53f6b5092884372f5f7afca495f331138d85a97c5bb83 d8072dc88010fc89108b60bc06d4f93c722e8908d7ce3c1ea3c70e9e65edd769 7db17ce0e012ad37d4030f33d30a73fd655b7a2e572f3378ac933dd75082f2f1 68702be19bc60cef6bd5f0ada180d21408c04b7f7db9b6dbaefe09e809a80ddf a5366d10930d3e68ca53e4721ff525853f4c784f2c2c3aa0129a34d9df00debc 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49.8132 /CMMI6 rf /Fd 150[ 39 39 13[ 46 1[ 120 7[ 88 39[ 67 22[ 50 50 3[ 28 12[{ } 9 83.022 /CMEX10 rf /Fe 128[ 50 3[ 50 40 47 45 65 45 52 32 40 41 45 50 50 55 80 25 45 30 30 50 45 30 45 50 45 45 50 12[ 70 55 71 75 66 75 1[ 87 61 1[ 51 38 72 75 64 66 74 70 1[ 72 6[ 30 5[ 50 50 50 50 2[ 30 35 30 2[ 40 40 20[ 50 6[ 55 60 11[{ } 58 99.6264 /CMTI12 rf /Ff 155[ 54 100[{ } 1 99.6264 /CMSL12 rf /Fg 149[ 20 2[ 35 35 52[ 71 19 12[ 35 1[ 71 11[ 55 55 19[ 55{ } 10 66.4176 /CMSY8 rf /Fh 133[ 33 35 40 3[ 25 33 2[ 36 34 43 1[ 21 37 29 24 4[ 36 31 10[ 58 1[ 41 9[ 48 3[ 58 3[ 58 1[ 53 53 2[ 55 35 55 20 24[ 33 5[ 31 40 36 2[ 35 2[ 41 8[ 45 11[{ } 32 66.4176 /CMMI8 rf /Fi 143[ 83 4[ 50 28 39 39 50 50 9[ 66 8[ 60 10[ 84 3[ 77 17[ 66 100 15[ 100 6[ 77 4[ 77 77 2[ 77 14[ 77 28 77{ } 21 99.6264 /CMSY10 rf /Fj 133[ 45 48 55 70 47 56 35 46 44 43 49 1[ 58 85 1[ 51 40 33 1[ 47 48 45 51 42 9[ 57 81 1[ 57 3[ 74 2[ 75 2[ 66 83 1[ 43 81 77 63 72 81 70 74 73 51 1[ 76 49 76 27 27 23[ 46 5[ 42 55 1[ 55 43 48 2[ 56 1[ 45 5[ 55 62 11[{ } 53 99.6264 /CMMI12 rf /Fk 138[ 90 63 64 66 1[ 90 81 90 134 45 2[ 45 90 1[ 49 74 90 72 1[ 78 12[ 112 1[ 120 1[ 110 6[ 60 7[ 122 13[ 81 81 81 49[{ } 24 143.462 /CMBX12 rf /Fl 128[ 49 3[ 49 43 51 51 70 51 54 38 38 38 51 54 49 54 81 27 51 30 27 54 49 30 43 54 43 54 49 3[ 27 49 27 60 73 1[ 100 73 73 70 54 72 76 66 76 73 89 61 76 50 35 73 77 64 66 75 70 69 73 3[ 76 1[ 27 27 49 49 49 49 49 49 49 49 49 49 49 27 33 27 76 1[ 38 38 27 4[ 49 11[ 49 2[ 49 4[ 81 1[ 54 57 9[ 81 61{ } 85 99.6264 /CMR12 rf /Fm 134[ 59 1[ 81 1[ 62 44 44 46 1[ 62 56 62 93 31 1[ 34 31 62 2[ 51 62 50 62 54 12[ 78 62 84 1[ 77 2[ 106 67 88 7[ 81 9[ 56 1[ 56 56 56 56 56 56 56 56 1[ 31 4[ 44 44 27[ 62 12[{ } 40 99.6264 /CMBX12 rf /Fn 255[ 87{ } 1 87.4741 /Ryumin-Light-H rf /Fo 139[ 41 41 43 14[ 46 58 51 31[ 79 65[{ } 7 90.9091 /CMBX10 rf /Fp 128[ 45 3[ 45 40 48 1[ 66 48 51 35 36 36 1[ 51 45 51 76 25 48 28 25 51 45 28 40 51 40 51 45 9[ 93 1[ 68 66 51 3[ 71 1[ 83 1[ 71 47 3[ 59 1[ 69 3[ 71 5[ 25 45 45 45 1[ 45 1[ 45 45 45 45 1[ 25 30 25 44[{ } 49 90.9091 /CMR10 rf /Fq 194[ 55 1[ 20 6[ 35 35 35 35 35 4[ 55 1[ 27 27 40[{ } 10 66.4176 /CMR8 rf /Fr 205[ 42 42 49[{ } 2 83.022 /CMR10 rf /Fs 138[ 65 1[ 46 46 2[ 59 65 98 1[ 62 1[ 33 65 2[ 52 65 52 1[ 59 12[ 85 10[ 42 88 72[{ } 16 119.552 /CMR12 rf /Ft 134[ 83 2[ 83 88 61 1[ 61 1[ 88 79 88 133 43 2[ 43 88 79 47 70 88 70 1[ 79 12[ 115 5[ 119 78[{ } 20 172.188 /CMR17 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop Ft 395 715 a(Note) p 776 715 a(on) p 995 715 a(the) p 1266 715 a(norm) p 1679 715 a(con) l(v) l(ergence) p 2550 715 a(of) p 2728 715 a(the) p 2999 715 a(unitary) 1117 923 y(T) p 1219 923 a(rotter) p 1663 923 a(pro) t(duct) p 2255 923 a(form) l(ula) p Fs 984 1218 a(T) p 1059 1218 a(ak) p 1173 1218 a(ashi) p 1414 1218 a(Ic) m(hinose) p Fr 1825 1175 a(1) p Fs 1909 1218 a(and) p 2136 1218 a(Hideo) p 2471 1218 a(T) p 2546 1218 a(am) m(ura) p Fr 2870 1175 a(2) p Fq 533 1335 a(1) p Fp 573 1368 a(Departmen) m(t) p 1079 1368 a(of) p 1183 1368 a(Mathematics,) p 1751 1368 a(F) p 1802 1368 a(acult) m(y) p 2076 1368 a(of) p 2179 1368 a(Science,) p 2523 1368 a(Kanaza) m(w) m(a) p 2957 1368 a(Univ) m(ersit) m(y) 516 1517 y(Kanaza) m(w) m(a,) p 975 1517 a(920{1192,) p 1395 1517 a(Japan.) p 1699 1517 a(e-mail:) p 2007 1517 a(ic) m(hinose@k) p 2431 1517 a(appa.s.k) p 2752 1517 a(anaza) m(w) m(a-u.ac.jp) p Fq 551 1634 a(2) p Fp 590 1667 a(Departmen) m(t) p 1097 1667 a(of) p 1200 1667 a(Mathematics,) p 1769 1667 a(F) p 1820 1667 a(acult) m(y) p 2094 1667 a(of) p 2197 1667 a(Science,) p 2541 1667 a(Ok) p 2655 1667 a(a) m(y) m(ama) p 2939 1667 a(Univ) m(ersit) m(y) 607 1816 y(Ok) p 721 1816 a(a) m(y) m(ama,) p 1031 1816 a(700{8530,) p 1451 1816 a(Japan.) p 1755 1816 a(e-mail:) p 2063 1816 a(tam) m(ura@math.ok) p 2739 1816 a(a) m(y) m(ama-u.ac.jp) p Fo 1749 2185 a(Abstract) p Fp 303 2352 a(When) p 564 2352 a(the) p 717 2352 a(unitary) p 1034 2352 a(T) p 1092 2352 a(rotter) p 1347 2352 a(pro) s(duct) p 1684 2352 a(form) m(ula) p 2014 2352 a(con) m(v) m(erges) p 2418 2352 a(in) p 2520 2352 a(op) s(erator) p 2883 2352 a(norm) p 3117 2352 a(is) p 3204 2352 a(discussed,) 303 2465 y(and) p 485 2465 a(the) p 646 2465 a(obtained) p 1025 2465 a(results) p 1319 2465 a(are) p 1476 2465 a(applied) p 1799 2465 a(to) p 1916 2465 a(the) p 2077 2465 a(unitary) p 2403 2465 a(group) p 2666 2465 a(generated) p 3086 2465 a(b) m(y) p 3217 2465 a(the) p 3379 2465 a(Dirac) 303 2577 y(op) s(erator) p 670 2577 a(and) p 846 2577 a(the) p 1003 2577 a(relativistic) p 1451 2577 a(Sc) m(hr\177) p 1626 2577 a(odinger) p 1949 2577 a(op) s(erator) p 2315 2577 a(with) p 2522 2577 a(suitable) p 2861 2577 a(p) s(oten) m(tials.) p Fn 3296 2577 a<2121>p Fm 59 2845 a(Mathematics) p 731 2845 a(Sub) p 923 2845 a(ject) p 1140 2845 a(Classi\014cation) p 1823 2845 a(\(2000\).) p Fl 2209 2845 a(47D06,) p 2538 2845 a(47B25,) p 2862 2845 a(81Q05,) p 3192 2845 a(81Q15.) p Fm 59 3015 a(Key) p 287 3015 a(w) m(ords.) p Fl 646 3015 a(T) p 708 3015 a(rotter) p 979 3015 a(pro) s(duct) p 1338 3015 a(form) m(ula,) p 1718 3015 a(Lie{T) p 1960 3015 a(rotter) p 2231 3015 a(pro) s(duct) p 2590 3015 a(form) m(ula,) p 2970 3015 a(unitary) p 3308 3015 a(group,) p 3607 3015 a(Dirac) 59 3135 y(op) s(erator,) p 479 3135 a(relativistic) p 959 3135 a(Sc) m(hr\177) p 1145 3135 a(odinger) p 1493 3135 a(op) s(erator.) p Fk 59 3468 a(1) p 301 3468 a(In) l(tro) t(duction) p 1243 3468 a(and) p 1555 3468 a(Results) p Fl 59 3687 a(Let) p Fj 231 3687 a(A) p Fl 334 3687 a(and) p Fj 520 3687 a(B) p Fl 629 3687 a(b) s(e) p 759 3687 a(selfadjoin) m(t) p 1226 3687 a(op) s(erators) p 1654 3687 a(in) p 1765 3687 a(a) p 1843 3687 a(Hilb) s(ert) p 2176 3687 a(space) p Fi 2434 3687 a(H) p Fl 2549 3687 a(with) p 2768 3687 a(domains) p Fj 3151 3687 a(D) p Fl 3235 3687 a(\() p Fj(A) p Fl(\)) p 3413 3687 a(and) p Fj 3600 3687 a(D) p Fl 3684 3687 a(\() p Fj(B) p Fl 3801 3687 a(\)) 59 3807 y(suc) m(h) p 275 3807 a(that) p 483 3807 a(the) p 647 3807 a(op) s(erator) p 1037 3807 a(sum) p Fj 1239 3807 a(H) p Fl 1355 3807 a(=) p Fj 1459 3807 a(A) p Fl 1547 3807 a(+) p Fj 1638 3807 a(B) p Fl 1745 3807 a(is) p 1839 3807 a(essen) m(tially) p 2303 3807 a(selfadjoin) m(t) p 2769 3807 a(on) p Fj 2900 3807 a(D) p Fl 2984 3807 a(\() p Fj(A) p Fl(\)) p Fi 3148 3807 a(\\) p Fj 3229 3807 a(D) p Fl 3313 3807 a(\() p Fj(B) p Fl 3430 3807 a(\).) p 3536 3807 a(Denote) 59 3928 y(the) p 222 3928 a(unique) p 533 3928 a(selfadjoin) m(t) p 997 3928 a(extension,) p 1451 3928 a(i.e.) p 1617 3928 a(the) p 1780 3928 a(closure) p 2100 3928 a(of) p Fj 2206 3928 a(A) p Fl 2290 3928 a(+) p Fj 2377 3928 a(B) p Fl 2483 3928 a(b) m(y) p 2613 3928 a(the) p 2776 3928 a(same) p Fj 3015 3928 a(H) p Fl 3104 3928 a(.) p 3172 3928 a(Here) p 3397 3928 a(w) m(e) p 3535 3928 a(include) 59 4048 y(the) p 233 4048 a(case) p 445 4048 a(where) p 732 4048 a(the) p 906 4048 a(extension) p 1343 4048 a(is) p 1447 4048 a(not) p 1626 4048 a(strict,) p 1915 4048 a(i.e.) p 2100 4048 a(when) p Fj 2361 4048 a(A) p Fl 2460 4048 a(+) p Fj 2562 4048 a(B) p Fl 2679 4048 a(itself) p 2921 4048 a(is) p 3025 4048 a(already) p 3375 4048 a(selfadjoin) m(t.) 59 4169 y(Then) p 319 4169 a(it) p 422 4169 a(w) m(as) p 614 4169 a(pro) m(v) m(ed) p 936 4169 a(b) m(y) p 1077 4169 a(T) p 1139 4169 a(rotter) p 1421 4169 a([T]) p 1583 4169 a(that) p 1799 4169 a(the) p 1973 4169 a(unitary) p 2322 4169 a(pro) s(duct) p 2693 4169 a(form) m(ula) p 3056 4169 a(in) p 3174 4169 a(strong) p 3478 4169 a(op) s(erator) 59 4289 y(top) s(ology) p 420 4289 a(,) 1181 4507 y(s-) p 1293 4507 a(lim) p Fh 1269 4557 a(n) p Fg(!1) p Fl 1453 4507 a(\() p Fj(e) p Fg 1536 4466 a(\000) p Fh(itA=n) p Fj 1775 4507 a(e) p Fg 1820 4466 a(\000) p Fh(itB) s(=n) p Fl 2064 4507 a(\)) p Fh 2102 4459 a(n) p Fl 2176 4507 a(=) p Fj 2280 4507 a(e) p Fg 2325 4466 a(\000) p Fh(itH) p Fj 2497 4507 a(;) p Fl 3638 4507 a(\(1.1\)) 1181 4690 y(s-) p 1293 4690 a(lim) p Fh 1269 4740 a(n) p Fg(!1) p Fl 1453 4690 a(\() p Fj(e) p Fg 1536 4649 a(\000) p Fh(itB) s(=) p Fq(2) p Fh(n) p Fj 1814 4690 a(e) p Fg 1859 4649 a(\000) p Fh(itA=n) p Fj 2099 4690 a(e) p Fg 2144 4649 a(\000) p Fh(itB) s(=) p Fq(2) p Fh(n) p Fl 2423 4690 a(\)) p Fh 2460 4641 a(n) p Fl 2535 4690 a(=) p Fj 2639 4690 a(e) p Fg 2684 4649 a(\000) p Fh(itH) p Fj 2856 4690 a(;) p Fl 3638 4690 a(\(1.2\)) 59 4923 y(holds) p 314 4923 a(uniformly) p 759 4923 a(on) p 894 4923 a(eac) m(h) p Fj 1114 4923 a(t) p Fl(-b) s(ounded) p 1580 4923 a(in) m(terv) p 1823 4923 a(al) p 1932 4923 a(in) p Fm 2046 4923 a(R) p Fl(.) 205 5044 y(The) p 404 5044 a(aim) p 591 5044 a(of) p 700 5044 a(this) p 888 5044 a(note) p 1102 5044 a(is) p 1198 5044 a(to) p 1315 5044 a(sho) m(w) p 1554 5044 a(the) p 1720 5044 a(follo) m(wing) p 2129 5044 a(theorem) p 2506 5044 a(on) p 2639 5044 a(the) p 2805 5044 a(norm) p 3057 5044 a(con) m(v) m(ergence) p 3594 5044 a(of) p 3703 5044 a(the) 59 5164 y(unitary) p 397 5164 a(T) p 459 5164 a(rotter) p 730 5164 a(pro) s(duct) p 1090 5164 a(form) m(ula) p 1442 5164 a(with) p 1658 5164 a(optimal) p 2010 5164 a(error) p 2242 5164 a(b) s(ounds,) p 2604 5164 a(under) p 2874 5164 a(some) p 3113 5164 a(conditions) p 3574 5164 a(on) p 3703 5164 a(the) 59 5285 y(domains) p 443 5285 a(of) p Fj 553 5285 a(A) p Fl 657 5285 a(and) p Fj 846 5285 a(B) p Fl 925 5285 a(.) p 995 5285 a(W) p 1087 5285 a(e) p 1161 5285 a(denote) p 1474 5285 a(b) m(y) p 1609 5285 a(\() p Fi(\001) p Fj(;) p Fi 1719 5285 a(\001) p Fl(\)) p 1815 5285 a(the) p 1981 5285 a(inner) p 2229 5285 a(pro) s(duct) p 2594 5285 a(of) p Fi 2704 5285 a(H) p Fl 2820 5285 a(and) p 3008 5285 a(b) m(y) p Fi 3142 5285 a(k) p 3212 5285 a(\001) p 3259 5285 a(k) p Fl 3340 5285 a(the) p 3507 5285 a(norm) p 3760 5285 a(of) 59 5405 y(b) s(ounded) p 457 5405 a(op) s(erators) p 889 5405 a(on) p Fi 1024 5405 a(H) p Fl 1109 5405 a(.) 205 5525 y(W) p 297 5525 a(e) p 373 5525 a(assume) p 710 5525 a(that) p 922 5525 a(there) p 1171 5525 a(exists) p 1440 5525 a(a) p 1522 5525 a(dense) p 1788 5525 a(subspace) p Fi 2195 5525 a(D) p 2303 5525 a(\032) p Fj 2408 5525 a(D) p Fl 2492 5525 a(\() p Fj(A) p Fl(\)) p Fi 2663 5525 a(\\) p Fj 2751 5525 a(D) p Fl 2835 5525 a(\() p Fj(B) p Fl 2952 5525 a(\)) p 3022 5525 a(suc) m(h) p 3242 5525 a(that) 205 5646 y(\() p Ff(d) p Fl(1\)) p Fj 417 5646 a(e) p Fg 462 5610 a(\000) p Fh(itA) p Fj 623 5646 a(;) p 684 5646 a(e) p Fg 729 5610 a(\000) p Fh(itB) p Fl 922 5646 a(:) p Fi 976 5646 a(D) p 1084 5646 a(!) p 1211 5646 a(D) p Fl 1340 5646 a(for) p Fj 1489 5646 a(t) p Fi 1552 5646 a(2) p Fm 1646 5646 a(R) p Fl(.) 1924 5895 y(1) p eop %%Page: 2 2 2 1 bop Fl 80 312 a(\() p Ff(d) p Fl(2\)) p 292 312 a(There) p 573 312 a(exists) p 843 312 a(a) p 924 312 a(symmetric) p 1399 312 a(op) s(erator) p Fj 1792 312 a(E) p Fl 1902 312 a(on) p Fi 2038 312 a(D) p Fl 2150 312 a(suc) m(h) p 2370 312 a(that) p Fj 1113 524 a(i) p Fl(\(\() p Fj(B) p 1301 524 a(u;) p 1401 524 a(Av) p Fl 1525 524 a(\)) p Fi 1584 524 a(\000) p Fl 1684 524 a(\() 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a(ounde) p 497 3523 a(d) p 581 3523 a(extensions) p 1052 3523 a(on) p Fi 1192 3523 a(H) p Fe 1277 3523 a(,) p 1342 3523 a(then) p Fi 727 3735 a(k) p Fl(\() p Fj(e) p Fg 860 3694 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(B) s(=) p Fq(2) p Fj 1229 3735 a(e) p Fg 1274 3694 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(A) p Fj 1569 3735 a(e) p Fg 1614 3694 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(B) s(=) p Fq(2) p Fl 1982 3735 a(\)) p Fh 2020 3686 a(n) p Fi 2090 3735 a(\000) p Fj 2189 3735 a(e) p Fg 2234 3694 a(\000) p Fh(itH) p Fi 2406 3735 a(k) p Fl 2483 3735 a(=) p Fj 2587 3735 a(O) p Fl 2665 3735 a(\() p Fj(n) p Fg 2761 3694 a(\000) p Fq(2) p Fl 2855 3735 a(\)) p Fj(;) p Fl 3513 3735 a(\(1.5\)) p Fe -66 3947 a(as) p Fj 58 3947 a(n) p Fi 144 3947 a(!) p 272 3947 a(1) p Fe(,) p 436 3947 a(uniformly) p 881 3947 a(on) p 1020 3947 a(e) p 1060 3947 a(ach) p 1239 3947 a(b) p 1279 3947 a(ounde) p 1526 3947 a(d) p Fj 1610 3947 a(t) p Fe(-interval) p 2038 3947 a(in) p Fm 2157 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a(e) p Fg 1112 4454 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(B) p Fl 1410 4495 a(\)) p Fh 1448 4446 a(n) p Fi 1517 4495 a(\000) p Fj 1617 4495 a(e) p Fg 1662 4454 a(\000) p Fh(itH) p Fi 1856 4495 a(\000) p Fj 1955 4495 a(i) p Fl(\() p Fj(t=) p Fl(2) p Fj(n) p Fl(\)[) p Fj(e) p Fg 2327 4454 a(\000) p Fh(itH) p Fj 2499 4495 a(;) p 2543 4495 a(A) p Fl(]) p Fi(k) p Fl 2721 4495 a(=) p Fj 2824 4495 a(O) p Fl 2902 4495 a(\() p Fj(n) p Fg 2998 4454 a(\000) p Fq(2) p Fl 3092 4495 a(\)) p Fj(;) p Fl 3513 4495 a(\(1.6\)) p Fi 639 4640 a(k) p Fl(\() p Fj(e) p Fg 772 4599 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(B) p Fj 1070 4640 a(e) p Fg 1115 4599 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(A) p Fl 1410 4640 a(\)) p Fh 1448 4592 a(n) p Fi 1517 4640 a(\000) p Fj 1617 4640 a(e) p Fg 1662 4599 a(\000) p Fh(itH) p Fi 1856 4640 a(\000) p Fj 1955 4640 a(i) p Fl(\() p Fj(t=) p Fl(2) p Fj(n) p Fl(\)[) p Fj(e) p Fg 2327 4599 a(\000) p Fh(itH) p Fj 2499 4640 a(;) p 2543 4640 a(B) p Fl 2622 4640 a(]) p Fi(k) p Fl 2727 4640 a(=) p Fj 2830 4640 a(O) p Fl 2908 4640 a(\() p Fj(n) p Fg 3004 4599 a(\000) p Fq(2) p Fl 3098 4640 a(\)) p Fj(;) p Fl 3513 4640 a(\(1.7\)) p Fe -66 4852 a(and) p Fi 448 4992 a(k) p Fl 508 4925 a(1) p 508 4969 49 4 v 508 5060 a(2) 566 4992 y(\(\() p Fj(e) p Fg 687 4951 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(A) p Fj 982 4992 a(e) p Fg 1027 4951 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(B) p Fl 1325 4992 a(\)) p Fh 1363 4944 a(n) p Fl 1432 4992 a(+) p 1530 4992 a(\() p Fj(e) p Fg 1613 4951 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(B) p Fj 1911 4992 a(e) p Fg 1956 4951 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(A) p Fl 2251 4992 a(\)) p Fh 2289 4944 a(n) p Fl 2336 4992 a(\)) p Fi 2396 4992 a(\000) p Fj 2496 4992 a(e) p Fg 2541 4951 a(\000) p Fh(itH) p Fi 2713 4992 a(k) p Fl 2790 4992 a(=) p Fj 2894 4992 a(O) p Fl 2972 4992 a(\() p Fj(n) p Fg 3068 4951 a(\000) p Fq(2) p Fl 3161 4992 a(\)) p 3513 4992 a(\(1.8\)) p Fe -66 5188 a(as) p Fj 58 5188 a(n) p Fi 144 5188 a(!) p 272 5188 a(1) p Fe(,) p 436 5188 a(uniformly) p 881 5188 a(on) p 1020 5188 a(e) p 1060 5188 a(ach) p 1239 5188 a(b) p 1279 5188 a(ounde) p 1526 5188 a(d) p Fj 1610 5188 a(t) p Fe(-interval) p 2038 5188 a(in) p Fm 2157 5188 a(R) p Fe(.) p Fl 80 5404 a(If) p 171 5404 a(the) p 333 5404 a(conditions) p 793 5404 a(of) p 898 5404 a(the) p 1060 5404 a(theorems) p 1472 5404 a(are) p 1628 5404 a(not) p 1795 5404 a(satis\014ed,) p 2192 5404 a(the) p 2354 5404 a(norm) p 2602 5404 a(con) m(v) m(ergence) p 3135 5404 a(of) p 3240 5404 a(the) p 3402 5404 a(unitary) -66 5524 y(T) p -4 5524 a(rotter) p 265 5524 a(pro) s(duct) p 623 5524 a(form) m(ula) p 972 5524 a(do) s(es) p 1184 5524 a(not) p 1350 5524 a(alw) m(a) m(ys) p 1654 5524 a(hold.) p 1906 5524 a(In) p 2020 5524 a([I2]) p 2183 5524 a(w) m(e) p 2319 5524 a(ha) m(v) m(e) p 2536 5524 a(observ) m(ed) p 2929 5524 a(there) p 3171 5524 a(are) p 3325 5524 a(examples) -66 5645 y(with) p Fj 169 5645 a(A) p Fl 291 5645 a(=) p Fi 416 5645 a(\000) p Fj(i) p Fh 557 5605 a(d) p 536 5621 77 4 v 536 5679 a(dx) p Fl 668 5645 a(and) p Fj 870 5645 a(B) p Fl 998 5645 a(=) p Fj 1123 5645 a(V) p Fl 1202 5645 a(\() p Fj(x) p Fl(\)) p Fi(\002) p Fl 1456 5645 a(in) p Fj 1582 5645 a(L) p Fq 1648 5608 a(2) p Fl 1688 5645 a(\() p Fm(R) p Fl(\)) p 1893 5645 a(for) p 2054 5645 a(whic) m(h) p 2346 5645 a(the) p 2527 5645 a(unitary) p 2883 5645 a(pro) s(duct) p 3262 5645 a(form) m(ula) p 3632 5645 a(in) 1799 5895 y(2) p eop %%Page: 3 3 3 2 bop Fl 59 312 a(op) s(erator) p 465 312 a(norm) p 733 312 a(holds) p 1002 312 a(as) p 1135 312 a(w) m(ell) p 1346 312 a(as) p 1479 312 a(do) s(es) p 1712 312 a(not) p 1899 312 a(hold.) p 2194 312 a(The) p 2408 312 a(optimalit) m(y) p 2893 312 a(of) p 3017 312 a(these) p 3280 312 a(error) p 3532 312 a(b) s(ounds) 59 433 y(has) p 231 433 a(already) p 574 433 a(b) s(een) p 803 433 a(discussed) p 1226 433 a(in) p 1338 433 a([ITTZ].) p 1686 433 a(T) p 1748 433 a(o) p 1828 433 a(pro) m(v) m(e) p 2089 433 a(our) p 2261 433 a(theorems,) p 2705 433 a(w) m(e) p 2847 433 a(shall) p 3073 433 a(use) p 3240 433 a(the) p 3407 433 a(metho) s(d) p 3760 433 a(of) 59 553 y(comm) m(utator) p 603 553 a(used) p 820 553 a(in) p 928 553 a(our) p 1095 553 a(recen) m(t) p 1379 553 a(pap) s(er) p 1646 553 a([IT2]) p 1882 553 a(to) p 1995 553 a(get) p 2151 553 a(optimal) p 2503 553 a(error) p 2735 553 a(b) s(ounds,) p 3097 553 a(for) p 3240 553 a(the) p 3402 553 a(selfadjoin) m(t) 59 673 y(T) p 121 673 a(rotter{Kato) p 661 673 a(pro) s(duct) p 1029 673 a(form) m(ula) p 1390 673 a(with) p 1615 673 a(Sc) m(hr\177) p 1801 673 a(odinger) p 2151 673 a(op) s(erators,) p 2613 673 a(on) p 2751 673 a(norm) p 3009 673 a(con) m(v) m(ergence) p 3551 673 a(as) p 3673 673 a(w) m(ell) 59 794 y(as) p 179 794 a(on) p 314 794 a(p) s(oin) m(t) m(wise) p 746 794 a(uniform) p 1112 794 a(appro) m(ximation) p 1762 794 a(to) p 1881 794 a(the) p 2049 794 a(in) m(tegral) p 2404 794 a(k) m(ernels) p 2730 794 a(concerned.) 205 963 y(In) p 323 963 a(passing,) p 690 963 a(the) p 854 963 a(selfadjoin) m(t) p 1319 963 a(T) p 1381 963 a(rotter{Kato) p 1914 963 a(pro) s(duct) p 2276 963 a(form) m(ula) p 2629 963 a(in) p 2739 963 a(the) p 2903 963 a(strong) p 3198 963 a(op) s(erator) p 3587 963 a(top) s(ol-) 59 1084 y(ogy) p 234 1084 a(w) m(as) p 416 1084 a(pro) m(v) m(ed) p 726 1084 a(b) m(y) p 856 1084 a(T) p 918 1084 a(rotter) p 1188 1084 a([T]) p 1339 1084 a(when) p 1587 1084 a(the) p 1749 1084 a(op) s(erator) p 2136 1084 a(sum) p 2336 1084 a(of) p 2441 1084 a(nonnegativ) m(e) p 2977 1084 a(selfadjoin) m(t) p 3440 1084 a(op) s(erators) p Fj 59 1204 a(A) p Fl 159 1204 a(and) p Fj 342 1204 a(B) p Fl 448 1204 a(is) p 540 1204 a(essen) m(tially) p 1001 1204 a(selfadjoin) m(t) p 1464 1204 a(on) p Fj 1593 1204 a(D) p Fl 1677 1204 a(\() p Fj(A) p Fl(\)) p Fi 1836 1204 a(\\) p Fj 1912 1204 a(D) p Fl 1996 1204 a(\() p Fj(B) p Fl 2113 1204 a(\),) p 2205 1204 a(and) p 2389 1204 a(b) m(y) p 2518 1204 a(Kato) p 2756 1204 a([K]) p 2913 1204 a(for) p 3056 1204 a(their) p 3283 1204 a(form) p 3507 1204 a(sum.) p 3749 1204 a(In) 59 1324 y([IT1],) p 324 1324 a([ITTZ],) p 668 1324 a(its) p 800 1324 a(con) m(v) m(ergence) p 1334 1324 a(has) p 1504 1324 a(b) s(een) p 1730 1324 a(pro) m(v) m(ed) p 2042 1324 a(ev) m(en) p 2259 1324 a(in) p 2369 1324 a(the) p 2532 1324 a(op) s(erator) p 2920 1324 a(norm) p 3170 1324 a(for) p 3315 1324 a(the) p 3478 1324 a(op) s(erator) 59 1445 y(sum) p 267 1445 a(of) p 380 1445 a(nonnegativ) m(e) p 923 1445 a(selfadjoin) m(t) p 1394 1445 a(op) s(erators) p Fj 1827 1445 a(A) p Fl 1934 1445 a(and) p Fj 2126 1445 a(B) p Fl 2239 1445 a(whic) m(h) p 2520 1445 a(is) p 2619 1445 a(selfadjoin) m(t) p 3090 1445 a(on) p Fj 3227 1445 a(D) p Fl 3311 1445 a(\() p Fj(A) p Fl(\)) p Fi 3483 1445 a(\\) p Fj 3573 1445 a(D) p Fl 3657 1445 a(\() p Fj(B) p Fl 3774 1445 a(\),) 59 1565 y(with) p 284 1565 a(optimal) p 644 1565 a(error) p 885 1565 a(b) s(ound) p Fj 1188 1565 a(O) p Fl 1266 1565 a(\() p Fj(n) p Fg 1362 1529 a(\000) p Fq(1) p Fl 1456 1565 a(\).) p 1571 1565 a(A) p 1679 1565 a(further) p 2010 1565 a(extension) p 2443 1565 a(is) p 2544 1565 a(also) p 2742 1565 a(giv) m(en) p 2999 1565 a(in) p 3115 1565 a([INZ]) p 3373 1565 a(to) p 3494 1565 a(the) p 3665 1565 a(case) 59 1686 y(of) p 169 1686 a(the) p 337 1686 a(form) p 566 1686 a(sum) p 772 1686 a(of) p 882 1686 a(t) m(w) m(o) p 1066 1686 a(nonnegativ) m(e) p 1607 1686 a(selfadjoin) m(t) p 2076 1686 a(op) s(erators) p 2506 1686 a(with) p 2728 1686 a(some) p 2972 1686 a(auxiliary) p 3377 1686 a(conditions.) 59 1806 y(The) p 261 1806 a(norm) p 516 1806 a(con) m(v) m(ergence) p 1057 1806 a(has) p 1232 1806 a(also) p 1428 1806 a(b) s(een) p 1660 1806 a(pro) m(v) m(ed) p 1978 1806 a(in) p 2093 1806 a([CNZ]) p 2384 1806 a(in) p 2499 1806 a(the) p 2668 1806 a(case) p 2875 1806 a(where) p 3158 1806 a(one) p 3338 1806 a(of) p 3450 1806 a(the) p 3619 1806 a(op) s(er-) 59 1926 y(ators) p Fj 308 1926 a(A) p Fl 419 1926 a(and) p Fj 613 1926 a(B) p Fl 730 1926 a(is) p 832 1926 a(nonnegativ) m(e) p 1379 1926 a(selfadjoin) m(t) p 1853 1926 a(and) p 2048 1926 a(the) p 2220 1926 a(second) p 2540 1926 a(is) p 2643 1926 a(an) p 2783 1926 a(accretiv) m(e) p 3194 1926 a(op) s(erator) p 3592 1926 a(whic) m(h) 59 2047 y(is) p 157 2047 a(relativ) m(ely) p 583 2047 a(b) s(ounded) p 981 2047 a(with) p 1203 2047 a(resp) s(ect) p 1537 2047 a(to) p 1656 2047 a(the) p 1824 2047 a(\014rst) p 2025 2047 a(with) p 2247 2047 a(relativ) m(e) p 2594 2047 a(b) s(ound) p 2895 2047 a(less) p 3075 2047 a(than) p 3302 2047 a(1,) p 3410 2047 a(with) p 3633 2047 a(error) 59 2167 y(b) s(ound) p Fj 355 2167 a(O) p Fl 433 2167 a(\(\(log) p Fj 651 2167 a(n) p Fl(\)) p Fj(=n) p Fl(\).) p 961 2167 a(W) p 1053 2167 a(e) p 1125 2167 a(note) p 1337 2167 a(here) p 1544 2167 a(that) p 1751 2167 a(the) p 1914 2167 a(metho) s(d) p 2265 2167 a(of) p 2372 2167 a(the) p 2535 2167 a(presen) m(t) p 2870 2167 a(note) p 3082 2167 a(can) p 3257 2167 a(giv) m(e) p 3453 2167 a(one) p 3627 2167 a(more) 59 2287 y(supplemen) m(t) p 570 2287 a(to) p 682 2287 a(the) p 843 2287 a(norm) p 1090 2287 a(con) m(v) m(ergence) p 1622 2287 a(of) p 1726 2287 a(the) p 1886 2287 a(selfadjoin) m(t) p 2348 2287 a(T) p 2410 2287 a(rotter{Kato) p 2940 2287 a(pro) s(duct) p 3299 2287 a(form) m(ula) p 3649 2287 a(with) 59 2408 y(optimal) p 423 2408 a(error) p 667 2408 a(b) s(ounds:) p 1057 2408 a(under) p 1339 2408 a(the) p 1513 2408 a(same) p 1764 2408 a(h) m(yp) s(otheses) p 2267 2408 a(as) p 2393 2408 a(in) p 2513 2408 a(eac) m(h) p 2739 2408 a(of) p 2856 2408 a(Theorems) p 3312 2408 a(1.1{1.3) p 3649 2408 a(with) 59 2528 y(additional) p 525 2528 a(assumption) p 1047 2528 a(that) p 1264 2528 a(b) s(oth) p Fj 1500 2528 a(A) p Fl 1612 2528 a(and) p Fj 1807 2528 a(B) p Fl 1925 2528 a(are) p 2093 2528 a(nonnegativ) m(e,) p 2669 2528 a(the) p 2843 2528 a(selfadjoin) m(t) p 3318 2528 a(pro) s(duct) p 3690 2528 a(for-) 59 2649 y(m) m(ula) p 295 2649 a(in) p 403 2649 a(op) s(erator) p 791 2649 a(norm) p 1040 2649 a(also) p 1231 2649 a(holds,) p 1509 2649 a(namely) p 1806 2649 a(,) p 1862 2649 a(the) p 2025 2649 a(same) p 2264 2649 a(assertion) p 2666 2649 a(as) p 2780 2649 a(in) p 2889 2649 a(eac) m(h) p 3103 2649 a(of) p 3209 2649 a(these) p 3453 2649 a(theorems) 59 2769 y(is) p 157 2769 a(v) p 203 2769 a(alid) p 393 2769 a(with) p Fj 615 2769 a(e) p Fg 660 2733 a(\000) p Fh(itA) p Fj 822 2769 a(;) p 899 2769 a(e) p Fg 944 2733 a(\000) p Fh(itB) p Fl 1141 2769 a(and) p Fj 1331 2769 a(e) p Fg 1376 2733 a(\000) p Fh(itH) p Fl 1580 2769 a(replaced) p 1965 2769 a(b) m(y) p Fj 2101 2769 a(e) p Fg 2146 2733 a(\000) p Fh(tA) p Fj 2283 2769 a(;) p 2360 2769 a(e) p Fg 2405 2733 a(\000) p Fh(tB) p Fl 2579 2769 a(and) p Fj 2769 2769 a(e) p Fg 2814 2733 a(\000) p Fh(tH) p Fl 2961 2769 a(.) 205 2889 y(F) p 261 2889 a(or) p 371 2889 a(some) p 607 2889 a(accoun) m(t) p 958 2889 a(for) p 1099 2889 a(the) p 1258 2889 a(unitary) p 1593 2889 a(and) p 1774 2889 a(selfadjoin) m(t) p 2234 2889 a(T) p 2296 2889 a(rotter) p 2564 2889 a(pro) s(duct) p 2921 2889 a(form) m(ulas) p 3308 2889 a(in) p 3413 2889 a(the) p 3572 2889 a(strong) 59 3010 y(op) s(erator) p 452 3010 a(top) s(ology) p 813 3010 a(,) p 872 3010 a(w) m(e) p 1016 3010 a(refer) p 1240 3010 a(to) p 1360 3010 a(Reed{Simon) p 1919 3010 a([RS].) 205 3130 y(In) p 342 3130 a(Section) p 698 3130 a(2,) p 824 3130 a(w) m(e) p 982 3130 a(pro) m(v) m(e) p 1260 3130 a(the) p 1442 3130 a(theorems,) p 1905 3130 a(and) p 2110 3130 a(in) p 2238 3130 a(Section) p 2594 3130 a(3,) p 2720 3130 a(giv) m(e) p 2935 3130 a(as) p 3070 3130 a(applications) p 3627 3130 a(some) 59 3250 y(examples) p 477 3250 a(that) p 685 3250 a(the) p 850 3250 a(norm) p 1102 3250 a(con) m(v) m(ergence) p 1638 3250 a(of) p 1746 3250 a(the) p 1911 3250 a(unitary) p 2253 3250 a(pro) s(duct) p 2615 3250 a(form) m(ula) p 2970 3250 a(holds) p 3223 3250 a(as) p 3339 3250 a(w) m(ell) p 3534 3250 a(as) p 3651 3250 a(do) s(es) 59 3371 y(not) p 237 3371 a(hold.) p 506 3371 a(In) p 632 3371 a(particular,) p 1115 3371 a(it) p 1217 3371 a(should) p 1531 3371 a(b) s(e) p 1668 3371 a(noted) p 1944 3371 a(that) p 2160 3371 a(the) p 2333 3371 a(unitary) p 2681 3371 a(T) p 2743 3371 a(rotter) p 3025 3371 a(pro) s(duct) p 3395 3371 a(form) m(ula) p 3757 3371 a(in) 59 3491 y(op) s(erator) p 448 3491 a(norm) p 698 3491 a(holds) p 949 3491 a(for) p 1094 3491 a(the) p 1257 3491 a(Dirac) p 1517 3491 a(op) s(erator) p 1906 3491 a(and) p 2091 3491 a(the) p 2255 3491 a(relativistic) p 2731 3491 a(Sc) m(hr\177) p 2917 3491 a(odinger) p 3260 3491 a(op) s(erator) p 3649 3491 a(with) 59 3612 y(suitable) p 423 3612 a(p) s(oten) m(tials.) p Fk 59 3944 a(2) p 301 3944 a(Pro) t(of) p 746 3944 a(of) p 930 3944 a(Theorems) p Fl 59 4163 a(First) p 297 4163 a(w) m(e) p 440 4163 a(prepare) p 793 4163 a(some) p 1037 4163 a(lemmas) p 1390 4163 a(and) p 1579 4163 a(then) p 1802 4163 a(pro) m(v) m(e) p 2064 4163 a(theorems.) 205 4283 y(W) p 297 4283 a(e) p 373 4283 a(mak) m(e) p 628 4283 a(use) p 797 4283 a(of) p 908 4283 a(the) p 1076 4283 a(comm) m(utator) p 1626 4283 a(relation) 1111 4520 y([) p Fj(e) p Fg 1183 4479 a(\000) p Fh(itX) p Fj 1355 4520 a(;) p 1399 4520 a(Y) p Fl 1477 4520 a(]) p 1532 4520 a(=) p Fj 1635 4520 a(i) p Fd 1685 4403 a(Z) p Fh 1768 4429 a(t) p Fq 1731 4592 a(0) p Fj 1814 4520 a(e) p Fg 1859 4479 a(\000) p Fh(isX) p Fl 2038 4520 a([) p Fj(Y) p 2127 4520 a(;) p 2171 4520 a(X) p Fl 2260 4520 a(]) p Fj(e) p Fg 2332 4479 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(X) p Fj 2663 4520 a(ds:) p Fl 3638 4520 a(\(2.1\)) 205 4765 y(Put) p Fj 1468 4982 a(G) p Fl(\() p Fj(t) p Fl(\)) p 1684 4982 a(=) p Fj 1787 4982 a(e) p Fg 1832 4941 a(\000) p Fh(itA) p Fj 1994 4982 a(e) p Fg 2039 4941 a(\000) p Fh(itB) p Fj 2204 4982 a(;) p Fl 3638 4982 a(\(2.2\)) p Fj 1468 5127 a(K) p Fl 1558 5127 a(\() p Fj(t) p Fl(\)) p 1697 5127 a(=) p Fj 1800 5127 a(e) p Fg 1845 5086 a(\000) p Fh(itB) s(=) p Fq(2) p Fj 2081 5127 a(e) p Fg 2126 5086 a(\000) p Fh(itA) p Fj 2288 5127 a(e) p Fg 2333 5086 a(\000) p Fh(itB) s(=) p Fq(2) p Fj 2569 5127 a(:) p Fl 3638 5127 a(\(2.3\)) p Fm 59 5443 a(Lemma) p 456 5443 a(2.1) p Fl(.) p 670 5443 a(Let) p Fj 845 5443 a(u;) p 960 5443 a(v) p Fi 1055 5443 a(2) p 1150 5443 a(D) p Fl 1230 5443 a(,) p 1289 5443 a(and) p 1478 5443 a(assume) p 1816 5443 a(that) p 2027 5443 a(\() p Ff(d) p Fl(1\){\() p Ff(d) p Fl(3\)) p 2466 5443 a(are) p 2628 5443 a(ful\014lled.) p 3016 5443 a(Then) 205 5607 y(\(1\)) p 396 5607 a(\(\() p Fj(Ae) p Fg 590 5566 a(\000) p Fh(itB) p Fi 777 5607 a(\000) p Fj 877 5607 a(e) p Fg 922 5566 a(\000) p Fh(itB) p Fj 1087 5607 a(A) p Fl(\)) p Fj(u;) p 1298 5607 a(v) p Fl 1349 5607 a(\)) p 1414 5607 a(=) p Fi 1517 5607 a(\000) p Fd 1611 5490 a(Z) p Fh 1694 5517 a(t) p Fq 1657 5679 a(0) p Fl 1724 5607 a(\() p Fj(E) p 1840 5607 a(e) p Fg 1885 5566 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(B) p Fj 2193 5607 a(u;) p 2293 5607 a(e) p Fh 2338 5566 a(isB) p Fj 2454 5607 a(v) p Fl 2505 5607 a(\)) p Fj(ds:) p Fl 1924 5895 a(3) p eop %%Page: 4 4 4 3 bop Fl 80 344 a(\(2\)) p 271 344 a(\() o(\() p Fj(B) p 425 344 a(e) p Fg 470 303 a(\000) p Fh(itA) p Fi 654 344 a(\000) p Fj 754 344 a(e) p Fg 799 303 a(\000) p Fh(itA) p Fj 961 344 a(B) p Fl 1040 344 a(\)) p Fj(u;) p 1178 344 a(v) p Fl 1229 344 a(\)) p 1293 344 a(=) p Fd 1397 227 a(Z) p Fh 1480 254 a(t) p Fq 1443 416 a(0) p Fl 1509 344 a(\() p Fj(E) p 1625 344 a(e) p Fg 1670 303 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(A) p Fj 1974 344 a(u;) p 2074 344 a(e) p Fh 2119 303 a(isA) p Fj 2233 344 a(v) p Fl 2284 344 a(\)) p Fj(ds:) p Fl 80 556 a(\(3\)) p 271 556 a(\() o(\() p Fj(E) p 424 556 a(e) p Fg 469 515 a(\000) p Fh(itB) p Fi 657 556 a(\000) p Fj 757 556 a(e) p Fg 802 515 a(\000) p Fh(itB) p Fj 967 556 a(E) p Fl 1045 556 a(\)) p Fj(u;) p 1183 556 a(v) p Fl 1234 556 a(\)) p 1298 556 a(=) p Fi 1402 556 a(\000) p Fd 1496 439 a(Z) p Fh 1579 465 a(t) p Fq 1542 627 a(0) p Fl 1609 556 a(\() p Fj(E) p Fh 1719 571 a(B) p Fj 1779 556 a(e) p Fg 1824 515 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(B) p Fj 2132 556 a(u;) p 2232 556 a(e) p Fh 2277 515 a(isB) p Fj 2394 556 a(v) p Fl 2445 556 a(\)) p Fj(ds:) p Fl 80 767 a(\(4\)) p 271 767 a(\() o(\() p Fj(E) p 424 767 a(e) p Fg 469 726 a(\000) p Fh(itA) p Fi 653 767 a(\000) p Fj 753 767 a(e) p Fg 798 726 a(\000) p Fh(itA) p Fj 959 767 a(E) p Fl 1037 767 a(\)) p Fj(u;) p 1175 767 a(v) p Fl 1226 767 a(\)) p 1291 767 a(=) p Fi 1395 767 a(\000) p Fd 1489 650 a(Z) p Fh 1572 677 a(t) p Fq 1535 839 a(0) p Fl 1601 767 a(\() p Fj(E) p Fh 1711 782 a(A) p Fj 1768 767 a(e) p Fg 1813 726 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(A) p Fj 2118 767 a(u;) p 2218 767 a(e) p Fh 2263 726 a(isA) p Fj 2376 767 a(v) p Fl 2427 767 a(\)) p Fj(ds:) p Fe -66 1002 a(Pr) p 36 1002 a(o) p 81 1002 a(of.) p Fl 234 1002 a(W) p 326 1002 a(e) p 402 1002 a(sho) m(w) p 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1590 a(B) p Fl 2875 1590 a(\() p Fj(e) p Fh 2958 1549 a(isB) p Fj 3075 1590 a(v) p Fl 3126 1590 a(\)\)) p Fd 3202 1494 a(\021) p Fj 3251 1590 a(ds:) p Fl 80 1822 a(Since) p 335 1822 a(b) m(y) p 470 1822 a(\() p Fe(d) p Fl(1\),) p 704 1822 a(b) s(oth) p Fj 935 1822 a(e) p Fg 980 1786 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(B) p Fj 1287 1822 a(u) p Fl 1375 1822 a(and) p Fj 1565 1822 a(e) p Fh 1610 1786 a(isB) p Fj 1728 1822 a(v) p Fl 1811 1822 a(are) p 1974 1822 a(in) p Fi 2087 1822 a(D) p Fl 2167 1822 a(,) p 2227 1822 a(w) m(e) p 2370 1822 a(ha) m(v) m(e) p Fj 1112 2053 a(f) p Fl 1171 2053 a(\() p Fj(t) p Fl(\)) p 1309 2053 a(=) p Fi 1413 2053 a(\000) p Fd 1507 1935 a(Z) p Fh 1590 1962 a(t) p Fq 1553 2124 a(0) p Fl 1620 2053 a(\() p Fj(E) p 1736 2053 a(e) p Fg 1781 2011 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(B) p Fj 2088 2053 a(u;) p 2188 2053 a(e) p Fh 2233 2011 a(isB) p Fj 2350 2053 a(v) p Fl 2401 2053 a(\)) p Fj(ds) p Fl -66 2273 a(b) m(y) p 69 2273 a(\() p Ff(d) p Fl(2\),) p 308 2273 a(sho) m(wing) p 680 2273 a(the) p 848 2273 a(desired) p 1179 2273 a(relation.) p Fm -66 2474 a(Lemma) p 331 2474 a(2.2) p Fl(.) p Fe 545 2474 a(On) p 709 2474 a(the) p 871 2474 a(same) p 1120 2474 a(hyp) p 1262 2474 a(othesis) p 1583 2474 a(as) p 1708 2474 a(in) p 1827 2474 a(The) p 1987 2474 a(or) p 2073 2474 a(em) p 2232 2474 a(1.1,) p 2426 2474 a(one) p 2611 2474 a(has) p Fi 1099 2660 a(k) p Fj(e) p Fg 1194 2619 a(\000) p Fh(itH) p Fi 1387 2660 a(\000) p Fj 1487 2660 a(G) p Fl(\() p Fj(t) p Fl(\)) p Fi(k) p Fl 1753 2660 a(=) p Fj 1856 2660 a(O) p Fl 1934 2660 a(\() p Fi(j) p Fj(t) p Fi(j) p Fq 2063 2619 a(2) p Fl 2101 2660 a(\)) p Fj(;) p 2283 2660 a(t) p Fi 2345 2660 a(!) p Fl 2473 2660 a(0) p Fj(:) p Fl 3513 2660 a(\(2.4\)) p Fe -66 3047 a(Pr) p 36 3047 a(o) p 81 3047 a(of.) p Fl 278 3047 a(Put) p Fj 483 3047 a(g) p Fl 534 3047 a(\() p Fj(t) p Fl(\)) p 697 3047 a(=) p 825 3047 a(\() p Fj(G) p Fl(\() p Fj(t) p Fl(\)) p Fj(u;) 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p Fj(t) p Fl(\)) p 3638 5048 a(=) -66 5169 y(\() p Fj(d=dt) p Fl(\)) p Fj(k) p Fl 250 5169 a(\() p Fj(t) p Fl(\).) p 431 5169 a(It) p 536 5169 a(has) p 710 5169 a(the) p 878 5169 a(decomp) s(osition) p Fj 1521 5169 a(k) p Fg 1575 5133 a(0) p Fl 1598 5169 a(\() p Fj(t) p Fl(\)) p 1737 5169 a(=) p Fj 1841 5169 a(k) p Fq 1892 5184 a(0) p Fl 1931 5169 a(\() p Fj(t) p Fl(\)) p 2064 5169 a(+) p Fj 2162 5169 a(k) p Fq 2213 5184 a(1) p Fl 2252 5169 a(\() p Fj(t) p Fl(\)) p 2386 5169 a(+) p Fj 2484 5169 a(k) p Fq 2535 5184 a(2) p Fl 2574 5169 a(\() p Fj(t) p Fl(\),) p 2745 5169 a(where) p Fj 211 5355 a(k) p Fq 262 5370 a(0) p Fl 301 5355 a(\() p Fj(t) p Fl(\)) p 440 5355 a(=) p 543 5355 a(\() p Fi(\000) p Fj(i) p Fl(\() p Fj(B) p 808 5355 a(=) p Fl(2\)) p Fj(K) p Fl 1034 5355 a(\() p Fj(t) p Fl(\)) p Fj(u;) p 1245 5355 a(v) p Fl 1296 5355 a(\)) p 1362 5355 a(=) p 1465 5355 a(\() p Fi(\000) p Fj(ie) p Fg 1658 5314 a(\000) p Fh(itA) p Fj 1820 5355 a(e) p Fg 1865 5314 a(\000) p Fh(it) p Fq(\() p 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a(\() p Fj(t) p Fl(\)) p 440 5646 a(=) p 543 5646 a(\() p Fj(e) p Fg 626 5605 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 917 5646 a(e) p Fg 962 5605 a(\000) p Fh(itA) p Fl 1124 5646 a(\() p Fi(\000) p Fj(i) p Fl(\() p Fj(B) p 1389 5646 a(=) p Fl(2\)\)) p Fj(e) p Fg 1608 5605 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 1899 5646 a(u;) p 1999 5646 a(v) p Fl 2050 5646 a(\)) p 2114 5646 a(=) p 2218 5646 a(\() p Fi(\000) p Fj(i) p Fl(\() p Fj(B) p 2483 5646 a(=) p Fl(2\)) p Fj(e) p Fg 2664 5605 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2955 5646 a(u;) p 3055 5646 a(e) p Fh 3100 5605 a(itA) p Fj 3206 5646 a(e) p Fh 3251 5605 a(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 3487 5646 a(v) p Fl 3538 5646 a(\)) p Fj 3575 5646 a(:) p Fl 1799 5895 a(4) p eop %%Page: 5 5 5 4 bop Fl 205 312 a(W) p 297 312 a(e) p 373 312 a(apply) p 642 312 a(Lemma) p 990 312 a(2.1) p 1147 312 a(\(1\)) p 1304 312 a(to) p Fj 1087 537 a(k) p Fq 1138 552 a(1) p Fl 1177 537 a(\() p Fj(t) p 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Fh(B) s(=) p Fq(2\)) p Fj 2984 1548 a(v) p Fl 3035 1548 a(\)) p Fj(ds) p Fl 59 1806 a(b) m(y) p 195 1806 a(making) p 539 1806 a(a) p 620 1806 a(c) m(hange) p 942 1806 a(of) p 1054 1806 a(v) p 1100 1806 a(ariable.) p 1457 1806 a(Similarly) p 1872 1806 a(w) m(e) p 2015 1806 a(apply) p 2284 1806 a(Lemma) p 2632 1806 a(2.1) p 2789 1806 a(\(2\)) p 2946 1806 a(to) p Fj 1107 2076 a(k) p Fq 1158 2091 a(2) p Fl 1198 2076 a(\() p Fj(t) p Fl(\)) p 1336 2076 a(=) p Fi 1440 2076 a(\000) p Fj 1535 2009 a(i) p 1527 2053 V Fl 1527 2145 a(2) 1586 2076 y(\() p Fj(e) p Fg 1669 2035 a(\000) p Fh(itA) p Fj 1831 2076 a(B) p Fl 1910 2076 a(\() p Fj(e) p Fg 1993 2035 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2283 2076 a(u) p Fl(\)) p Fj(;) p 2421 2076 a(e) p Fh 2466 2035 a(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2701 2076 a(v) p Fl 2752 2076 a(\)) 59 2318 y(to) p 178 2318 a(get) p Fj 1217 2443 a(k) p Fq 1268 2458 a(2) p Fl 1307 2443 a(\() p Fj(t) p Fl(\)) p 1445 2443 a(=) p 1549 2443 a(\() p Fi(\000) p Fj(i) p Fl(\() p Fj(B) p 1814 2443 a(=) p Fl(2\)) p Fj(K) p Fl 2040 2443 a(\() p Fj(t) p Fl(\)) p Fj(u;) p 2251 2443 a(v) p Fl 2302 2443 a(\)) p 2362 2443 a(+) p Fj 2460 2443 a(r) p Fq 2504 2458 a(2) p Fl 2543 2443 a(\() p Fj(t) p Fl(\)) p Fj(;) p Fl 59 2623 a(where) p Fj 846 2768 a(r) p Fq 890 2783 a(2) p Fl 929 2768 a(\() p Fj(t) p Fl(\)) p 1068 2768 a(=) p Fj 1189 2701 a(i) p 1181 2745 V Fl 1181 2836 a(2) p Fd 1257 2651 a(Z) p Fh 1340 2677 a(t) p Fq 1303 2840 a(0) p Fl 1369 2768 a(\() p Fj(e) p Fg 1452 2727 a(\000) p Fh(isA) p Fj 1621 2768 a(E) p Fl 1699 2768 a(\() p Fj(e) p Fg 1782 2727 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(A) p Fj 2086 2768 a(e) p Fg 2131 2727 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2422 2768 a(u) p Fl(\)) p Fj(;) p 2560 2768 a(e) p Fh 2605 2727 a(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2840 2768 a(v) p Fl 2891 2768 a(\)) p Fj 2928 2768 a(ds:) p Fl 205 2983 a(W) p 297 2983 a(e) p 373 2983 a(apply) p 642 2983 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Fj(i=) p Fl(2\)) p Fj(t) p Fl(\() p Fj 946 3432 a(E) p 1024 3432 a(e) p Fg 1069 3396 a(\000) p Fh(itA) p Fj 1231 3432 a(e) p Fg 1276 3396 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 1567 3432 a(u;) p 1667 3432 a(e) p Fh 1712 3396 a(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 1947 3432 a(v) p Fl 1998 3432 a(\)) p 2068 3432 a(and) p Fj 1031 3656 a(r) p Fq 1075 3671 a(10) p Fl 1150 3656 a(\() p Fj(t) p Fl(\)) p 1289 3656 a(=) p 1392 3656 a(\() p Fj(R) p Fq 1504 3671 a(10) p Fl 1579 3656 a(\() p Fj(t) p Fl(\)) p Fj(u;) p 1790 3656 a(v) p Fl 1841 3656 a(\)) p Fj(;) p 2019 3656 a(r) p Fq 2063 3671 a(20) p Fl 2138 3656 a(\() p Fj(t) p Fl(\)) p 2277 3656 a(=) p 2380 3656 a(\() p Fj(R) p Fq 2492 3671 a(20) p Fl 2567 3656 a(\() p Fj(t) p Fl(\)) p Fj(u;) p 2778 3656 a(v) p Fl 2829 3656 a(\)) 59 3881 y(with) p Fj 600 4126 a(R) p Fq 674 4141 a(10) p Fl 749 4126 a(\() p Fj(t) p Fl(\)) p 943 4126 a(=) p Fi 1102 4126 a(\000) p Fj 1198 4058 a(i) p 1189 4103 V Fl 1189 4194 a(4) p Fd 1265 4009 a(Z) p Fh 1348 4035 a(t) p Fq 1311 4197 a(0) p Fd 1394 4009 a(Z) p Fh 1477 4035 a(s) p Fq 1441 4197 a(0) p Fj 1531 4126 a(e) p Fg 1576 4085 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(\033) p Fq 1804 4085 a(\)\() p Fh(B) s(=) p Fq(2\)) p Fj 2019 4126 a(E) p Fh 2091 4141 a(B) p Fj 2152 4126 a(e) p Fg 2197 4085 a(\000) p Fh(i\033) p Fq 2318 4085 a(\() p Fh(B) s(=) p Fq(2\)) p Fj 2505 4126 a(e) p Fg 2550 4085 a(\000) p Fh(itA) p Fj 2711 4126 a(e) p Fg 2756 4085 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 3047 4126 a(d\033) t(ds;) 600 4363 y(R) p Fq 674 4378 a(20) p Fl 749 4363 a(\() p Fj(t) p Fl(\)) p 943 4363 a(=) p Fi 1102 4363 a(\000) p Fj 1198 4296 a(i) p 1189 4340 V Fl 1189 4432 a(2) p Fd 1265 4246 a(Z) p Fh 1348 4272 a(t) p Fq 1311 4435 a(0) p Fd 1394 4246 a(Z) p Fh 1477 4272 a(s) p Fq 1441 4435 a(0) p Fj 1531 4363 a(e) p Fg 1576 4322 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 1867 4363 a(e) p Fg 1912 4322 a(\000) p Fh(i\033) r(A) p Fj 2090 4363 a(E) p Fh 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5072 a(\() p Fj(t) p Fl(\)) p 629 5072 a(=) p Fj 733 5072 a(K) p Fl 823 5072 a(\() p Fj(t) p Fl(\)) p Fj(u) p Fl(,) p 1049 5072 a(w) m(e) p 1193 5072 a(see) p 1351 5072 a(that) p Fj 1562 5072 a(w) p Fl 1635 5072 a(\() p Fj(t) p Fl(\)) p 1778 5072 a(satis\014es) 1279 5297 y(\() p Fj(w) p Fg 1390 5255 a(0) p Fl 1413 5297 a(\() p Fj(t) p Fl(\)) p Fj(;) p 1568 5297 a(v) p Fl 1619 5297 a(\)) p 1684 5297 a(=) p 1787 5297 a(\() p Fi(\000) p Fj(iH) p 2024 5297 a(w) p Fl 2097 5297 a(\() p Fj(t) p Fl(\)) p Fj(;) p 2252 5297 a(v) p Fl 2303 5297 a(\)) p 2363 5297 a(+) p Fj 2461 5297 a(r) p Fl 2508 5297 a(\() p Fj(t) p Fl(\)) 59 5521 y(with) p Fj 964 5646 a(r) p Fl 1011 5646 a(\() p Fj(t) p Fl(\)) p 1150 5646 a(=) p Fj 1253 5646 a(r) p Fq 1297 5661 a(10) p Fl 1372 5646 a(\() p Fj(t) p Fl(\)) p 1505 5646 a(+) p Fj 1603 5646 a(r) p Fq 1647 5661 a(20) p Fl 1722 5646 a(\() p Fj(t) p Fl(\)) p 1861 5646 a(=) p 1964 5646 a(\(\() p Fj(R) p Fq 2114 5661 a(10) p Fl 2189 5646 a(\() p Fj(t) p Fl(\)) p 2322 5646 a(+) p Fj 2420 5646 a(R) p Fq 2494 5661 a(20) p Fl 2569 5646 a(\() p Fj(t) p Fl(\)\)) p Fj(u;) p 2818 5646 a(v) p Fl 2869 5646 a(\)) p Fj 2906 5646 a(:) p Fl 1924 5895 a(5) p eop %%Page: 6 6 6 5 bop Fl -66 312 a(Since) p Fj 189 312 a(u) p Fl 277 312 a(and) p Fj 466 312 a(v) p Fl 550 312 a(range) p 815 312 a(o) m(v) m(er) p 1024 312 a(the) p 1192 312 a(dense) p 1458 312 a(subspace) p Fi 1865 312 a(D) p Fl 1945 312 a(,) p 2005 312 a(w) m(e) p 2148 312 a(ha) m(v) m(e) p Fj 780 569 a(e) p Fg 825 528 a(\000) p Fh(itH) p Fi 1019 569 a(\000) p Fj 1118 569 a(K) p Fl 1208 569 a(\() p Fj(t) p Fl(\)) p 1347 569 a(=) p Fi 1451 569 a(\000) p Fd 1545 452 a(Z) p Fh 1628 478 a(t) p Fq 1591 640 a(0) p Fj 1674 569 a(e) p Fg 1719 528 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(H) p Fl 2033 569 a(\() p Fj(R) p Fq 2145 584 a(10) p Fl 2220 569 a(\() p Fj(s) p Fl(\)) p 2364 569 a(+) p Fj 2462 569 a(R) p Fq 2536 584 a(20) p Fl 2611 569 a(\() p Fj(s) p Fl(\)\)) p Fj(ds) p Fl -66 815 a(b) m(y) p 69 815 a(Duhamel's) p 551 815 a(principle.) p 990 815 a(This) p 1213 815 a(yields) p 1487 815 a(the) p 1655 815 a(desired) p 1986 815 a(b) s(ound.) 80 1034 y(The) p 281 1034 a(pro) s(of) p 535 1034 a(of) p 647 1034 a(Theorem) p 1058 1034 a(1.3) p 1216 1034 a(needs) p 1482 1034 a(the) p 1650 1034 a(follo) m(wing) p 2062 1034 a(lemma.) p Fm -66 1252 a(Lemma) p 329 1252 a(2.4) p Fl(.) p 543 1252 a(Assume) p 903 1252 a(that) p 1113 1252 a(\() p Ff(d) p Fl(1\)) p 1323 1252 a(and) p 1511 1252 a(\() p Ff(d) p Fl(2\)) p 1721 1252 a(are) p 1883 1252 a(ful\014lled.) p 2270 1252 a(If) p Fj 2366 1252 a(E) p Fl 2475 1252 a(admids) p 2810 1252 a(a) p 2890 1252 a(b) s(ounded) p 3287 1252 a(extension,) -66 1372 y(then) p Fi 1107 1493 a(k) p Fj(G) p Fl(\() p Fj(t) p Fl(\)) p Fi 1367 1493 a(\000) p Fj 1467 1493 a(K) p Fl 1557 1493 a(\() p Fj(t) p Fl(\)) p Fi(k) p Fl 1746 1493 a(=) p Fj 1849 1493 a(O) p Fl 1927 1493 a(\() p Fi(j) p Fj(t) p Fi(j) p Fq 2056 1452 a(2) p Fl 2095 1493 a(\)) p 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2302 a(e) p Fg 1637 2261 a(\000) p Fh(isA) p Fj 1806 2302 a(e) p Fg 1851 2261 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2142 2302 a(e) p Fg 2187 2261 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(A) p Fd 2491 2203 a(\014) 2491 2253 y(\014) 2491 2302 y(\014) p Fh 2518 2229 a(t) 2518 2356 y(s) p Fq(=0) p Fl 1433 2521 a(=) p Fj 1592 2521 a(i) p Fd 1642 2404 a(Z) p Fh 1725 2431 a(t) p Fq 1688 2593 a(0) p Fj 1771 2521 a(e) p Fg 1816 2480 a(\000) p Fh(isA) p Fl 1985 2521 a([) p Fj(e) p Fg 2057 2480 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2348 2521 a(;) p 2392 2521 a(A) p Fl(]) p Fj(e) p Fg 2537 2480 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)) p Fh(A) p Fj 2841 2521 a(ds) p Fl -66 2767 a(and) 886 2907 y([) p Fj(e) p Fg 958 2866 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 1249 2907 a(;) p 1293 2907 a(A) p Fl(]) p 1420 2907 a(=) 1534 2840 y(1) p 1534 2884 49 4 v 1534 2976 a(2) p Fd 1609 2790 a(Z) p Fh 1692 2817 a(t) p Fq 1655 2979 a(0) p Fj 1738 2907 a(e) p Fg 1783 2866 a(\000) p Fh(is) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 2081 2907 a(E) p 2159 2907 a(e) p Fg 2204 2866 a(\000) p Fh(i) p Fq(\() p Fh(t) p Fg(\000) p Fh(s) p Fq(\)\() p Fh(B) s(=) p Fq(2\)) p Fj 2638 2907 a(ds:) p Fl -66 3109 a(By) p 87 3109 a(assumption,) p Fj 630 3109 a(E) p Fl 741 3109 a(admits) p 1061 3109 a(a) p 1142 3109 a(b) s(ounded) p 1540 3109 a(extension,) p 1999 3109 a(and) p 2189 3109 a(hence) p 2460 3109 a(it) p 2557 3109 a(follo) m(ws) p 2877 3109 a(that) p Fi 1303 3327 a(k) p Fl 1370 3327 a([) p Fj(e) p Fg 1442 3286 a(\000) p Fh(it) p Fq(\() p Fh(B) s(=) p Fq(2\)) p Fj 1732 3327 a(;) p 1776 3327 a(A) p Fl(]) p Fi 1893 3327 a(k) p Fl 1970 3327 a(=) p Fj 2074 3327 a(O) p Fl 2152 3327 a(\() p Fi(j) p Fj(t) p Fi(j) p Fl(\)) p Fj(:) p Fl -66 3544 a(This) p 157 3544 a(pro) m(v) m(es) p 458 3544 a(the) p 626 3544 a(lemma.) 80 3763 y(No) m(w) p 302 3763 a(w) m(e) p 446 3763 a(pro) m(v) m(e) p 709 3763 a(theorems.) p Fe -66 3982 a(Pr) p 36 3982 a(o) p 81 3982 a(of) p 194 3982 a(of) p 308 3982 a(The) p 468 3982 a(or) p 554 3982 a(em) p 711 3982 a(1.1) p Fl(.) p 911 3982 a(W) p 1003 3982 a(e) p 1078 3982 a(sho) m(w) p 1318 3982 a(\(1.3\).) p 1589 3982 a(With) p Fj 1839 3982 a(\034) p Fl 1920 3982 a(=) p Fj 2024 3982 a(t=n) p Fl 2197 3982 a(and) p Fj 2386 3982 a(D) p Fq 2467 3997 a(1) p Fl 2506 3982 a(\() p Fj(\034) p Fl 2597 3982 a(\)) p 2663 3982 a(=) p Fj 2767 3982 a(e) p Fg 2812 3945 a(\000) p Fh(i\034) p 2930 3945 a(H) p Fi 3017 3982 a(\000) p Fj 3114 3982 a(G) p Fl(\() p Fj(\034) p Fl 3282 3982 a(\),) p 3379 3982 a(w) m(e) p 3521 3982 a(ha) m(v) m(e) p Fj 860 4257 a(e) p Fg 905 4216 a(\000) p Fh(itH) p Fi 1099 4257 a(\000) p Fj 1198 4257 a(G) p Fl(\() p Fj(\034) p Fl 1366 4257 a(\)) p Fh 1404 4216 a(n) p Fl 1479 4257 a(=) p Fj 1583 4257 a(e) p Fg 1628 4216 a(\000) p Fh(in\034) p 1789 4216 a(H) p Fi 1878 4257 a(\000) p Fj 1978 4257 a(G) p Fl(\() p Fj(\034) p Fl 2146 4257 a(\)) p Fh 2184 4216 a(n) p Fl 2259 4257 a(=) p Fh 2405 4149 a(n) p Fd 2367 4174 a(X) p Fh 2362 4358 a(k) p Fq 2401 4358 a(=1) p Fj 2507 4257 a(X) p Fh 2588 4272 a(k) p Fl 2631 4257 a(\() p Fj(\034) p Fl 2722 4257 a(\)) p Fj(;) p Fl -66 4541 a(where) p Fj 829 4661 a(X) p Fh 910 4676 a(k) p Fl 952 4661 a(\() p Fj(\034) p Fl 1043 4661 a(\)) p 1109 4661 a(=) p Fj 1213 4661 a(e) p Fg 1258 4620 a(\000) p Fh(i) p Fq(\() p Fh(k) p Fg 1403 4620 a(\000) p Fq(1\)) p Fh(\034) p 1559 4620 a(H) p Fj 1627 4661 a(D) p Fq 1708 4676 a(1) p Fl 1747 4661 a(\() p Fj(\034) p Fl 1838 4661 a(\)) p Fj(G) p Fl(\() p Fj(\034) p Fl 2044 4661 a(\)) p Fh 2082 4620 a(n) p Fg(\000) p Fh(k) p Fj 2223 4661 a(;) p Fl 2365 4661 a(1) p Fi 2441 4661 a(\024) p Fj 2546 4661 a(k) p Fi 2628 4661 a(\024) p Fj 2733 4661 a(n:) p Fl -66 4835 a(Since) p 181 4835 a(b) m(y) p 309 4835 a(Lemma) p 650 4835 a(2.2) p Fi 800 4835 a(k) p Fj(X) p Fh 931 4850 a(k) p Fl 974 4835 a(\() p Fj(\034) p Fl 1065 4835 a(\)) p Fi(k) p 1180 4835 a(\024) p 1286 4835 a(k) p Fj(D) p Fq 1417 4850 a(1) p Fl 1456 4835 a(\() p Fj(\034) p Fl 1547 4835 a(\)) p Fi(k) p 1663 4835 a(\024) p Fj 1768 4835 a(O) p Fl 1846 4835 a(\() p Fi(j) p Fj(\034) p Fi 1965 4835 a(j) p Fq 1993 4799 a(2) p Fl 2031 4835 a(\)) p 2095 4835 a(for) p 2236 4835 a(ev) m(ery) p Fj 2486 4835 a(k) p Fl 2540 4835 a(,) p 2594 4835 a(w) m(e) p 2731 4835 a(ha) m(v) m(e) p Fi 2948 4835 a(k) p Fj(e) p Fg 3043 4799 a(\000) p Fh(itH) p Fi 3222 4835 a(\000) p Fj 3306 4835 a(G) p Fl(\() p Fj(\034) p Fl 3474 4835 a(\)) p Fh 3512 4799 a(n) p Fi 3560 4835 a(k) p Fl 3638 4835 a(=) p Fj -66 4955 a(O) p Fl 12 4955 a(\() p Fi(j) p Fj(\034) p Fi 131 4955 a(j) p Fl(\),) p 254 4955 a(sho) m(wing) p 624 4955 a(\(1.3\).) p 895 4955 a(W) p 987 4955 a(e) p 1061 4955 a(can) p 1238 4955 a(sho) m(w) p 1479 4955 a(\(1.4\)) p 1710 4955 a(similarly) p 2067 4955 a(,) p 2127 4955 a(noting) p 2429 4955 a(that) p 2638 4955 a(Lemma) p 2985 4955 a(2.2) p 3141 4955 a(together) p 3524 4955 a(with) -66 5075 y(Lemma) p 282 5075 a(2.4) p 439 5075 a(implies) p 770 5075 a(that) p Fi 982 5075 a(k) p Fj(e) p Fg 1077 5039 a(\000) p Fh(itH) p Fi 1270 5075 a(\000) p Fj 1370 5075 a(K) p Fl 1460 5075 a(\() p Fj(t) p Fl(\)) p Fi(k) p Fl 1649 5075 a(=) p Fj 1752 5075 a(O) p Fl 1830 5075 a(\() p Fi(j) p Fj(t) p Fi(j) p Fq 1959 5039 a(2) p Fl 1998 5075 a(\).) p 2106 5075 a(This) p 2329 5075 a(pro) m(v) m(es) p 2630 5075 a(the) p 2798 5075 a(theorem.) p Fe -66 5294 a(Pr) p 36 5294 a(o) p 81 5294 a(of) p 195 5294 a(of) p 310 5294 a(The) p 470 5294 a(or) p 556 5294 a(em) p 715 5294 a(1.2) p Fl(.) p 915 5294 a(With) p Fj 1167 5294 a(\034) p Fl 1248 5294 a(=) p Fj 1351 5294 a(t=n) p Fl 1526 5294 a(and) p Fj 1716 5294 a(D) p Fq 1797 5309 a(2) p Fl 1836 5294 a(\() p Fj(\034) p Fl 1927 5294 a(\)) p 1993 5294 a(=) p Fj 2097 5294 a(e) p Fg 2142 5258 a(\000) p Fh(i\034) p 2260 5258 a(H) p Fi 2349 5294 a(\000) p Fj 2449 5294 a(K) p Fl 2539 5294 a(\() p Fj(\034) p Fl 2630 5294 a(\),) p 2728 5294 a(w) m(e) p 2872 5294 a(ha) m(v) m(e) p Fj 859 5569 a(e) p Fg 904 5528 a(\000) p Fh(itH) p Fi 1098 5569 a(\000) p Fj 1197 5569 a(K) p Fl 1287 5569 a(\() p Fj(\034) p Fl 1378 5569 a(\)) p Fh 1416 5528 a(n) p Fl 1491 5569 a(=) p Fj 1595 5569 a(e) p Fg 1640 5528 a(\000) p Fh(in\034) p 1801 5528 a(H) p Fi 1890 5569 a(\000) p Fj 1990 5569 a(K) p Fl 2080 5569 a(\() p Fj(\034) p Fl 2171 5569 a(\)) p Fh 2209 5528 a(n) p Fl 2284 5569 a(=) p Fh 2431 5461 a(n) p Fd 2392 5486 a(X) p Fh 2388 5671 a(k) p Fq 2427 5671 a(=1) p Fj 2533 5569 a(Y) p Fh 2590 5584 a(k) p Fl 2632 5569 a(\() p Fj(\034) p Fl 2723 5569 a(\)) p Fj(;) p Fl 1799 5895 a(6) p eop %%Page: 7 7 7 6 bop Fl 59 312 a(where) p Fj 960 433 a(Y) p Fh 1017 448 a(k) p Fl 1059 433 a(\() p Fj(\034) p Fl 1150 433 a(\)) p 1216 433 a(=) p Fj 1319 433 a(e) p Fg 1364 392 a(\000) p Fh(i) p Fq(\() p Fh(k) p Fg 1509 392 a(\000) p Fq(1\)) p Fh(\034) p 1665 392 a(H) p Fj 1733 433 a(D) p Fq 1814 448 a(2) p Fl 1854 433 a(\() p Fj(\034) p Fl 1945 433 a(\)) p Fj(K) p Fl 2073 433 a(\() p Fj(\034) p Fl 2164 433 a(\)) p Fh 2202 392 a(n) p Fg(\000) p Fh(k) p Fj 2343 433 a(;) p Fl 2484 433 a(1) p Fi 2561 433 a(\024) p Fj 2666 433 a(k) p Fi 2748 433 a(\024) p Fj 2853 433 a(n:) p Fl 59 598 a(Since) p 307 598 a(b) m(y) p 436 598 a(Lemma) p 778 598 a(2.3) p Fi 929 598 a(k) p Fj(Y) p Fh 1036 613 a(k) p Fl 1078 598 a(\() p Fj(\034) p Fl 1169 598 a(\)) p Fi(k) p 1285 598 a(\024) p 1390 598 a(k) p Fj(D) p Fq 1521 613 a(2) p Fl 1560 598 a(\() p Fj(\034) p Fl 1651 598 a(\)) p Fi(k) p 1767 598 a(\024) p Fj 1872 598 a(O) p Fl 1950 598 a(\() p Fi(j) p Fj(\034) p Fi 2069 598 a(j) p Fq 2097 562 a(3) p Fl 2135 598 a(\)) p 2199 598 a(for) p 2342 598 a(ev) m(ery) p Fj 2593 598 a(k) p Fl 2647 598 a(,) p 2701 598 a(w) m(e) p 2838 598 a(ha) m(v) m(e) p Fi 3057 598 a(k) p Fj(e) p Fg 3152 562 a(\000) p Fh(itH) p Fi 3332 598 a(\000) p Fj 3418 598 a(K) p Fl 3508 598 a(\() p Fj(\034) p Fl 3599 598 a(\)) p Fh 3637 562 a(n) p Fi 3685 598 a(k) p Fl 3763 598 a(=) p Fj 59 719 a(O) p Fl 137 719 a(\() p Fi(j) p Fj(\034) p Fi 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5525 a(in) p 2466 5525 a(the) p 2633 5525 a(pro) s(of) p 2887 5525 a(ab) s(o) m(v) m(e) p 3162 5525 a(can) p 3340 5525 a(mak) m(e) p 3594 5525 a(sense.) 59 5646 y(The) p 260 5646 a(assumption) p 776 5646 a(\() p Ff(d) p Fl(1\){\() p Ff(d) p Fl(3\)) p 1214 5646 a(and/or) p 1540 5646 a(\() p Ff(d) p Fl(4\)) p 1751 5646 a(is) p 1849 5646 a(one) p 2028 5646 a(of) p 2139 5646 a(the) p 2307 5646 a(su\016cien) m(t) p 2717 5646 a(for) p 2866 5646 a(this.) 1924 5895 y(7) p eop %%Page: 8 8 8 7 bop Fk -66 312 a(3) p 176 312 a(Applications) p Fl -66 531 a(In) p 50 531 a([I2]) p 215 531 a(w) m(e) p 353 531 a(ha) m(v) m(e) p 572 531 a(sho) m(wn) p 863 531 a(that) p 1068 531 a(if) p Fj 1152 531 a(A) p Fl 1253 531 a(=) p Fi 1357 531 a(\000) p Fj(i) p Fh 1497 492 a(d) p 1477 508 77 4 v 1477 566 a(dx) p Fl 1563 531 a(,) p Fj 1618 531 a(B) p Fl 1725 531 a(=) p Fj 1829 531 a(x) p Fh 1884 495 a(k) p Fl 1927 531 a(,) p 1982 531 a(with) p Fj 2199 531 a(k) p Fl 2280 531 a(b) s(eing) p 2537 531 a(a) p 2612 531 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a(V) p Fl 1010 2220 a(\() p Fj(x) p Fl(\)) p 1177 2220 a(for) p Fi 1330 2220 a(j) p Fj(\013) p Fi 1421 2220 a(j) p Fl 1482 2220 a(=) p 1591 2220 a(1) p 1676 2220 a(or) p Fi 1799 2220 a(j) p Fj(\013) p Fi 1890 2220 a(j) p Fl 1951 2220 a(=) p 2061 2220 a(2.) p 2191 2220 a(In) p 2316 2220 a(particular,) p 2798 2220 a(it) p 2899 2220 a(holds) p 3157 2220 a(for) p 3310 2220 a(the) p 3482 2220 a(Dirac) -66 2340 y(op) s(erator) p Fj 331 2340 a(A) p Fl 439 2340 a(=) p Fj 550 2340 a(D) p Fq 631 2355 a(0) p Fi 706 2340 a(\021) p 818 2340 a(\000) p Fj(i) p Fd 945 2274 a(P) p Fq 1033 2300 a(3) p Fh 1033 2365 a(j) p Fq 1066 2365 a(=1) p Fj 1177 2340 a(\013) p Fh 1239 2355 a(j) p Fj 1275 2340 a(@) p Fh 1326 2355 a(x) p Fc 1366 2365 a(j) p Fl 1428 2340 a(+) p Fj 1529 2340 a(m\014) p Fl 1675 2340 a(,) p 1740 2340 a(with) p 1967 2340 a(mass) p Fj 2210 2340 a(m) p Fi 2331 2340 a(\025) p Fl 2443 2340 a(0,) p 2557 2340 a(in) p Fj 2675 2340 a(L) p Fq 2741 2304 a(2) p Fl 2781 2340 a(\() p Fm(R) p Fq 2903 2304 a(3) p Fl 2942 2340 a(\)) p Fq 2980 2304 a(4) p Fl 3019 2340 a(,) p 3084 2340 a(and) p Fj 3278 2340 a(B) p Fl 3393 2340 a(=) p Fj 3504 2340 a(V) p Fl 3582 2340 a(\() p Fj(x) p Fl(\)) -66 2460 y(a) p 23 2460 a(real-v) p 259 2460 a(alued) p Fj 527 2460 a(C) p Fq 604 2424 a(1) p Fl 684 2460 a(or) p Fj 811 2460 a(C) p Fq 888 2424 a(2) p Fl 968 2460 a(smo) s(oth) p 1321 2460 a(function.) p 1765 2460 a(Let) p Fj 1947 2460 a(H) p Fl 2076 2460 a(b) s(e) p 2217 2460 a(the) p 2393 2460 a(unique) p 2718 2460 a(selfadjoin) m(t) p 3195 2460 a(extension) p 3635 2460 a(of) p Fj -66 2581 a(A) p Fl 29 2581 a(+) p Fj 127 2581 a(B) p Fl 234 2581 a(=) p Fj 337 2581 a(D) p Fq 418 2596 a(0) p Fl 480 2581 a(+) p Fj 578 2581 a(V) p Fl 657 2581 a(\() p Fj(x) p Fl(\).) p Fm -66 2797 a(Prop) s(osition) p 535 2797 a(3.1) p Fl([) p Fe(Dir) p 845 2797 a(ac) p 971 2797 a(op) p 1066 2797 a(er) p 1147 2797 a(ator) p 1351 2797 a(on) p Fi 1484 2797 a(H) p Fl 1597 2797 a(=) p Fj 1701 2797 a(L) p Fq 1767 2761 a(2) p 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a(\000) p Fh(itH) p Fi 2200 3130 a(k) p Fl 2277 3130 a(=) p Fj 2381 3130 a(O) p Fl 2459 3130 a(\() p Fj(n) p Fg 2555 3089 a(\000) p Fq(1) p Fl 2648 3130 a(\)) p Fj(;) p Fl 3513 3130 a(\(3.1\)) p Fi 1083 3276 a(k) p Fl(\() p Fj(e) p Fg 1216 3235 a(\000) p Fh(itD) p Fb 1378 3244 a(0) p Fh 1413 3235 a(=n) p Fj 1495 3276 a(e) p Fg 1540 3235 a(\000) p Fh(itV) p 1702 3235 a(=n) p Fl 1784 3276 a(\)) p Fh 1822 3235 a(n) p Fi 1891 3276 a(\000) p Fj 1991 3276 a(e) p Fg 2036 3235 a(\000) p Fh(itH) p Fi 2207 3276 a(k) p Fl 2285 3276 a(=) p Fj 2389 3276 a(O) p Fl 2467 3276 a(\() p Fj(n) p Fg 2563 3235 a(\000) p Fq(1) p Fl 2656 3276 a(\)) p Fj(:) p Fl 3513 3276 a(\(3.2\)) -17 3489 y(\(ii\)) p Fe 163 3489 a(Assume) p 542 3489 a(that) p Fj 757 3489 a(V) p Fl 835 3489 a(\() p Fj(x) p Fl(\)) p Fe 1017 3489 a(is) p 1137 3489 a(a) p 1237 3489 a(r) p 1273 3489 a(e) p 1313 3489 a(al-value) p 1635 3489 a(d) p Fj 1735 3489 a(C) p Fq 1812 3453 a(2) p Fe 1902 3489 a(smo) p 2067 3489 a(oth) p 2248 3489 a(function) p 2647 3489 a(with) p 2875 3489 a(b) p 2915 3489 a(ounde) p 3162 3489 a(d) p 3261 3489 a(derivatives) p Fj -66 3609 a(@) p Fh -10 3573 a(\013) -15 3634 y(x) p Fj 40 3609 a(V) p Fl 119 3609 a(\() p Fj(x) p Fl(\)) p Fe 285 3609 a(for) p Fi 441 3609 a(j) p Fj(\013) p Fi 532 3609 a(j) p Fl 586 3609 a(=) p 690 3609 a(2) p Fe(.) p 813 3609 a(Then,) p 1097 3609 a(as) p Fj 1222 3609 a(n) p Fi 1308 3609 a(!) p 1435 3609 a(1) p Fe(,) p 1599 3609 a(one) p 1784 3609 a(has) p Fi 833 3822 a(k) p Fl(\() p Fj(e) p Fg 966 3781 a(\000) p Fh(itV) p 1119 3781 a(=) p Fq(2) p Fh(n) p Fj 1237 3822 a(e) p Fg 1282 3781 a(\000) p Fh(itD) p Fb 1444 3790 a(0) p Fh 1479 3781 a(=n) p Fj 1561 3822 a(e) p Fg 1606 3781 a(\000) p Fh(itV) p 1759 3781 a(=) p Fq(2) p Fh(n) p Fl 1877 3822 a(\)) p Fh 1915 3781 a(n) p Fi 1984 3822 a(\000) p Fj 2084 3822 a(e) p Fg 2129 3781 a(\000) p Fh(itH) p Fi 2301 3822 a(k) p Fl 2378 3822 a(=) p Fj 2482 3822 a(O) p Fl 2560 3822 a(\() p Fj(n) p Fg 2656 3781 a(\000) p Fq(2) p Fl 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Fj(n) p Fl(\)[) p Fj(e) p Fg 2205 4473 a(\000) p Fh(itH) p Fj 2377 4514 a(;) p 2421 4514 a(V) p Fl 2500 4514 a(]) p Fi(k) p Fl 2604 4514 a(=) p Fj 2708 4514 a(O) p Fl 2786 4514 a(\() p Fj(n) p Fg 2882 4473 a(\000) p Fq(2) p Fl 2976 4514 a(\)) p Fj(;) p Fl 3513 4514 a(\(3.5\)) p Fi 478 4704 a(k) p Fl 538 4637 a(1) p 538 4681 49 4 v 538 4772 a(2) 596 4704 y(\(\() p Fj(e) p Fg 717 4663 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(D) p Fb 1011 4672 a(0) p Fj 1051 4704 a(e) p Fg 1096 4663 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(V) p Fl 1395 4704 a(\)) p Fh 1433 4656 a(n) p Fl 1502 4704 a(+) p 1600 4704 a(\() p Fj(e) p Fg 1683 4663 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(V) p Fj 1981 4704 a(e) p Fg 2026 4663 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(D) p Fb 2320 4672 a(0) p Fl 2360 4704 a(\)) p Fh 2398 4656 a(n) p Fl 2445 4704 a(\)) p Fi 2505 4704 a(\000) p Fj 2605 4704 a(e) p Fg 2650 4663 a(\000) p Fh(itH) p Fi 2822 4704 a(k) p Fl 2899 4704 a(=) p Fj 3003 4704 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5285 a(2) p Fj 1768 5285 a(H) p Fq 1857 5248 a(1) p Fl 1896 5285 a(\() p Fm(R) p Fq 2018 5248 a(3) p Fl 2057 5285 a(\)) p Fq 2095 5248 a(4) p Fl 2168 5285 a(for) p 2318 5285 a(ev) m(ery) p Fj 2559 5285 a(L) p Fi 2665 5285 a(\025) p Fl 2781 5285 a(0) p Fi(g) p Fl(,) p 2948 5285 a(where) p Fi 3237 5285 a(h) p Fj(x) p Fi(i) p Fl 3409 5285 a(=) p 3524 5285 a(\(1) p 3638 5285 a(+) p Fj -66 5405 a(x) p Fq -11 5369 a(2) p Fl 29 5405 a(\)) p Fq 67 5369 a(1) p Fh(=) p Fq(2) p Fl 177 5405 a(.) p 273 5405 a(Then) p 537 5405 a(\() p Ff(d) p Fl(1\)) p 757 5405 a(is) p 864 5405 a(easy) p 1087 5405 a(to) p 1215 5405 a(c) m(hec) m(k,) p 1516 5405 a(and) p 1715 5405 a(the) p 1891 5405 a(op) s(erators) p Fj 2331 5405 a(E) p 2409 5405 a(;) p 2470 5405 a(E) p Fh 2542 5420 a(A) p Fl 2640 5405 a(and) p Fj 2839 5405 a(E) p Fh 2911 5420 a(B) p Fl 3013 5405 a(act) p 3184 5405 a(on) p Fi 3328 5405 a(D) p Fl 3449 5405 a(as) p 3578 5405 a(the) -66 5525 y(comm) m(utators) p Fj 536 5525 a(i) p Fl([) p Fj(D) p Fq 677 5540 a(0) p Fj 716 5525 a(;) p 760 5525 a(V) p Fl 839 5525 a(],) p Fi 959 5525 a(\000) p Fl([) p Fj(D) p Fq 1144 5540 a(0) p Fj 1184 5525 a(;) p Fl 1228 5525 a([) p Fj(D) p Fq 1336 5540 a(0) p Fj 1375 5525 a(;) p 1419 5525 a(V) p Fl 1497 5525 a(]]) p 1597 5525 a(and) p Fi 1800 5525 a(\000) p Fl([) p Fj(V) p 1966 5525 a(;) p Fl 2010 5525 a([) p Fj(D) p Fq 2118 5540 a(0) p Fj 2158 5525 a(;) p 2202 5525 a(V) p Fl 2280 5525 a(]]) p 2380 5525 a(as) p 2513 5525 a(in) p 2640 5525 a(Remark) p 3021 5525 a(1.1.) p 3256 5525 a(It) p 3374 5525 a(is) p 3486 5525 a(clear,) -66 5646 y(b) s(ecause) p 303 5646 a([) p Fj(D) p Fq 411 5661 a(0) p Fj 451 5646 a(;) p 495 5646 a(V) p Fl 573 5646 a(]) p 641 5646 a(is) p 748 5646 a(essen) m(tially) p 1224 5646 a(the) p 1400 5646 a(deriv) p 1608 5646 a(ativ) m(es) p Fj 1895 5646 a(@) p Fh 1946 5661 a(x) p Fj 1990 5646 a(V) p Fl 2068 5646 a(\() p Fj(x) p Fl(\)) p 2241 5646 a(and) p 2439 5646 a(the) p 2616 5646 a([) p Fj(D) p Fq 2724 5661 a(0) p Fj 2763 5646 a(;) p Fl 2807 5646 a([) p Fj(D) p Fq 2915 5661 a(0) p Fj 2955 5646 a(;) p 2999 5646 a(V) p Fl 3077 5646 a(]]) p 3172 5646 a(is) p 3279 5646 a(essen) m(tially) 1799 5895 y(8) p eop %%Page: 9 9 9 8 bop Fl 59 312 a(the) p 235 312 a(deriv) p 443 312 a(ativ) m(es) p Fj 729 312 a(@) p Fh 785 276 a(\013) 780 337 y(x) p Fj 836 312 a(V) p Fl 914 312 a(\() p Fj(x) p Fl(\)) p 1087 312 a(for) p Fi 1244 312 a(j) p Fj(\013) p Fi 1335 312 a(j) p Fl 1404 312 a(=) p 1522 312 a(2,) p 1641 312 a(and) p 1839 312 a([) p Fj(V) p 1928 312 a(;) p Fl 1972 312 a([) p Fj(D) p Fq 2080 327 a(0) p Fj 2119 312 a(;) p 2163 312 a(V) p Fl 2242 312 a(]]) p 2338 312 a(=) p 2455 312 a(0.) p 2600 312 a(W) p 2692 312 a(e) p 2776 312 a(can) p 2963 312 a(see) p 3130 312 a(also) p 3334 312 a(that) p 3553 312 a(\() p Ff(d) p Fl(4\)) p 3773 312 a(is) 59 433 y(satis\014ed.) p 472 433 a(Therefore) p 914 433 a(Prop) s(osition) p 1439 433 a(3.1) p 1596 433 a(follo) m(ws) p 1916 433 a(from) p 2146 433 a(Theorems) p 2597 433 a(1.1,) p 2781 433 a(1.2) p 2938 433 a(and) p 3128 433 a(1.3.) 205 653 y(Indeed,) p 547 653 a(there) p 793 653 a(is) p 888 653 a(a) p 966 653 a(v) m(ery) p 1177 653 a(p) s(eculiar) p 1546 653 a(case) p 1749 653 a(of) p 1857 653 a(the) p 2022 653 a(Stark) p 2282 653 a(Hamiltonian) p Fj 2839 653 a(H) p Fl 2956 653 a(=) p Fj 3059 653 a(A) p Fl 3148 653 a(+) p Fj 3240 653 a(B) p Fl 3347 653 a(:=) p Fi 3477 653 a(\000) p Fl(\001) p 3651 653 a(+) p Fj 3743 653 a(x) p Fq 3798 668 a(1) p Fl 59 773 a(in) p Fj 187 773 a(L) p Fq 253 737 a(2) p Fl 293 773 a(\() p Fm(R) p Fh 415 737 a(d) p Fl 455 773 a(\)) p 539 773 a(with) p Fj 776 773 a(x) p Fl 883 773 a(=) p 1011 773 a(\() p Fj(x) p Fq 1104 788 a(1) p Fj 1144 773 a(;) p 1188 773 a(:) p 1232 773 a(:) p 1276 773 a(:) p 1318 773 a(;) p 1362 773 a(x) p Fh 1417 788 a(d) p Fl 1458 773 a(\)) p Fi 1548 773 a(2) p Fm 1666 773 a(R) p Fh 1750 737 a(d) p Fl 1837 773 a(where) p 2133 773 a(Theorem) p 2559 773 a(1.2) p 2730 773 a(holds) p 2999 773 a(b) s(ecause) p 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p Fl 1735 1134 a(\() p Fj(x) p Fl(\),) p 1925 1134 a(since) p 2164 1134 a(it) p 2261 1134 a(do) s(es) p 2481 1134 a(not) p 2654 1134 a(satisfy) p 2958 1134 a(the) p 3126 1134 a(conditions) p 3592 1134 a(of) p 3703 1134 a(the) 59 1255 y(theorems.) p 521 1255 a(Ho) m(w) m(ev) m(er,) p Fe 944 1255 a(it) p 1043 1255 a(do) p 1138 1255 a(es) p 1259 1255 a(hold) p Fl 1468 1255 a(for) p 1619 1255 a(the) p 1789 1255 a(relativistic) p 2271 1255 a(Sc) m(hr\177) p 2457 1255 a(odinger) p 2807 1255 a(op) s(erator) p Fj 3202 1255 a(H) p Fl 3322 1255 a(=) p Fj 3429 1255 a(A) p Fl 3526 1255 a(+) p Fj 3625 1255 a(B) p Fl 3736 1255 a(:=) p Fj 59 1375 a(H) p Fq 140 1390 a(0) p Fl 208 1375 a(+) p Fj 312 1375 a(V) p Fi 435 1375 a(\021) 556 1294 y(p) p 639 1294 404 4 v 639 1375 a(\000) p Fl(\001) p 820 1375 a(+) p Fj 918 1375 a(m) p Fq 1003 1346 a(2) p Fl 1071 1375 a(+) p Fj 1176 1375 a(V) p Fl 1254 1375 a(\() p Fj(x) p Fl(\)) p 1428 1375 a(in) p Fj 1551 1375 a(L) p Fq 1617 1339 a(2) p Fl 1657 1375 a(\() p Fm(R) p Fh 1779 1339 a(d) p Fl 1819 1375 a(\)) p 1899 1375 a(with) p 2130 1375 a(some) p 2384 1375 a(real-v) p 2620 1375 a(alued) p 2889 1375 a(p) s(oten) m(tials) p Fj 3349 1375 a(V) p Fl 3428 1375 a(\() p Fj(x) p Fl(\).) p 3658 1375 a(It) p 3773 1375 a(is) 59 1495 y(kno) m(wn) p 360 1495 a([I) s(I]) p 511 1495 a(that) p Fj 715 1495 a(H) p Fl 828 1495 a(is) p 918 1495 a(essen) m(tially) p 1377 1495 a(selfadjoin) m(t) p 1838 1495 a(on) p Fj 1965 1495 a(C) p Fg 2042 1459 a(1) p Fq 2035 1520 a(0) p Fl 2117 1495 a(\() p Fm(R) p Fh 2239 1459 a(d) p Fl 2279 1495 a(\)) p 2341 1495 a(if) p 2422 1495 a(the) p 2582 1495 a(p) s(oten) m(tial) p Fj 2986 1495 a(V) p Fl 3065 1495 a(\() p Fj(x) p Fl(\)) p 3220 1495 a(is) p 3310 1495 a(a) p 3383 1495 a(function) p 3757 1495 a(in) p Fj 59 1616 a(L) p Fq 125 1580 a(2) p Fh 125 1640 a(l) q(oc) p Fl 216 1616 a(\() p Fm(R) p Fh 338 1580 a(d) p Fl 378 1616 a(\)) p 440 1616 a(satisfying) p Fj 867 1616 a(V) p Fl 945 1616 a(\() p Fj(x) p Fl(\)) p Fi 1104 1616 a(\025) p 1210 1616 a(\000) p Fj(c) p Fq 1329 1631 a(1) p Fj 1368 1616 a(e) p Fh 1413 1580 a(c) p Fb 1444 1589 a(2) p Fg 1479 1580 a(j) p Fh(x) p Fg(j) p Fl 1586 1616 a(with) p Fj 1800 1616 a(c) p Fq 1842 1631 a(1) p Fj 1882 1616 a(;) p 1942 1616 a(c) p Fq 1984 1631 a(2) p Fl 2048 1616 a(b) s(eing) p 2302 1616 a(nonnegativ) m(e) p 2836 1616 a(constan) m(ts,) p 3289 1616 a(in) p 3394 1616 a(particular,) 59 1736 y(under) p 325 1736 a(the) p 482 1736 a(assumption) p 987 1736 a(of) p 1088 1736 a(the) p 1245 1736 a(follo) m(wing) p 1646 1736 a(prop) s(osition.) p 2193 1736 a(Denote) p 2517 1736 a(the) p 2675 1736 a(unique) p 2981 1736 a(selfadjoin) m(t) p 3440 1736 a(extension) 59 1857 y(of) p Fj 170 1857 a(H) p Fq 251 1872 a(0) p Fl 313 1857 a(+) p Fj 411 1857 a(V) p Fl 522 1857 a(b) m(y) p 657 1857 a(the) p 825 1857 a(same) p Fj 1070 1857 a(H) p Fl 1159 1857 a(.) p Fm 59 2027 a(Prop) s(osition) p 681 2027 a(3.2) p Fl 870 2027 a([) p Fe(massive) p Fl 1273 2027 a(\() p Fe(r) p 1347 2027 a(esp.) p 1595 2027 a(massless) p Fl(\)) p Fe 2038 2027 a(r) p 2074 2027 a(elativistic) p 2525 2027 a(Schr\177) p 2716 2027 a(odinger) p 3079 2027 a(op) p 3174 2027 a(er) p 3255 2027 a(ator) p 3475 2027 a(on) p Fi 3626 2027 a(H) p Fl 3763 2027 a(=) p Fj 59 2147 a(L) p Fq 125 2111 a(2) p Fl 165 2147 a(\() p Fm(R) p Fh 287 2111 a(d) p Fl 327 2147 a(\)) p 382 2147 a(].) p 481 2147 a(\(i\)) p Fe 618 2147 a(Assume) p 982 2147 a(in) p 1103 2147 a(c) p 1143 2147 a(ase) p Fj 1313 2147 a(m) p 1427 2147 a(>) p Fl 1532 2147 a(0) p 1631 2147 a(\() p Fe(r) p 1705 2147 a(esp.) p Fj 1932 2147 a(m) p Fl 2046 2147 a(=) p 2151 2147 a(0\)) p Fe 2271 2147 a(that) p Fj 2471 2147 a(V) p Fl 2550 2147 a(\() p Fj(x) p Fl(\)) p Fe 2717 2147 a(is) p 2822 2147 a(a) p 2907 2147 a(r) p 2943 2147 a(e) p 2983 2147 a(al-value) p 3305 2147 a(d) p Fj 3390 2147 a(C) p Fq 3467 2111 a(2) p Fe 3542 2147 a(smo) p 3707 2147 a(oth) 59 2268 y(function) p 445 2268 a(with) p 658 2268 a(b) p 698 2268 a(ounde) p 945 2268 a(d) p 1032 2268 a(derivatives) p Fj 1521 2268 a(@) p Fh 1577 2231 a(\013) 1572 2292 y(x) p Fj 1627 2268 a(V) p Fl 1705 2268 a(\() p Fj(x) p Fl(\)) p Fe 1874 2268 a(for) p Fl 2031 2268 a(1) p Fi 2112 2268 a(\024) p 2221 2268 a(j) p Fj(\013) p Fi 2312 2268 a(j) p 2370 2268 a(\024) p Fl 2479 2268 a(2) p 2563 2268 a(\() p Fe(r) p 2637 2268 a(esp.) p Fl 2851 2268 a(0) p Fi 2931 2268 a(\024) p 3040 2268 a(j) p Fj(\013) p Fi 3131 2268 a(j) p 3190 2268 a(\024) p Fl 3299 2268 a(2\).) p Fe 3462 2268 a(Then,) p 3749 2268 a(as) p Fj 59 2388 a(n) p Fi 145 2388 a(!) p 272 2388 a(1) p Fe(,) p 437 2388 a(one) p 621 2388 a(has) p Fi 1208 2608 a(k) p Fl(\() p Fj(e) p Fg 1341 2567 a(\000) p Fh(itH) p Fb 1503 2576 a(0) p Fh 1538 2567 a(=n) p Fj 1621 2608 a(e) p Fg 1666 2567 a(\000) p Fh(itV) p 1819 2567 a(=n) p Fl 1901 2608 a(\)) p Fh 1939 2567 a(n) p Fi 2008 2608 a(\000) p Fj 2108 2608 a(e) p Fg 2153 2567 a(\000) p Fh(itH) p Fi 2325 2608 a(k) p Fl 2402 2608 a(=) p Fj 2506 2608 a(O) p Fl 2584 2608 a(\() p Fj(n) p Fg 2680 2567 a(\000) p Fq(1) p Fl 2774 2608 a(\)) p Fj(;) p Fl 3638 2608 a(\(3.7\)) p Fi 1208 2753 a(k) p Fl(\() p Fj(e) p Fg 1341 2712 a(\000) p Fh(itV) p 1503 2712 a(=n) p Fj 1585 2753 a(e) p Fg 1630 2712 a(\000) p Fh(itH) p Fb 1792 2721 a(0) p Fh 1827 2712 a(=n) p Fl 1909 2753 a(\)) p Fh 1947 2712 a(n) p Fi 2016 2753 a(\000) p Fj 2116 2753 a(e) p Fg 2161 2712 a(\000) p Fh(itH) p Fi 2333 2753 a(k) p Fl 2410 2753 a(=) p Fj 2514 2753 a(O) p Fl 2592 2753 a(\() p Fj(n) p Fg 2688 2712 a(\000) p Fq(1) p Fl 2782 2753 a(\)) p Fj(:) p Fl 3638 2753 a(\(3.8\)) 105 2973 y(\(ii\)) p Fe 281 2973 a(Assume) p 657 2973 a(in) p 788 2973 a(c) p 828 2973 a(ase) p Fj 1010 2973 a(m) p 1146 2973 a(>) p Fl 1272 2973 a(0) p 1338 2973 a(\() p Fj(r) s(esp:) p 1607 2973 a(m) p Fl 1741 2973 a(=) p 1867 2973 a(0\)) p Fe 2001 2973 a(and) p 2202 2973 a(that) p Fj 2414 2973 a(V) p Fl 2493 2973 a(\() p Fj(x) p Fl(\)) p Fe 2671 2973 a(is) p 2788 2973 a(a) p 2885 2973 a(r) p 2921 2973 a(e) p 2961 2973 a(al-value) p 3283 2973 a(d) p Fj 3379 2973 a(C) p Fq 3456 2937 a(4) p Fe 3542 2973 a(smo) p 3707 2973 a(oth) 59 3094 y(function) p 444 3094 a(with) p 658 3094 a(b) p 698 3094 a(ounde) p 945 3094 a(d) p 1030 3094 a(derivatives) p Fj 1519 3094 a(@) p Fh 1575 3058 a(\013) 1570 3118 y(x) p Fj 1625 3094 a(V) p Fl 1704 3094 a(\() p Fj(x) p Fl(\)) p Fe 1872 3094 a(for) p Fl 2029 3094 a(1) p Fi 2109 3094 a(\024) p 2217 3094 a(j) p Fj(\013) p Fi 2308 3094 a(j) p 2366 3094 a(\024) p Fl 2474 3094 a(4) p Fe 2559 3094 a(\(r) p 2635 3094 a(esp.) p Fl 2850 3094 a(0) p Fi 2929 3094 a(\024) p 3037 3094 a(j) p Fj(\013) p Fi 3128 3094 a(j) p 3186 3094 a(\024) p Fl 3295 3094 a(4) p Fe(\).) p 3463 3094 a(Then,) p 3749 3094 a(as) p Fj 59 3214 a(n) p Fi 145 3214 a(!) p 272 3214 a(1) p Fe(,) p 437 3214 a(one) p 621 3214 a(has) p Fi 571 3434 a(k) p Fl(\() p Fj(e) p Fg 704 3393 a(\000) p Fh(itV) p 857 3393 a(=) p Fq(2) p Fh(n) p Fj 975 3434 a(e) p Fg 1020 3393 a(\000) p Fh(itH) p Fb 1182 3402 a(0) p Fh 1217 3393 a(=n) p Fj 1299 3434 a(e) p Fg 1344 3393 a(\000) p Fh(itV) p 1497 3393 a(=) p Fq(2) p Fh(n) p Fl 1615 3434 a(\)) p Fh 1653 3393 a(n) p Fi 1723 3434 a(\000) p Fj 1822 3434 a(e) p Fg 1867 3393 a(\000) p Fh(itH) p Fi 2039 3434 a(k) p Fl 2116 3434 a(=) p Fj 2220 3434 a(O) p Fl 2298 3434 a(\() p Fj(n) p Fg 2394 3393 a(\000) p Fq(2) p Fl 2488 3434 a(\)) p Fj(;) p Fl 3638 3434 a(\(3.9\)) p Fi 571 3579 a(k) p Fl(\() p Fj(e) p Fg 704 3538 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(H) p Fb 998 3547 a(0) p Fj 1038 3579 a(e) p Fg 1083 3538 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(V) p Fl 1382 3579 a(\)) p Fh 1420 3531 a(n) p Fi 1489 3579 a(\000) p Fj 1588 3579 a(e) p Fg 1633 3538 a(\000) p Fh(itH) p Fi 1827 3579 a(\000) p Fj 1927 3579 a(i) p Fl(\() p Fj(t=) p Fl(2) p Fj(n) p Fl(\)[) p Fj(e) p Fg 2299 3538 a(\000) p Fh(itH) p Fj 2471 3579 a(;) p 2515 3579 a(H) p Fq 2596 3594 a(0) p Fl 2635 3579 a(]) p Fi(k) p Fl 2740 3579 a(=) p Fj 2843 3579 a(O) p Fl 2921 3579 a(\() p Fj(n) p Fg 3017 3538 a(\000) p Fq(2) p Fl 3111 3579 a(\)) p Fj(;) p Fl 3589 3579 a(\(3.10\)) p Fi 571 3725 a(k) p Fl(\() p Fj(e) p Fg 704 3684 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(V) p Fj 1002 3725 a(e) p Fg 1047 3684 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(H) p Fb 1341 3693 a(0) p Fl 1382 3725 a(\)) p Fh 1420 3676 a(n) p Fi 1489 3725 a(\000) p Fj 1588 3725 a(e) p Fg 1633 3684 a(\000) p Fh(itH) p Fi 1827 3725 a(\000) p Fj 1927 3725 a(i) p Fl(\() p Fj(t=) p Fl(2) p Fj(n) p Fl(\)[) p Fj(e) p Fg 2299 3684 a(\000) p Fh(itH) p Fj 2471 3725 a(;) p 2515 3725 a(V) p Fl 2593 3725 a(]) p Fi(k) p Fl 2698 3725 a(=) p Fj 2801 3725 a(O) p Fl 2879 3725 a(\() p Fj(n) p Fg 2975 3684 a(\000) p Fq(2) p Fl 3069 3725 a(\)) p Fj(;) p Fl 3589 3725 a(\(3.11\)) p Fi 571 3914 a(k) p Fl 631 3847 a(1) p 631 3891 49 4 v 631 3983 a(2) 690 3914 y(\(\() p Fj(e) p Fg 811 3873 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(H) p Fb 1105 3882 a(0) p Fj 1145 3914 a(e) p Fg 1190 3873 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(V) p Fl 1488 3914 a(\)) p Fh 1526 3866 a(n) p Fl 1595 3914 a(+) p 1693 3914 a(\() p Fj(e) p Fg 1776 3873 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(V) p Fj 2075 3914 a(e) p Fg 2120 3873 a(\000) p Fh(i) p Fq(\() p Fh(t=n) p Fq(\)) p Fh(H) p 2419 3873 a(H) p Fb 2477 3882 a(0) p Fl 2517 3914 a(\)) p Fh 2555 3866 a(n) p Fl 2602 3914 a(\)) p Fi 2662 3914 a(\000) p Fj 2762 3914 a(e) p Fg 2807 3873 a(\000) p Fh(itH) p Fi 2979 3914 a(k) p Fl 3056 3914 a(=) p Fj 3160 3914 a(O) p Fl 3238 3914 a(\() p Fj(n) p Fg 3334 3873 a(\000) p Fq(2) p Fl 3428 3914 a(\)) p Fj(:) p Fl 3589 3914 a(\(3.12\)) p Fe 205 4166 a(In) p 346 4166 a(al) p 426 4166 a(l) p 499 4166 a(formulas) p Fl 914 4166 a(\(3.7\){\(3.12\)) p Fe 1461 4166 a(ab) p 1551 4166 a(ove,) p 1772 4166 a(the) p 1947 4166 a(c) p 1987 4166 a(onver) p 2218 4166 a(genc) p 2403 4166 a(e) p 2495 4166 a(is) p 2613 4166 a(uniform) p 2999 4166 a(on) p 3151 4166 a(e) p 3191 4166 a(ach) p 3384 4166 a(b) p 3424 4166 a(ounde) p 3671 4166 a(d) p Fj 3768 4166 a(t) p Fe(-) 59 4286 y(interval) p 416 4286 a(in) p Fm 536 4286 a(R) p Fe(.) p Fl 205 4506 a(In) p 334 4506 a(Prop) s(osition) p 866 4506 a(3.2) p 1031 4506 a(w) m(e) p 1181 4506 a(ha) m(v) m(e) p 1413 4506 a(made) p 1681 4506 a(the) p 1856 4506 a(assumption) p 2379 4506 a(on) p 2521 4506 a(the) p 2696 4506 a(p) s(oten) m(tial) p Fj 3115 4506 a(V) p Fl 3194 4506 a(\() p Fj(x) p Fl(\)) p 3365 4506 a(as) p 3492 4506 a(minimal) 59 4626 y(as) p 185 4626 a(p) s(ossible.) p 608 4626 a(F) p 664 4626 a(or) p 789 4626 a(the) p 963 4626 a(pro) s(of) p 1224 4626 a(of) p 1341 4626 a(this) p 1538 4626 a(prop) s(osition,) p 2085 4626 a(w) m(e) p 2235 4626 a(will) p 2425 4626 a(not) p 2605 4626 a(use) p Fj 2779 4626 a(H) p Fq 2860 4641 a(0) p Fl 2938 4626 a(=) p Fi 3052 4545 a(p) p 3135 4545 404 4 v 3135 4626 a(\000) p Fl(\001) p 3316 4626 a(+) p Fj 3414 4626 a(m) p Fq 3499 4598 a(2) p Fl 3577 4626 a(as) p 3703 4626 a(the) 59 4747 y(pseudo) s(di\013eren) m(tial) p 839 4747 a(op) 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a(the) p 2361 4988 a(follo) m(wing) p 2777 4988 a(expression) p 3252 4988 a(as) p 3376 4988 a(an) p 3516 4988 a(in) m(tegral) 59 5108 y(op) s(erator:) 386 5352 y(\() p Fj(H) p Fq 505 5367 a(0) p Fj 544 5352 a(u) p Fl(\)\() p Fj(x) p Fl(\)) p 796 5352 a(:) p 906 5352 a(=) p Fj 1065 5352 a(mu) p Fl(\() p Fj(x) p Fl(\)) p Fi 1360 5352 a(\000) p Fd 1459 5235 a(Z) p Fg 1505 5424 a(j) p Fh(y) p Fg 1562 5424 a(j) p Fh(>) p Fq(0) p Fl 1676 5352 a([) p Fj(u) p Fl(\() p Fj(x) p Fl 1874 5352 a(+) p Fj 1972 5352 a(y) p Fl 2024 5352 a(\)) p Fi 2083 5352 a(\000) p Fj 2183 5352 a(u) p Fl(\() p Fj(x) p Fl(\)) p Fi 2392 5352 a(\000) p Fj 2492 5352 a(I) p Fg 2535 5368 a(fj) p Fh(y) p Fg 2627 5368 a(j) p Fh(<) p Fq(1) p Fg(g) p Fj 2793 5352 a(y) p Fi 2866 5352 a(\001) p Fj 2916 5352 a(@) p Fh 2967 5367 a(x) p Fj 3011 5352 a(u) p Fl(\() p Fj(x) p Fl(\)]) p Fj(n) p Fl(\() p Fj(y) p Fl 3373 5352 a(\)) p Fj(dy) p Fl 906 5591 a(=) p Fj 1065 5591 a(mu) p Fl(\() p Fj(x) p Fl(\)) p Fi 1360 5591 a(\000) p Fl 1459 5591 a(lim) p Fh 1475 5651 a(") p Fg(#) p Fq(0) p Fd 1611 5474 a(Z) p Fg 1657 5662 a(j) p Fh(y) p Fg 1714 5662 a(j\025) p Fh(") p Fl 1825 5591 a([) p Fj(u) p Fl(\() p Fj(x) p Fl 2024 5591 a(+) p Fj 2122 5591 a(y) p Fl 2174 5591 a(\)) p Fi 2233 5591 a(\000) p Fj 2332 5591 a(u) p Fl(\() p Fj(x) p Fl(\)]) p Fj(n) p Fl(\() p Fj(y) p Fl 2694 5591 a(\)) p Fj(dy) p Fl 3589 5591 a(\(3.13\)) 1924 5895 y(9) p eop %%Page: 10 10 10 9 bop Fl -66 312 a(for) p Fj 92 312 a(u) p Fi 190 312 a(2) p 300 312 a(S) p Fl 367 312 a(\() p Fm(R) p Fh 489 276 a(d) p Fl 530 312 a(\)) p 609 312 a(\(e.g.) p 864 312 a([I1,) p 1046 312 a(Eq.) p 1261 312 a(\(2.7\)],) p 1560 312 a(cf.) p 1730 312 a([LL,) p 1948 312 a(Chap.) p 2273 312 a(7]\).) p 2485 312 a(Here) p Fj 2724 312 a(I) p Fg 2767 328 a(fj) p Fh(y) p Fg 2859 328 a(j) p Fh(<) p Fq(1) p Fg(g) p Fl 3050 312 a(is) p 3157 312 a(the) p 3334 312 a(indicator) -66 433 y(function) p 324 433 a(of) p 442 433 a(the) p 618 433 a(set) p Fi 778 433 a(fj) p Fj(y) p Fi 908 433 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5646 a(follo) m(wing) p 2748 5646 a(Lemma) p 3095 5646 a(3.1) p 3250 5646 a(b) s(elo) m(w\).) p 3602 5646 a(T) p 3664 5646 a(o) 1775 5895 y(10) p eop %%Page: 11 11 11 10 bop Fl 59 312 a(this) p 246 312 a(end,) p 455 312 a(note) p 668 312 a(that) p 876 312 a(in) p 987 312 a(the) p 1152 312 a(pro) s(of) p 1403 312 a(the) p 1568 312 a(dense) p 1830 312 a(subspace) p Fi 2235 312 a(D) p Fl 2344 312 a(in) p 2454 312 a(the) p 2619 312 a(massiv) m(e) p 2974 312 a(case) p 3177 312 a(is) p 3272 312 a(tak) m(en) p 3535 312 a(smaller) 59 433 y(than) p 287 433 a(in) p 400 433 a(the) p 568 433 a(massless) p 955 433 a(case.) p Fm 59 628 a(Lemma) p 457 628 a(3.1) p Fl(.) p Fe 674 628 a(In) p 802 628 a(b) p 842 628 a(oth) p 1010 628 a(massive) p 1374 628 a(and) p 1565 628 a(massless) p 1959 628 a(c) p 1999 628 a(ases,) p 2239 628 a(if) p Fj 2335 628 a(V) p Fl 2413 628 a(\() p Fj(x) p Fl(\)) p Fe 2580 628 a(satis\014es) p 2948 628 a(the) p 3110 628 a(same) p 3360 628 a(assumption) 59 748 y(as) p 184 748 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a(\024) p Fl 1107 5271 a(1) p 1107 5315 49 4 v 1107 5406 a(2) p Fi 1166 5338 a(k) p Fj(V) p Fg 1295 5297 a(00) p Fi 1337 5338 a(k) p Fg 1387 5353 a(1) p Fd 1462 5242 a(h) 1501 5221 y(Z) 1584 5242 y(\020) 1633 5221 y(Z) p Fq 1679 5409 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 1826 5409 a(j) p Fh(<) p Fq(1) p Fi 1957 5338 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 2156 5338 a(+) p Fj 2254 5338 a(y) p Fl 2306 5338 a(\)) p Fi(jj) p Fj(y) p Fi 2452 5338 a(j) p Fq 2480 5297 a(2) p Fj 2516 5338 a(n) p Fl(\() p Fj(y) p Fl 2664 5338 a(\)) p Fj(dy) p Fd 2805 5242 a(\021) p Fq 2853 5265 a(2) p Fj 2909 5338 a(dx) p Fd 3015 5242 a(i) p Fq 3054 5265 a(1) p Fh(=) p Fq(2) p Fi 937 5591 a(\024) p Fl 1107 5523 a(1) p 1107 5568 V 1107 5659 a(2) p Fi 1166 5591 a(k) p Fj(V) p Fg 1295 5550 a(00) p Fi 1337 5591 a(k) p Fg 1387 5606 a(1) p Fd 1478 5474 a(Z) p Fq 1524 5662 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 1671 5662 a(j) p Fh(<) p Fq(1) p Fi 1802 5591 a(j) p Fj(y) p Fi 1882 5591 a(j) p Fq 1910 5550 a(2) p Fj 1948 5591 a(n) p Fl(\() p Fj(y) p Fl 2096 5591 a(\)) p Fj(dy) p Fi 2251 5591 a(k) p Fj(u) p Fi(k) p 2434 5591 a(\024) p Fl 2549 5523 a(1) p 2549 5568 V 2549 5659 a(2) p Fj 2608 5591 a(n) p Fq 2666 5606 a(0) p Fh(;) p Fq(2) p Fi 2761 5591 a(k) p Fj(V) p Fg 2889 5550 a(00) p Fi 2931 5591 a(k) p Fg 2981 5606 a(1) p Fi 3056 5591 a(k) p Fj(u) p Fi(k) p Fj(:) p Fl 1900 5895 a(11) p eop %%Page: 12 12 12 11 bop Fl 80 312 a(F) p 136 312 a(or) p Fj 255 312 a(u) p Fq 311 327 a(3) p Fl 350 312 a(,) p 410 312 a(in) p 523 312 a(case) p Fj 730 312 a(m) p 843 312 a(>) p Fl 946 312 a(0,) p 1055 312 a(w) m(e) p 1198 312 a(ha) m(v) m(e) p 1423 312 a(b) m(y) p 1559 312 a(the) p 1727 312 a(Sc) m(h) m(w) m(arz) p 2103 312 a(inequalit) m(y) p Fi 632 571 a(k) p Fj(u) p Fq 738 586 a(3) p Fi 777 571 a(k) p 910 571 a(\024) p 1070 571 a(k) p Fj(V) p Fg 1198 529 a(0) p Fi 1222 571 a(k) p Fg 1272 586 a(1) p Fd 1346 474 a(h) 1385 453 y(Z) 1468 474 y(\020) 1518 453 y(Z) p Fg 1564 642 a(j) p Fh(y) p Fg 1621 642 a(j\025) p Fq(1) p Fi 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a(\() p Fj(E) p Fh 914 5348 a(") p Fj 951 5333 a(u) p Fl(\)\() p Fj(x) p Fl(\)) p 1208 5333 a(for) p Fj 1357 5333 a(u) p Fi 1440 5333 a(2) p 1534 5333 a(S) p Fl 1601 5333 a(\() p Fm(R) p Fl(\),) p 1821 5333 a(where) 671 5591 y(\() p Fj(E) p Fh 781 5606 a(") p Fj 818 5591 a(u) p Fl(\)\() p Fj(x) p Fl(\)) p 1070 5591 a(=) p Fi 1174 5591 a(\000) p Fj(i) p Fd 1301 5474 a(Z) p Fg 1347 5662 a(j) p Fh(y) p Fg 1404 5662 a(j\025) p Fh(") p Fl 1515 5591 a(\() p Fj(V) p Fl 1632 5591 a(\() p Fj(x) p Fl 1747 5591 a(+) p Fj 1845 5591 a(y) p Fl 1897 5591 a(\)) p Fi 1957 5591 a(\000) p Fj 2056 5591 a(V) p Fl 2135 5591 a(\() p Fj(x) p Fl(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fl 2475 5591 a(+) p Fj 2573 5591 a(y) p Fl 2625 5591 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 2811 5591 a(\)) p Fj(dy) t(:) p Fl 1775 5895 a(12) p eop %%Page: 13 13 13 12 bop Fl 59 312 a(By) p 211 312 a(de\014nition,) p 671 312 a(\() p Fj(E) p Fh 781 327 a(A) p Fj 838 312 a(u;) p 938 312 a(v) p Fl 989 312 a(\)) p 1053 312 a(=) p Fj 1157 312 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a(") p Fl 2483 1938 a(+) p Fj 2589 1938 a(q) p Fh 2632 1953 a(") p Fl 2715 1938 a(admits) p 3048 1938 a(the) p 3228 1938 a(decomp) s(osition) p Fj 59 2058 a(r) p Fh 103 2073 a(") p Fl 162 2058 a(+) p Fj 260 2058 a(r) p Fq 304 2073 a(1) p Fh(") p Fl 398 2058 a(+) p Fj 496 2058 a(r) p Fq 540 2073 a(2) p Fh(") p Fl 612 2058 a(,) p 672 2058 a(where) p Fj 249 2272 a(r) p Fh 293 2287 a(") p Fl 358 2272 a(=) p Fi 461 2272 a(\000) p Fd 555 2155 a(Z) p 655 2155 a(Z) p 755 2155 a(Z) p Fh 801 2343 a(D) p Fc 859 2351 a(") p Fl 896 2272 a(\() p Fj(V) p Fl 1013 2272 a(\() p Fj(x) p Fl 1128 2272 a(+) p Fj 1226 2272 a(y) p Fl 1278 2272 a(\)) p Fi 1337 2272 a(\000) p Fl 1437 2272 a(2) p Fj(V) p Fl 1564 2272 a(\() p Fj(x) p Fl(\)) p 1718 2272 a(+) p Fj 1816 2272 a(V) p Fl 1894 2272 a(\() p Fj(x) p Fl 2010 2272 a(+) p Fj 2108 2272 a(z) p Fl 2157 2272 a(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fl 2405 2272 a(+) p Fj 2503 2272 a(y) p Fl 2555 2272 a(\)) t(\026) p Fj 2593 2272 a(v) p Fl 2642 2272 a(\() p Fj(x) p Fl 2758 2272 a(+) p Fj 2856 2272 a(z) p Fl 2905 2272 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 3091 2272 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 3274 2272 a(\)) p Fj(dy) t(dz) t(dx;) p Fl 59 2498 a(and) p Fj 713 2687 a(r) p Fq 757 2702 a(1) p Fh(") p Fl 857 2687 a(=) p Fd 960 2570 a(Z) p 1060 2570 a(Z) p 1159 2570 a(Z) p Fh 1205 2759 a(D) p Fc 1263 2767 a(") p Fl 1301 2687 a(\() p Fj(V) p Fl 1417 2687 a(\() p Fj(x) p Fl 1533 2687 a(+) p Fj 1631 2687 a(y) p Fl 1683 2687 a(\)) p Fi 1742 2687 a(\000) p Fj 1842 2687 a(V) p Fl 1920 2687 a(\() p Fj(x) p Fl(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fl 2261 2687 a(+) p Fj 2359 2687 a(y) p Fl 2411 2687 a(\)) t(\026) p Fj 2449 2687 a(v) p Fl 2498 2687 a(\() p Fj(x) p Fl(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 2777 2687 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 2960 2687 a(\)) p Fj(dy) t(dz) t(dx;) 713 2917 y(r) p Fq 757 2932 a(2) p Fh(") p Fl 857 2917 a(=) p Fd 960 2800 a(Z) p 1060 2800 a(Z) p 1159 2800 a(Z) p Fh 1205 2989 a(D) p Fc 1263 2997 a(") p Fl 1301 2917 a(\() p Fj(V) p Fl 1417 2917 a(\() p Fj(x) p Fl 1533 2917 a(+) p Fj 1631 2917 a(z) p Fl 1680 2917 a(\)) p Fi 1741 2917 a(\000) p Fj 1840 2917 a(V) p Fl 1919 2917 a(\() p Fj(x) p Fl(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fl(\)) t(\026) p Fj 2275 2917 a(v) p Fl 2326 2917 a(\() p Fj(x) p Fl 2441 2917 a(+) p Fj 2539 2917 a(z) p Fl 2588 2917 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 2774 2917 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 2957 2917 a(\)) p Fj(dy) t(dz) t(dx:) p Fl 59 3149 a(W) p 151 3149 a(e) p 226 3149 a(consider) p 604 3149 a(the) p 770 3149 a(in) m(tegral) p Fj 1124 3149 a(r) p Fh 1168 3164 a(") p Fl 1205 3149 a(,) p 1263 3149 a(and) p 1451 3149 a(mak) m(e) p 1704 3149 a(a) p 1784 3149 a(c) m(hange) p 2105 3149 a(of) p 2215 3149 a(v) p 2261 3149 a(ariables) p 2618 3149 a(\() p Fj(x) p Fl 2730 3149 a(+) p Fj 2825 3149 a(z) t(;) p 2918 3149 a(z) p Fl 2967 3149 a(\)) p Fi 3034 3149 a(!) p Fl 3161 3149 a(\() p Fj(x;) p 3298 3149 a(z) p Fl 3347 3149 a(\).) p 3456 3149 a(It) p 3560 3149 a(is) p 3656 3149 a(easy) 59 3269 y(to) p 178 3269 a(see) p 336 3269 a(that) p 547 3269 a(the) p 715 3269 a(in) m(tegration) p 1211 3269 a(domain) p Fj 1558 3269 a(D) p Fh 1639 3284 a(") p Fl 1708 3269 a(is) p 1806 3269 a(in) m(v) p 1930 3269 a(arian) m(t) p 2216 3269 a(under) p 2492 3269 a(this) p 2682 3269 a(transformation,) p 3374 3269 a(and) p 3563 3269 a(w) m(e) p 3707 3269 a(get) p Fj 162 3483 a(r) p Fh 206 3498 a(") p Fl 270 3483 a(=) p Fi 374 3483 a(\000) p Fd 468 3366 a(Z) p 568 3366 a(Z) p 667 3366 a(Z) p Fh 713 3554 a(D) p Fc 771 3562 a(") p Fl 809 3483 a(\() p Fj(V) p Fl 925 3483 a(\() p Fj(x) p Fi 1041 3483 a(\000) p Fj 1140 3483 a(z) p Fl 1212 3483 a(+) p Fj 1310 3483 a(y) p Fl 1362 3483 a(\)) p Fi 1422 3483 a(\000) p Fl 1521 3483 a(2) p Fj(V) p Fl 1649 3483 a(\() p Fj(x) p Fi 1764 3483 a(\000) p Fj 1864 3483 a(z) p Fl 1913 3483 a(\)) p 1974 3483 a(+) p Fj 2072 3483 a(V) p Fl 2150 3483 a(\() p Fj(x) p Fl(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fi 2490 3483 a(\000) p Fj 2590 3483 a(z) p Fl 2662 3483 a(+) p Fj 2760 3483 a(y) p Fl 2812 3483 a(\)) t(\026) p Fj 2850 3483 a(v) p Fl 2900 3483 a(\() p Fj(x) p Fl(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 3179 3483 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 3362 3483 a(\)) p Fj(dy) t(dz) t(dx;) p Fl 59 3709 a(W) p 151 3709 a(e) p 227 3709 a(further) p 555 3709 a(c) m(hange) p Fi 877 3709 a(\000) p Fj(z) p Fi 1032 3709 a(!) p Fj 1160 3709 a(z) p Fl 1242 3709 a(to) p 1361 3709 a(obtain) p 1665 3709 a(that) p Fj 164 3922 a(r) p Fh 208 3937 a(") p Fl 273 3922 a(=) p Fi 376 3922 a(\000) p Fd 470 3805 a(Z) p 570 3805 a(Z) p 670 3805 a(Z) p Fh 716 3994 a(D) p Fc 774 4002 a(") p Fl 811 3922 a(\() p Fj(V) p Fl 928 3922 a(\() p Fj(x) p Fl 1043 3922 a(+) p Fj 1141 3922 a(y) p Fl 1215 3922 a(+) p Fj 1313 3922 a(z) p Fl 1362 3922 a(\)) p Fi 1422 3922 a(\000) p Fl 1522 3922 a(2) p Fj(V) p Fl 1649 3922 a(\() p Fj(x) p Fl 1765 3922 a(+) p Fj 1863 3922 a(z) p Fl 1912 3922 a(\)) p 1973 3922 a(+) p Fj 2071 3922 a(V) p Fl 2149 3922 a(\() p Fj(x) p Fl(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fl 2490 3922 a(+) p Fj 2588 3922 a(y) p Fl 2661 3922 a(+) p Fj 2759 3922 a(z) p Fl 2808 3922 a(\)) t(\026) p Fj 2846 3922 a(v) p Fl 2897 3922 a(\() p Fj(x) p Fl(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 3176 3922 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 3359 3922 a(\)) p Fj(dy) t(dz) t(dx:) p Fl 59 4148 a(Similarly) p 474 4148 a(w) m(e) p 617 4148 a(ha) m(v) m(e) p Fj 476 4362 a(r) p Fq 520 4377 a(2) p Fh(") p Fl 619 4362 a(=) p Fd 723 4245 a(Z) p 822 4245 a(Z) p 922 4245 a(Z) p Fh 968 4434 a(D) p Fc 1026 4442 a(") p Fl 1064 4362 a(\() p Fj(V) p Fl 1180 4362 a(\() p Fj(x) p Fl(\)) p Fi 1333 4362 a(\000) p Fj 1433 4362 a(V) p Fl 1512 4362 a(\() p Fj(x) p Fi 1627 4362 a(\000) p Fj 1727 4362 a(z) p Fl 1776 4362 a(\)\)) p Fj(u) p Fl(\() p Fj(x) p Fi 2023 4362 a(\000) p Fj 2123 4362 a(z) p Fl 2172 4362 a(\)) t(\026) p Fj 2210 4362 a(v) p Fl 2261 4362 a(\() p Fj(x) p Fl(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 2540 4362 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 2723 4362 a(\)) p Fj(dy) t(dz) t(dx) p Fl 3098 4362 a(=) p Fi 3202 4362 a(\000) p Fj(r) p Fq 3323 4377 a(1) p Fh(") p Fj 3395 4362 a(;) p Fl 59 4594 a(so) p 179 4594 a(that) p 390 4594 a(\() p Fj(E) p Fh 500 4609 a(A) p Fj 557 4594 a(u;) p 657 4594 a(v) p Fl 708 4594 a(\)) p 773 4594 a(=) p 876 4594 a(lim) p Fh 1012 4609 a(") p Fg(!) p Fq(0) p Fj 1171 4594 a(r) p Fh 1215 4609 a(") p Fl 1252 4594 a(.) p 1322 4594 a(Th) m(us) p 1569 4594 a(w) m(e) p 1713 4594 a(ha) m(v) m(e) p 1938 4594 a(sho) m(wn) p 2234 4594 a(that) p Fj 2445 4594 a(E) p Fh 2517 4609 a(A) p Fl 2607 4594 a(acts) p 2808 4594 a(on) p Fi 2943 4594 a(S) p Fl 3010 4594 a(\() p Fm(R) p Fl(\)) p 3203 4594 a(as) p 3323 4594 a(in) p 3437 4594 a(\(3.27\).) 205 4714 y(Th) m(us) p 453 4714 a(w) m(e) p 596 4714 a(ha) m(v) m(e) p 821 4714 a(from) p 1051 4714 a(\(3.27\)) 544 4903 y(\([) p Fj(H) p Fq 690 4918 a(0) p Fj 730 4903 a(;) p Fl 774 4903 a([) p Fj(H) p Fq 882 4918 a(0) p Fj 921 4903 a(;) p 965 4903 a(V) p Fl 1043 4903 a(]]) p Fj(u) p Fl(\)\() p Fj(x) p Fl(\)) 372 5078 y(=) p 544 5078 a(lim) p Fh 560 5138 a(") p Fg(#) p Fq(0) p Fd 696 4961 a(Z) p Fg 743 5150 a(j) p Fh(y) p Fg 800 5150 a(j\025) p Fh(") p Fd 927 4961 a(Z) p Fg 973 5150 a(j) p Fh(z) p Fg 1029 5150 a(j\025) p Fh(") p Fl 1140 5078 a(\() p Fj(V) p Fl 1256 5078 a(\() p Fj(x) p Fl 1372 5078 a(+) p Fj 1470 5078 a(y) p Fl 1543 5078 a(+) p Fj 1641 5078 a(z) p Fl 1690 5078 a(\)) p Fi 1751 5078 a(\000) p Fj 1851 5078 a(V) p Fl 1929 5078 a(\() p Fj(x) p Fl 2045 5078 a(+) p Fj 2143 5078 a(y) p Fl 2195 5078 a(\)) p Fi 2254 5078 a(\000) p Fj 2353 5078 a(V) p Fl 2432 5078 a(\() p Fj(x) p Fl 2548 5078 a(+) p Fj 2646 5078 a(z) p Fl 2695 5078 a(\)) p 2755 5078 a(+) p Fj 2853 5078 a(V) p Fl 2932 5078 a(\() p Fj(x) p Fl(\)\)) p Fi 1520 5274 a(\002) p Fj(u) p Fl(\() p Fj(x) p Fl 1768 5274 a(+) p Fj 1866 5274 a(y) p Fl 1940 5274 a(+) p Fj 2038 5274 a(z) p Fl 2087 5274 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 2273 5274 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 2456 5274 a(\)) p Fj(dy) t(dz) p Fl 372 5450 a(=) p 544 5450 a(lim) p Fh 560 5510 a(") p Fg(#) p Fq(0) p Fd 696 5333 a(Z) p Fh 743 5521 a(") p Fg(\024j) p Fh(y) p Fg 888 5521 a(j) p Fh(<) p Fq(1) p Fd 1017 5333 a(Z) p Fh 1064 5521 a(") p Fg(\024j) p Fh(z) p Fg 1208 5521 a(j) p Fh(<) p Fq(1) p Fl 1370 5450 a(+) p 1463 5450 a(lim) p Fh 1479 5510 a(") p Fg(#) p Fq(0) p Fd 1615 5333 a(Z) p Fh 1661 5521 a(") p Fg(\024j) p Fh(y) p Fg 1806 5521 a(j) p Fh(<) p Fq(1) p Fd 1936 5333 a(Z) p Fg 1982 5521 a(j) p Fh(z) p Fg 2038 5521 a(j\025) p Fq(1) p Fl 2201 5450 a(+) p 2294 5450 a(lim) p Fh 2309 5510 a(") p Fg(#) p Fq(0) p Fd 2445 5333 a(Z) p Fg 2491 5521 a(j) p Fh(y) p Fg 2548 5521 a(j\025) p Fq(1) p Fd 2679 5333 a(Z) p Fh 2725 5521 a(") p Fg(\024j) p Fh(z) p Fg 2869 5521 a(j) p Fh(<) p Fq(1) p Fl 3064 5450 a(+) p Fd 3157 5333 a(Z) p Fg 3203 5521 a(j) p Fh(y) p Fg 3260 5521 a(j\025) p Fq(1) p Fd 3390 5333 a(Z) p Fg 3437 5521 a(j) p Fh(z) p Fg 3493 5521 a(j\025) p Fq(1) p Fl 358 5646 a(=:) p Fj 544 5646 a(v) p Fq 591 5661 a(00) p Fl 666 5646 a(\() p Fj(x) p Fl(\)) p 820 5646 a(+) p Fj 918 5646 a(v) p Fq 965 5661 a(0) p Fg(1) p Fl 1075 5646 a(\() p Fj(x) p Fl(\)) p 1228 5646 a(+) p Fj 1326 5646 a(v) p Fg 1373 5661 a(1) p Fq(0) p Fl 1483 5646 a(\() p Fj(x) p Fl(\)) p 1637 5646 a(+) p Fj 1735 5646 a(v) p Fg 1782 5661 a(11) p Fl 1927 5646 a(\() p Fj(x) p Fl(\)) p Fj(:) p Fl 3589 5646 a(\(3.28\)) 1900 5895 y(13) p eop %%Page: 14 14 14 13 bop Fl -66 312 a(By) p 87 312 a(the) p 255 312 a(mean) p 515 312 a(v) p 561 312 a(alue) p 767 312 a(theorem) p 1146 312 a(w) m(e) p 1290 312 a(ha) m(v) m(e) p Fj 479 492 a(V) p Fl 557 492 a(\() p Fj(x) p Fl 673 492 a(+) p Fj 771 492 a(y) p Fl 844 492 a(+) p Fj 942 492 a(z) p Fl 991 492 a(\)) p Fi 1052 492 a(\000) p Fj 1152 492 a(V) p Fl 1230 492 a(\() p Fj(x) p Fl 1346 492 a(+) p Fj 1444 492 a(y) p Fl 1496 492 a(\)) p Fi 1555 492 a(\000) p Fj 1655 492 a(V) p Fl 1733 492 a(\() p Fj(x) p Fl 1849 492 a(+) p Fj 1947 492 a(z) p Fl 1996 492 a(\)) p 2057 492 a(+) p Fj 2155 492 a(V) p Fl 2233 492 a(\() p Fj(x) p Fl(\)) 320 684 y(=) p Fj 479 684 a(z) p Fl 528 684 a(\() p Fj(V) p Fg 645 643 a(0) p Fl 668 684 a(\() p Fj(x) p Fl 784 684 a(+) p Fj 882 684 a(y) p Fl 934 684 a(\)) p Fi 993 684 a(\000) p Fj 1093 684 a(V) p Fg 1171 643 a(0) p Fl 1195 684 a(\() p Fj(x) p Fl(\)\)) p 1386 684 a(+) p Fj 1484 684 a(z) p Fq 1533 643 a(2) p Fd 1590 567 a(Z) p Fq 1673 593 a(1) 1636 755 y(0) p Fl 1712 684 a(\(1) p Fi 1821 684 a(\000) p Fj 1921 684 a(\022) p Fl 1969 684 a(\)[) p Fj(V) p Fg 2112 643 a(00) p Fl 2155 684 a(\() p Fj(x) p Fl 2270 684 a(+) p Fj 2368 684 a(y) p Fl 2442 684 a(+) p Fj 2540 684 a(\022) s(z) p Fl 2637 684 a(\)) p Fi 2698 684 a(\000) p Fj 2797 684 a(V) p Fg 2876 643 a(00) p Fl 2918 684 a(\() p Fj(x) p Fl 3034 684 a(+) p Fj 3132 684 a(\022) s(z) p Fl 3229 684 a(\)]) p Fj 3311 684 a(d\022) p Fl 320 867 a(=) p Fj 479 867 a(z) p Fl 528 867 a(\() p Fj(V) p Fg 645 826 a(0) p Fl 668 867 a(\() p Fj(x) p Fl 784 867 a(+) p Fj 882 867 a(y) p Fl 934 867 a(\)) p Fi 993 867 a(\000) p Fj 1093 867 a(V) p Fg 1171 826 a(0) p Fl 1195 867 a(\() p Fj(x) p Fl(\)) p Fi 1348 867 a(\000) p Fj 1448 867 a(y) t(V) p Fg 1577 826 a(00) p Fl 1620 867 a(\() p Fj(x) p Fl(\)\)) p 1811 867 a(+) p Fj 1909 867 a(y) t(z) t(V) p Fg 2089 826 a(00) p Fl 2131 867 a(\() p Fj(x) p Fl(\)) 479 1058 y(+) p Fj(z) p Fq 604 1017 a(2) p Fd 661 941 a(Z) p Fq 744 968 a(1) 707 1130 y(0) p Fl 783 1058 a(\(1) p Fi 892 1058 a(\000) p Fj 991 1058 a(\022) p Fl 1039 1058 a(\)[) p Fj(V) p Fg 1183 1017 a(00) p Fl 1226 1058 a(\() p Fj(x) p Fl 1341 1058 a(+) p Fj 1439 1058 a(y) p Fl 1512 1058 a(+) p Fj 1610 1058 a(\022) s(z) p Fl 1707 1058 a(\)) p Fi 1768 1058 a(\000) p Fj 1868 1058 a(V) p Fg 1947 1017 a(00) p Fl 1989 1058 a(\() p Fj(x) p Fl 2105 1058 a(+) p Fj 2203 1058 a(\022) s(z) p Fl 2300 1058 a(\)) p Fi 2361 1058 a(\000) p Fj 2460 1058 a(y) t(V) p Fg 2590 1017 a(000) p Fl 2651 1058 a(\() p Fj(x) p Fl 2767 1058 a(+) p Fj 2865 1058 a(\022) s(z) p Fl 2962 1058 a(\)]) p Fj 3044 1058 a(d\022) p Fl 479 1297 a(+) p Fj(z) p Fq 604 1256 a(2) p Fj 644 1297 a(y) p Fd 712 1180 a(Z) p Fq 795 1206 a(1) 758 1368 y(0) p Fl 834 1297 a(\(1) p Fi 943 1297 a(\000) p Fj 1043 1297 a(\022) p Fl 1091 1297 a(\)) p Fj(V) p Fg 1207 1256 a(000) p Fl 1269 1297 a(\() p Fj(x) p Fl 1384 1297 a(+) p Fj 1482 1297 a(\022) s(z) p Fl 1579 1297 a(\)) p Fj 1634 1297 a(d\022) s(;) p Fl 3464 1297 a(\(3.29\)) -66 1505 y(and) p 124 1505 a(the) p 292 1505 a(same) p 536 1505 a(is) p 634 1505 a(v) p 680 1505 a(alid) p 870 1505 a(with) p Fj 1092 1505 a(y) p Fl 1176 1505 a(and) p Fj 1365 1505 a(z) p Fl 1448 1505 a(exc) m(hanged.) 80 1626 y(F) p 136 1626 a(or) p 255 1626 a(the) p 423 1626 a(function) p Fj 805 1626 a(v) p Fq 852 1641 a(00) p Fl 959 1626 a(in) p 1073 1626 a(\(3.28\)) p 1355 1626 a(w) m(e) p 1499 1626 a(ha) m(v) m(e) p 1724 1626 a(b) m(y) p 1859 1626 a(\(3.29\)) p Fj 343 1805 a(v) p Fq 390 1820 a(00) p Fl 465 1805 a(\() p Fj(x) p Fl(\)) 184 1981 y(=) p 343 1981 a(lim) p Fh 359 2041 a(") p Fg(#) p Fq(0) p Fd 479 1884 a(h) 518 1864 y(Z) p Fh 564 2052 a(") p Fg(\024j) p Fh(y) p Fg 709 2052 a(j) p Fh(<) p Fq(1) p Fd 839 1864 a(Z) p Fh 885 2052 a(") p Fg(\024j) p Fh(z) p Fg 1029 2052 a(j) p Fh(<) p Fq(1) p Fj 1158 1981 a(z) p Fl 1207 1981 a([) p Fj(V) p Fg 1314 1940 a(0) p Fl 1337 1981 a(\() p Fj(x) p Fl 1452 1981 a(+) p Fj 1550 1981 a(y) p Fl 1602 1981 a(\)) p Fi 1662 1981 a(\000) p Fj 1761 1981 a(V) p Fg 1840 1940 a(0) p Fl 1863 1981 a(\() p Fj(x) p Fl(\)) p Fi 2017 1981 a(\000) p Fj 2116 1981 a(y) t(V) p Fg 2246 1940 a(00) p Fl 2288 1981 a(\() p Fj(x) p Fl(\)]) p Fj(u) p Fl(\() p Fj(x) p Fl 2618 1981 a(+) p Fj 2716 1981 a(y) p Fl 2789 1981 a(+) p Fj 2887 1981 a(z) p Fl 2936 1981 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 3122 1981 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 3305 1981 a(\)) p Fj(dy) t(dz) p Fl 343 2219 a(+) p Fj(V) p Fg 498 2178 a(00) p Fl 540 2219 a(\() p Fj(x) p Fl(\)) p Fd 688 2102 a(Z) p Fh 734 2291 a(") p Fg(\024j) p Fh(y) p Fg 879 2291 a(j) p Fh(<) p Fq(1) p Fd 992 2123 a(\020) 1042 2102 y(Z) p Fh 1088 2291 a(") p Fg(\024j) p Fh(z) p Fg 1232 2291 a(j) p Fh(<) p Fq(1) p Fj 1361 2219 a(u) p Fl(\() p Fj(x) p Fl 1532 2219 a(+) p Fj 1630 2219 a(y) p Fl 1704 2219 a(+) p Fj 1802 2219 a(z) p Fl 1851 2219 a(\)) p Fj(y) t(n) p Fl(\() p Fj(y) p Fl 2089 2219 a(\)) p Fj(dy) p Fd 2230 2123 a(\021) p Fj 2277 2219 a(z) t(n) p Fl(\() p Fj(z) p Fl 2471 2219 a(\)) p Fj(dz) p Fl 343 2474 a(+) p Fd 436 2357 a(Z) p Fh 482 2546 a(") p Fg(\024j) p Fh(z) p Fg 626 2546 a(j) p Fh(<) p Fq(1) p Fj 755 2474 a(z) p Fq 804 2433 a(2) p Fj 844 2474 a(n) p Fl(\() p Fj(z) p Fl 989 2474 a(\)) p Fj(dz) p Fd 1145 2357 a(Z) p Fh 1191 2546 a(") p Fg(\024j) p Fh(y) p Fg 1336 2546 a(j) p Fh(<) p Fq(1) p Fd 1449 2378 a(\020) 1499 2357 y(Z) p Fq 1582 2383 a(1) 1545 2546 y(0) p Fl 1621 2474 a(\(1) p Fi 1730 2474 a(\000) p Fj 1830 2474 a(\022) p Fl 1878 2474 a(\)) p Fi 441 2695 a(\002) p Fl([) p Fj(V) p Fg 624 2654 a(00) p Fl 666 2695 a(\() p Fj(x) p Fl 782 2695 a(+) p Fj 880 2695 a(y) p Fl 953 2695 a(+) p Fj 1051 2695 a(\022) s(z) p Fl 1148 2695 a(\)) p Fi 1209 2695 a(\000) p Fj 1309 2695 a(V) p Fg 1387 2654 a(00) p Fl 1430 2695 a(\() p Fj(x) p Fl 1545 2695 a(+) p Fj 1643 2695 a(\022) s(z) p Fl 1740 2695 a(\)) p Fi 1801 2695 a(\000) p Fj 1901 2695 a(y) t(V) p Fg 2030 2654 a(000) p Fl 2092 2695 a(\() p Fj(x) p Fl 2208 2695 a(+) p Fj 2306 2695 a(\022) s(z) p Fl 2403 2695 a(\)]) p Fj(d\022) p Fd 2567 2599 a(\021) p Fj 2617 2695 a(u) p Fl(\() p Fj(x) p Fl 2788 2695 a(+) p Fj 2886 2695 a(y) p Fl 2959 2695 a(+) p Fj 3057 2695 a(z) p Fl 3106 2695 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 3292 2695 a(\)) p Fj(dy) p Fl 343 2912 a(+) p Fd 436 2795 a(Z) p Fh 482 2983 a(") p Fg(\024j) p Fh(z) p Fg 626 2983 a(j) p Fh(<) p Fq(1) p Fj 755 2912 a(z) p Fq 804 2871 a(2) p Fj 844 2912 a(n) p Fl(\() p Fj(z) p Fl 989 2912 a(\)) p Fj(dz) p Fd 1127 2815 a(\020) 1178 2795 y(Z) p Fq 1261 2821 a(1) 1224 2983 y(0) p Fl 1300 2912 a(\(1) p Fi 1409 2912 a(\000) p Fj 1509 2912 a(\022) p Fl 1557 2912 a(\)\() p Fj(V) p Fg 1712 2871 a(000) p Fl 1773 2912 a(\() p Fj(x) p Fl 1889 2912 a(+) p Fj 1987 2912 a(\022) s(z) p Fl 2084 2912 a(\)) p Fj(d\022) p Fd 2221 2815 a(\021) 2288 2795 y(Z) p Fh 2334 2983 a(") p Fg(\024j) p Fh(y) p Fg 2479 2983 a(j) p Fh(<) p Fq(1) p Fj 2609 2912 a(u) p Fl(\() p Fj(x) p Fl 2780 2912 a(+) p Fj 2878 2912 a(y) p Fl 2951 2912 a(+) p Fj 3049 2912 a(z) p Fl 3098 2912 a(\)) p Fj(y) t(n) p Fl(\() p Fj(y) p Fl 3336 2912 a(\)) p Fj(dy) p Fd 3477 2815 a(i) p Fj 3514 2912 a(:) p Fl -66 3147 a(Therefore) p 376 3147 a(b) m(y) p 511 3147 a(\(3.17\)) p 793 3147 a(and) p 983 3147 a(\(3.18\),) p 1291 3147 a(its) p Fj 1427 3147 a(L) p Fq 1493 3110 a(2) p Fl 1566 3147 a(norm) p 1820 3147 a(ob) s(eys) p Fi 80 3371 a(k) p Fj(v) p Fq 177 3386 a(00) p Fi 251 3371 a(k) p 384 3371 a(\024) p Fl 555 3303 a(1) p 555 3348 49 4 v 555 3439 a(2) p Fi 613 3371 a(k) p Fj(V) p Fg 742 3330 a(000) p Fi 803 3371 a(k) p Fg 853 3386 a(1) p Fd 944 3254 a(Z) p Fq 991 3442 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 1138 3442 a(j) p Fh(<) p Fq(1) p Fi 1268 3371 a(j) p Fj(y) p Fi 1348 3371 a(j) p Fq 1376 3330 a(2) p Fj 1414 3371 a(n) p Fl(\() p Fj(y) p Fl 1562 3371 a(\)) p Fj(dy) p Fi 1703 3371 a(k) p Fj(K) p 1843 3371 a(u) p Fi(k) p Fl 1969 3371 a(+) p Fi 2067 3371 a(k) p Fj(V) p Fg 2195 3330 a(00) p Fi 2237 3371 a(k) p Fg 2287 3386 a(1) p Fi 2362 3371 a(k) p Fj(K) p Fq 2502 3330 a(2) p Fj 2541 3371 a(u) p Fi(k) p Fl 385 3624 a(+) 555 3556 y(1) p 555 3600 V 555 3692 a(4) p Fi 613 3624 a(k) p Fj(V) p Fq 742 3583 a(\(4\)) p Fi 836 3624 a(k) p Fg 886 3639 a(1) p Fd 961 3527 a(h) 1000 3507 y(Z) 1083 3527 y(\020) 1132 3507 y(Z) p Fq 1178 3695 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 1325 3695 a(j) p Fh(<) p Fq(1) p Fd 1456 3507 a(Z) p Fq 1502 3695 a(0) p Fh(<) p Fg(j) p Fh(z) p Fg 1648 3695 a(j) p Fh(<) p Fq(1) p Fi 1778 3624 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 1977 3624 a(+) p Fj 2075 3624 a(y) p Fl 2148 3624 a(+) p Fj 2246 3624 a(z) p Fl 2295 3624 a(\)) p Fi(jj) p Fj(y) p Fi 2441 3624 a(j) p Fq 2469 3583 a(2) p Fj 2507 3624 a(n) p Fl(\() p Fj(y) p Fl 2655 3624 a(\)) p Fi(j) p Fj(z) p Fi 2770 3624 a(j) p Fq 2798 3583 a(2) p Fj 2837 3624 a(n) p Fl(\() p Fj(z) p Fl 2982 3624 a(\)) p Fj(dy) t(dz) p Fd 3223 3527 a(\021) p Fq 3273 3550 a(2) p Fj 3312 3624 a(dx) p Fd 3418 3527 a(i) p Fq 3458 3550 a(1) p Fh(=) p Fq(2) p Fl 385 3877 a(+) 555 3809 y(1) p 555 3853 V 555 3945 a(2) p Fi 613 3877 a(k) p Fj(V) p Fg 742 3835 a(000) p Fi 803 3877 a(k) p Fg 853 3892 a(1) p Fd 928 3780 a(h) 967 3759 y(Z) 1050 3780 y(\020) 1100 3759 y(Z) p Fq 1146 3948 a(0) p Fh(<) p Fg(j) p Fh(z) p Fg 1292 3948 a(j) p Fh(<) p Fq(1) p Fj 1422 3877 a(z) p Fq 1471 3835 a(2) p Fj 1511 3877 a(n) p Fl(\() p Fj(z) p Fl 1656 3877 a(\)) p Fj(dz) p Fl 1794 3877 a(\() p Fj(K) p 1922 3877 a(u) p Fl(\)\() p Fj(x) p Fl 2132 3877 a(+) p Fj 2230 3877 a(z) p Fl 2279 3877 a(\)) p Fd 2317 3780 a(\021) p Fq 2367 3803 a(2) p Fj 2407 3877 a(dx) p Fd 2513 3780 a(i) p Fq 2552 3803 a(1) p Fh(=) p Fq(2) p Fi 384 4129 a(\024) p Fd 545 4033 a(h) p Fj 584 4129 a(C) p Fq 661 4088 a(2) p Fi 700 4129 a(k) p Fj(V) p Fg 829 4088 a(00) p Fi 871 4129 a(k) p Fg 921 4144 a(1) p Fl 1018 4129 a(+) p Fj 1116 4129 a(C) p 1193 4129 a(n) p Fq 1251 4144 a(0) p Fh(;) p Fq(2) p Fi 1345 4129 a(k) p Fj(V) p Fg 1474 4088 a(000) p Fi 1535 4129 a(k) p Fg 1585 4144 a(1) p Fl 1682 4129 a(+) 1790 4062 y(1) p 1790 4106 V 1790 4198 a(4) p Fj 1849 4129 a(n) p Fq 1907 4088 a(2) 1907 4154 y(0) p Fh(;) p Fq(2) p Fi 2001 4129 a(k) p Fj(V) p Fq 2129 4088 a(\(4\)) p Fi 2224 4129 a(k) p Fg 2274 4144 a(1) p Fd 2348 4033 a(i) p Fi 2387 4129 a(k) p Fj(u) p Fi(k) p Fj(:) p Fl 80 4340 a(F) p 136 4340 a(or) p Fj 255 4340 a(v) p Fq 302 4355 a(0) p Fg(1) p Fl 445 4340 a(and) p Fj 634 4340 a(v) p Fg 681 4355 a(1) p Fq(0) p Fl 791 4340 a(,) p 851 4340 a(w) m(e) p 995 4340 a(ha) m(v) m(e) p 1220 4340 a(b) m(y) p 1355 4340 a(\(3.29\)) p 1637 4340 a(and) p 1827 4340 a(\(3.17\)) p Fj 246 4550 a(v) p Fq 293 4565 a(0) p Fg(1) p Fl 486 4550 a(=) p Fd 645 4433 a(Z) p Fg 691 4622 a(j) p Fh(z) p Fg 747 4622 a(j\025) p Fq(1) p Fl 861 4550 a(\() p Fj(V) p Fg 977 4509 a(0) p Fl 1000 4550 a(\() p Fj(x) p Fl 1116 4550 a(+) p Fj 1214 4550 a(z) p Fl 1263 4550 a(\)) p Fi 1324 4550 a(\000) p Fj 1423 4550 a(V) p Fg 1502 4509 a(0) p Fl 1525 4550 a(\() p Fj(x) p Fl(\)\)\() p Fj(K) p 1822 4550 a(u) p Fl(\)\() p Fj(x) p Fl 2032 4550 a(+) p Fj 2130 4550 a(z) p Fl 2179 4550 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 2362 4550 a(\)) p Fj(dz) p Fl 645 4805 a(+) p Fd 738 4688 a(Z) p Fg 784 4877 a(j) p Fh(z) p Fg 840 4877 a(j\025) p Fq(1) p Fj 970 4805 a(n) p Fl(\() p Fj(z) p Fl 1115 4805 a(\)) p Fj(dz) p Fd 1271 4688 a(Z) p Fq 1317 4877 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 1464 4877 a(j) p Fh(<) p Fq(1) p Fd 1594 4688 a(Z) p Fq 1677 4714 a(1) 1640 4877 y(0) p Fl 1717 4805 a(\(1) p Fi 1826 4805 a(\000) p Fj 1925 4805 a(\022) p Fl 1973 4805 a(\)[) p Fj(V) p Fg 2117 4764 a(00) p Fl 2159 4805 a(\() p Fj(x) p Fl 2275 4805 a(+) p Fj 2373 4805 a(z) p Fl 2445 4805 a(+) p Fj 2543 4805 a(\022) s(y) p Fl 2643 4805 a(\)) p Fi 2702 4805 a(\000) p Fj 2802 4805 a(V) p Fg 2880 4764 a(00) p Fl 2923 4805 a(\() p Fj(x) p Fl 3038 4805 a(+) p Fj 3136 4805 a(\022) s(y) p Fl 3236 4805 a(\)]) p Fj(d\022) p Fi 1036 5010 a(\002) p Fj(u) p Fl(\() p Fj(x) p Fl 1284 5010 a(+) p Fj 1382 5010 a(y) p Fl 1455 5010 a(+) p Fj 1553 5010 a(z) p Fl 1602 5010 a(\)) p Fj(y) p Fq 1692 4969 a(2) p Fj 1732 5010 a(n) p Fl(\() p Fj(y) p Fl 1880 5010 a(\)) p Fj(dy) t(;) 246 5186 y(v) p Fg 293 5201 a(1) p Fq(0) p Fl 486 5186 a(=) p Fd 645 5068 a(Z) p Fg 691 5257 a(j) p Fh(y) p Fg 748 5257 a(j\025) p Fq(1) p Fl 862 5186 a(\() p Fj(V) p Fg 979 5144 a(0) p Fl 1002 5186 a(\() p Fj(x) p Fl 1118 5186 a(+) p Fj 1216 5186 a(y) p Fl 1268 5186 a(\)) p Fi 1327 5186 a(\000) p Fj 1426 5186 a(V) p Fg 1505 5144 a(0) p Fl 1528 5186 a(\() p Fj(x) p Fl(\)\)\() p Fj(K) p 1825 5186 a(u) p Fl(\)\() p Fj(x) p Fl 2035 5186 a(+) p Fj 2133 5186 a(y) p Fl 2185 5186 a(\)) p Fj(n) p Fl(\() p Fj(y) p Fl 2371 5186 a(\)) p Fj(dy) p Fl 645 5441 a(+) p Fd 738 5323 a(Z) p Fg 784 5512 a(j) p Fh(y) p Fg 841 5512 a(j\025) p Fq(1) p Fj 971 5441 a(n) p Fl(\() p Fj(y) p Fl 1119 5441 a(\)) p Fj(dy) p Fd 1275 5323 a(Z) p Fq 1321 5512 a(0) p Fh(<) p Fg(j) p Fh(z) p Fg 1467 5512 a(j) p Fh(<) p Fq(1) p Fd 1597 5323 a(Z) p Fq 1680 5350 a(1) 1643 5512 y(0) p Fl 1720 5441 a(\(1) p Fi 1828 5441 a(\000) p Fj 1928 5441 a(\022) p Fl 1976 5441 a(\)[) p Fj(V) p Fg 2120 5399 a(00) p Fl 2162 5441 a(\() p Fj(x) p Fl 2278 5441 a(+) p Fj 2376 5441 a(y) p Fl 2449 5441 a(+) p Fj 2547 5441 a(\022) s(z) p Fl 2644 5441 a(\)) p Fi 2705 5441 a(\000) p Fj 2805 5441 a(V) p Fg 2883 5399 a(00) p Fl 2926 5441 a(\() p Fj(x) p Fl 3041 5441 a(+) p Fj 3139 5441 a(\022) s(z) p Fl 3236 5441 a(\)]) p Fj(d\022) p Fi 1036 5646 a(\002) p Fj(u) p Fl(\() p Fj(x) p Fl 1284 5646 a(+) p Fj 1382 5646 a(y) p Fl 1455 5646 a(+) p Fj 1553 5646 a(z) p Fl 1602 5646 a(\)) p Fj(z) p Fq 1689 5605 a(2) p Fj 1730 5646 a(n) p Fl(\() p Fj(z) p Fl 1875 5646 a(\)) p Fj(dz) t(:) p Fl 1775 5895 a(14) p eop %%Page: 15 15 15 14 bop Fl 205 312 a(Therefore,) p 674 312 a(in) p 788 312 a(case) p Fj 994 312 a(m) p 1107 312 a(>) p Fl 1211 312 a(0,) p 1319 312 a(b) m(y) p 1455 312 a(\(3.18\),) p Fi 284 558 a(k) p Fj(v) p Fq 381 573 a(0) p Fg(1) p Fi 491 558 a(k) p 624 558 a(\024) p 784 558 a(k) p Fj(V) p Fg 913 517 a(00) p Fi 955 558 a(k) p Fg 1005 573 a(1) p Fd 1096 441 a(Z) p Fg 1142 630 a(j) p Fh(z) p Fg 1198 630 a(j\025) p Fq(1) p Fi 1328 558 a(j) p Fj(z) p Fi 1405 558 a(j) p Fj(n) p Fl(\() p Fj(z) p Fl 1578 558 a(\)) p Fj(dz) p Fi 1716 558 a(k) p Fj(K) p 1856 558 a(u) p Fi(k) p Fl 784 803 a(+) p Fi(k) p Fj(V) p Fg 989 762 a(000) p Fi 1050 803 a(k) p Fg 1100 818 a(1) p Fd 1175 706 a(h) 1214 686 y(Z) 1297 706 y(\020) 1347 686 y(Z) p Fg 1393 874 a(j) p Fh(z) p Fg 1449 874 a(j\025) p Fq(1) p Fi 1578 803 a(j) p Fj(z) p Fi 1655 803 a(j) p Fj(n) p Fl(\() p Fj(z) p Fl 1828 803 a(\)) p Fj(dz) p Fd 1984 686 a(Z) p Fq 2031 874 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 2178 874 a(j) p Fh(<) p Fq(1) p Fi 2308 803 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 2507 803 a(+) p Fj 2605 803 a(y) p Fl 2678 803 a(+) p Fj 2776 803 a(z) p Fl 2825 803 a(\)) p Fi(j) p Fj(y) p Fq 2943 762 a(2) p Fj 2982 803 a(n) p Fl(\() p Fj(y) p Fl 3130 803 a(\)) p Fj(dy) p Fd 3271 706 a(\021) p Fq 3319 729 a(2) p Fj 3358 803 a(dx) p Fd 3464 706 a(i) p Fq 3504 729 a(1) p Fh(=) p Fq(2) p Fi 624 1002 a(\024) p Fl 784 1002 a([) p Fj(C) p 888 1002 a(n) p Fq 946 1017 a(+;) p Fg(1) p Fh(;) p Fq(1) p Fi 1151 1002 a(k) p Fj(V) p Fg 1279 961 a(00) p Fi 1322 1002 a(k) p Fg 1372 1017 a(1) p Fl 1468 1002 a(+) p Fj 1566 1002 a(n) p Fq 1624 1017 a(+;) p Fg(1) p Fh(;) p Fq(1) p Fj 1829 1002 a(n) p Fq 1887 1017 a(0) p Fh(;) p Fq(2) p Fi 1981 1002 a(k) p Fj(V) p Fg 2110 961 a(000) p Fi 2171 1002 a(k) p Fg 2221 1017 a(1) p Fl 2296 1002 a(]) p Fi(k) p Fj(u) p Fi(k) p Fj(:) p Fl 205 1218 a(In) p 327 1218 a(case) p Fj 534 1218 a(m) p Fl 647 1218 a(=) p 750 1218 a(0,) p Fi 322 1459 a(k) p Fj(v) p Fq 419 1474 a(0) p Fg(1) p Fi 529 1459 a(k) p 662 1459 a(\024) p Fl 822 1459 a(2) p Fi(k) p Fj(V) p Fg 999 1418 a(0) p Fi 1023 1459 a(k) p Fg 1073 1474 a(1) p Fd 1164 1341 a(Z) p Fg 1210 1530 a(j) p Fh(z) p Fg 1266 1530 a(j\025) p Fq(1) p Fj 1396 1459 a(n) p Fl(\() p Fj(z) p Fl 1541 1459 a(\)) p Fj(dz) p Fi 1679 1459 a(k) p Fj(K) p 1819 1459 a(u) p Fi(k) p Fl 822 1703 a(+2) p Fi(k) p Fj(V) p Fg 1075 1662 a(00) p Fi 1118 1703 a(k) p Fg 1168 1718 a(1) p Fd 1242 1607 a(h) 1281 1586 y(Z) 1364 1607 y(\020) 1414 1586 y(Z) p Fg 1460 1775 a(j) p Fh(z) p Fg 1516 1775 a(j\025) p Fq(1) p Fj 1646 1703 a(n) p Fl(\() p Fj(z) p Fl 1791 1703 a(\)) p Fj(dz) p Fd 1947 1586 a(Z) p Fq 1993 1775 a(0) p Fh(<) p Fg(j) p Fh(y) p Fg 2140 1775 a(j) p Fh(<) p Fq(1) p Fi 2270 1703 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 2469 1703 a(+) p Fj 2567 1703 a(y) p Fl 2640 1703 a(+) p Fj 2738 1703 a(z) p Fl 2787 1703 a(\)) p Fi(j) p Fj(y) p Fq 2905 1662 a(2) p Fj 2944 1703 a(n) p Fl(\() p Fj(y) p Fl 3092 1703 a(\)) p Fj(dy) p Fd 3233 1607 a(\021) p Fq 3281 1630 a(2) p Fj 3320 1703 a(dx) p Fd 3426 1607 a(i) p Fq 3466 1630 a(1) p Fh(=) p Fq(2) p Fi 662 1902 a(\024) p Fl 822 1902 a([2) p Fj(C) p 975 1902 a(n) p Fq 1033 1917 a(0;) p Fg(1) p Fh(;) p Fq(0) p Fi 1218 1902 a(k) p Fj(V) p Fg 1346 1861 a(0) p Fi 1369 1902 a(k) p Fg 1419 1917 a(1) p Fl 1516 1902 a(+) p 1614 1902 a(2) p Fj(n) p Fq 1721 1917 a(0;) p Fg(1) p Fh(;) p Fq(0) p Fj 1906 1902 a(n) p Fq 1964 1917 a(0) p Fh(;) p Fq(2) p Fi 2058 1902 a(k) p Fj(V) p Fg 2186 1861 a(00) p Fi 2229 1902 a(k) p Fg 2279 1917 a(1) p Fl 2353 1902 a(]) p Fi(k) p Fj(u) p Fi(k) p Fj(:) p Fl 205 2118 a(The) p 406 2118 a(same) p 650 2118 a(is) p 748 2118 a(v) p 794 2118 a(alid) p 984 2118 a(for) p Fj 1133 2118 a(v) p Fg 1180 2133 a(1) p Fq(0) p Fl 1290 2118 a(.) 205 2239 y(F) p 261 2239 a(or) p Fj 380 2239 a(v) p Fg 427 2254 a(11) p Fl 573 2239 a(,) p 632 2239 a(in) p 746 2239 a(case) p Fj 952 2239 a(m) p 1065 2239 a(>) p Fl 1169 2239 a(0,) p Fi 258 2485 a(k) p Fj(v) p Fg 355 2500 a(11) p Fi 500 2485 a(k) p 633 2485 a(\024) p 793 2485 a(k) p Fj(V) p Fg 922 2444 a(00) p Fi 964 2485 a(k) p Fg 1014 2500 a(1) p Fd 1089 2389 a(h) 1128 2368 y(Z) 1211 2389 y(\020) 1261 2368 y(Z) p Fg 1307 2557 a(j) p Fh(y) p Fg 1364 2557 a(j\025) p Fq(1) p Fd 1494 2368 a(Z) p Fg 1540 2557 a(j) p Fh(z) p Fg 1596 2557 a(j\025) p Fq(1) p Fi 1726 2485 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 1925 2485 a(+) p Fj 2023 2485 a(y) p Fl 2096 2485 a(+) p Fj 2194 2485 a(z) p Fl 2243 2485 a(\)) p Fi(jj) p Fj(y) p Fi 2389 2485 a(j) p Fj(n) p Fl(\() p Fj(y) p Fl 2565 2485 a(\)) p Fi(j) p Fj(z) p Fi 2680 2485 a(j) p Fj(n) p Fl(\() p Fj(z) p Fl 2853 2485 a(\)) p Fj(dy) t(dz) p Fd 3094 2389 a(\021) p Fq 3142 2412 a(2) p Fj 3181 2485 a(dx) p Fd 3287 2389 a(i) p Fq 3327 2412 a(1) p Fh(=) p Fq(2) p Fl 793 2738 a(+) 879 2671 y(1) p 879 2715 49 4 v 879 2807 a(2) p Fi 938 2738 a(k) p Fj(V) p Fg 1066 2697 a(000) p Fi 1128 2738 a(k) p Fg 1178 2753 a(1) p Fd 1252 2642 a(h) 1292 2621 y(Z) 1375 2642 y(\020) 1424 2621 y(Z) p Fg 1470 2810 a(j) p Fh(y) p Fg 1527 2810 a(j\025) p Fq(1) p Fd 1658 2621 a(Z) p Fg 1704 2810 a(j) p Fh(z) p Fg 1760 2810 a(j\025) p Fq(1) p Fi 1890 2738 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 2088 2738 a(+) p Fj 2186 2738 a(y) p Fl 2260 2738 a(+) p Fj 2358 2738 a(z) p Fl 2407 2738 a(\)) p Fi(jj) p Fj(y) p Fi 2553 2738 a(j) p Fj(n) p Fl(\() p Fj(y) p Fl 2729 2738 a(\)) p Fi(j) p Fj(z) p Fi 2844 2738 a(j) p Fq 2872 2697 a(2) p Fj 2909 2738 a(n) p Fl(\() p Fj(z) p Fl 3054 2738 a(\)) p Fj(dy) t(dz) p Fd 3295 2642 a(\021) p Fq 3345 2665 a(2) p Fj 3384 2738 a(dx) p Fd 3490 2642 a(i) p Fq 3530 2665 a(1) p Fh(=) p Fq(2) p Fi 633 2991 a(\024) p Fl 793 2991 a([) p Fj(n) p Fq 878 2950 a(2) 878 3016 y(+;) p Fg(1) p Fh(;) p Fq(1) p Fi 1083 2991 a(k) p Fj(V) p Fg 1211 2950 a(00) p Fi 1254 2991 a(k) p Fg 1304 3006 a(1) p Fl 1400 2991 a(+) 1508 2924 y(1) p 1508 2968 V 1508 3059 a(2) p Fj 1567 2991 a(n) p Fq 1625 3006 a(+;) p Fg(1) p Fh(;) p Fq(1) p Fj 1829 2991 a(n) p Fq 1887 3006 a(+;) p Fg(1) p Fh(;) p Fq(2) p Fi 2092 2991 a(k) p Fj(V) p Fg 2220 2950 a(000) p Fi 2282 2991 a(k) p Fg 2332 3006 a(1) p Fl 2406 2991 a(]) p Fi(k) p Fj(u) p Fi(k) p Fj(:) p Fl 59 3232 a(In) p 181 3232 a(case) p Fj 387 3232 a(m) p Fl 500 3232 a(=) p 604 3232 a(0,) p Fi 462 3478 a(k) p Fj(v) p Fg 559 3493 a(11) p Fi 704 3478 a(k) p 837 3478 a(\024) p Fl 998 3478 a(4) p Fi(k) p Fj(V) p Fi 1175 3478 a(k) p Fg 1225 3493 a(1) p Fd 1299 3382 a(h) 1339 3361 y(Z) 1422 3382 y(\020) 1471 3361 y(Z) p Fg 1517 3549 a(j) p Fh(y) p Fg 1574 3549 a(j\025) p Fq(1) p Fd 1705 3361 a(Z) p Fg 1751 3549 a(j) p Fh(z) p Fg 1807 3549 a(j\025) p Fq(1) p Fi 1937 3478 a(j) p Fj(u) p Fl(\() p Fj(x) p Fl 2135 3478 a(+) p Fj 2233 3478 a(y) p Fl 2307 3478 a(+) p Fj 2405 3478 a(z) p Fl 2454 3478 a(\)) p Fi(j) p Fj(n) p Fl(\() p Fj(y) p Fl 2668 3478 a(\)) p Fj(n) p Fl(\() p Fj(z) p Fl 2851 3478 a(\)) p Fj(dy) t(dz) p Fd 3092 3382 a(\021) p Fq 3141 3405 a(2) p Fj 3180 3478 a(dx) p Fd 3286 3382 a(i) p Fq 3326 3405 a(1) p Fh(=) p Fq(2) p Fi 837 3683 a(\024) p Fl 998 3683 a(4) p Fj(n) p Fq 1105 3642 a(2) 1105 3708 y(0;) p Fg(1) p Fh(;) p Fq(0) p Fi 1289 3683 a(k) p Fj(V) p Fi 1417 3683 a(k) p Fg 1467 3698 a(1) p Fi 1542 3683 a(k) p Fj(u) p Fi(k) p Fj(:) p Fl 59 3899 a(Th) m(us) p 308 3899 a(putting) p 658 3899 a(all) p 795 3899 a(the) p 966 3899 a(estimates) p Fi 1397 3899 a(k) p Fj(v) p Fq 1494 3914 a(00) p Fi 1569 3899 a(k) p Fj(;) p Fi 1679 3899 a(k) p Fj(v) p Fq 1776 3914 a(0) p Fg(1) p Fi 1886 3899 a(k) p Fj(;) p Fi 1996 3899 a(k) p Fj(v) p Fg 2093 3914 a(1) p Fq(0) p Fi 2203 3899 a(k) p Fl 2288 3899 a(and) p Fi 2480 3899 a(k) p Fj(v) p Fg 2577 3914 a(11) p Fi 2722 3899 a(k) p Fl 2807 3899 a(ab) s(o) m(v) m(e) p 3085 3899 a(together,) p 3500 3899 a(w) m(e) p 3646 3899 a(ha) m(v) m(e) 59 4020 y(sho) m(wn) p 360 4020 a(\(iii\).) p 603 4020 a(Therefore) p 1049 4020 a(w) m(e) p 1198 4020 a(ha) m(v) m(e) p 1428 4020 a(pro) m(v) m(ed) p 1750 4020 a(Lemma) p 2103 4020 a(3.1,) p 2294 4020 a(completing) p 2797 4020 a(the) p 2970 4020 a(pro) s(of) p 3230 4020 a(of) p 3346 4020 a(Prop) s(osition) 59 4140 y(3.2.) p Fa 59 4428 a(Ac) l(kno) l (wledgmen) l(ts) p Fl 59 4613 a(The) p 250 4613 a(researc) m(h) p 617 4613 a(b) m(y) p 742 4613 a(the) p 900 4613 a(authors) p 1243 4613 a(has) p 1407 4613 a(b) s(een) p 1627 4613 a(partially) p 2010 4613 a(supp) s(orted) p 2458 4613 a(b) m(y) p 2584 4613 a(the) p 2742 4613 a(Gran) m(t-in-Aid) p 3318 4613 a(for) p 3457 4613 a(Scien) m(ti\014c) 59 4733 y(Researc) m(hes) p 552 4733 a(\(B\)) p 729 4733 a(No.) p 911 4733 a(16340038) p 1333 4733 a(and) p 1523 4733 a(\(C\)) p 1701 4733 a(No.) p 1883 4733 a(15540206,) p 2333 4733 a(Japan) p 2621 4733 a(So) s(ciet) m(y) p 2960 4733 a(for) p 3109 4733 a(the) p 3276 4733 a(Promotion) p 3760 4733 a(of) 59 4854 y(Science.) p Fk 59 5186 a(References) p Fl 59 5405 a([CHZ]) p 449 5405 a(Cac) m(hia,) p 800 5405 a(V) p 907 5405 a(.;) p 996 5405 a(Neidhardt,) p 1488 5405 a(H.) p 1621 5405 a(and) p 1812 5405 a(Zagrebno) m(v,) p 2318 5405 a(V.) p 2452 5405 a(A.:) p 2638 5405 a(Accretiv) m(e) p 3070 5405 a(p) s(erturbations) p 3681 5405 a(and) 449 5525 y(error) p 699 5525 a(estimates) p 1139 5525 a(for) p 1299 5525 a(the) p 1478 5525 a(T) p 1540 5525 a(rotter) p 1827 5525 a(pro) s(duct) p 2204 5525 a(form) m(ula,) p Fe 2635 5525 a(Inte) p 2800 5525 a(gr) p 2881 5525 a(al) p 3000 5525 a(Equations) p 3465 5525 a(Op) p 3585 5525 a(er) p 3666 5525 a(ator) 449 5646 y(The) p 609 5646 a(ory) p Fm 779 5646 a(39) p Fl 924 5646 a(\(2001\),) p 1255 5646 a(396{412.) 1900 5895 y(15) p eop %%Page: 16 16 16 15 bop Fl -66 312 a([I1]) p 324 312 a(Ic) m(hinose,) p 727 312 a(T.:) p 910 312 a(Essen) m(tial) p 1323 312 a(selfadjoin) m(tness) p 1968 312 a(of) p 2080 312 a(the) p 2249 312 a(W) p 2341 312 a(eyl) p 2497 312 a(quan) m(tized) p 2942 312 a(relativistic) p 3423 312 a(Hamil-) 324 433 y(tonian,) p Fe 703 433 a(A) n(nn.) p 958 433 a(Inst.) p 1198 433 a(H.) p 1346 433 a(Poinc) p 1587 433 a(ar) n(\023) p 1679 433 a(e,) p 1801 433 a(Phys.) p 2079 433 a(Th) n(\023) p 2200 433 a(eor.) p Fm 2409 433 a(51) p Fl 2565 433 a(\(1989\),) p 2910 433 a(265{298;) p Fe 3329 433 a(Err) p 3472 433 a(atum) p Fl(,) 324 553 y(In:) p 483 553 a(Ic) m(hinose,) p 884 553 a(T.) p 1014 553 a(and) p 1203 553 a(Tsuc) m(hida,) p 1650 553 a(T.:) p 1818 553 a(On) p 1979 553 a(Kato's) p 2288 553 a(inequalit) m(y) p 2740 553 a(for) p 2888 553 a(the) p 3056 553 a(W) p 3148 553 a(eyl) p 3302 553 a(quan) m(tized) 324 673 y(relativistic) p 804 673 a(Hamiltonian,) p Fe 1392 673 a(Manuscripta) p 1959 673 a(Math.) p Fm 2241 673 a(76) p Fl 2385 673 a(\(1992\),) p 2716 673 a(269{280.) -66 877 y([I2]) p 324 877 a(Ic) m(hinose,) p 726 877 a(T.:) p 904 877 a(Time-sliced) p 1425 877 a(appro) m(ximation) p 2075 877 a(to) p 2195 877 a(path) p 2422 877 a(in) m(tegral) p 2777 877 a(and) p 2967 877 a(Lie{T) p 3209 877 a(rotter{Kato) 324 997 y(pro) s(duct) p 692 997 a(form) m(ula,) p 1093 997 a(In:) p Fe 1257 997 a(A) p 1366 997 a(Gar) p 1527 997 a(den) p 1713 997 a(of) p 1829 997 a(Quanta,) p 2210 997 a(Essays) p 2530 997 a(in) p 2651 997 a(Honor) p 2955 997 a(of) p 3072 997 a(Hir) p 3210 997 a(oshi) p 3416 997 a(Ezawa) p Fl(,) 324 1118 y(W) p 416 1118 a(orld) p 617 1118 a(Scien) m(ti\014c) p 1031 1118 a(2003,) p 1286 1118 a(pp.) p 1454 1118 a(77{) p 1633 1118 a(93.) -66 1321 y([I) s(I]) p 324 1321 a(Ic) m(hinose,) p 721 1321 a(T.) p 845 1321 a(and) p 1029 1321 a(Ic) m(hinose,) p 1425 1321 a(W.:) p 1627 1321 a(On) p 1784 1321 a(the) p 1946 1321 a(essen) m(tial) p 2328 1321 a(self-adjoin) m(tness) p 2999 1321 a(of) p 3104 1321 a(the) p 3266 1321 a(relativistic) 324 1441 y(Hamiltonian) p 887 1441 a(with) p 1111 1441 a(a) p 1195 1441 a(negativ) m(e) p 1582 1441 a(scalar) p 1861 1441 a(p) s(oten) m(tial,) p Fe 2318 1441 a(R) p 2384 1441 a(ev.) p 2540 1441 a(Math.) p 2827 1441 a(Phys.) p Fm 3094 1441 a(7) p Fl 3185 1441 a(\(1995\),) p 3518 1441 a(709{) 324 1562 y(721.) -66 1765 y([INZ]) p 324 1765 a(Ic) m(hinose,) p 740 1765 a(T.;) p 915 1765 a(Neidhardt,) p 1420 1765 a(H.) p 1565 1765 a(and) p 1766 1765 a(Zagrebno) m(v,) p 2285 1765 a(V.) p 2430 1765 a(A.) p 2574 1765 a(:) p 2769 1765 a(T) p 2831 1765 a(rotter{Kato) p 3380 1765 a(pro) s(duct) 324 1886 y(form) m(ula) p 682 1886 a(and) p 872 1886 a(fractional) p 1308 1886 a(p) s(o) m(w) m(ers) p 1632 1886 a(of) p 1743 1886 a(self-adjoin) m(t) p 2245 1886 a(generators,) p Fe 2756 1886 a(J.) p 2872 1886 a(F) p 2929 1886 a(unctional) p 3357 1886 a(A) n(nalysis) p Fm 324 2006 a(207) p Fl 525 2006 a(\(2004\),) p 855 2006 a(33{57.) -66 2209 y([IT1]) p 324 2209 a(Ic) m(hinose,) p 717 2209 a(T.) p 837 2209 a(and) p 1017 2209 a(T) p 1079 2209 a(am) m(ura,) p 1399 2209 a(H.:) p 1569 2209 a(The) p 1759 2209 a(norm) p 2004 2209 a(con) m(v) m(ergence) p 2533 2209 a(of) p 2634 2209 a(the) p 2791 2209 a(T) p 2853 2209 a(rotter{Kato) p 3380 2209 a(pro) s(duct) 324 2330 y(form) m(ula) p 682 2330 a(with) p 904 2330 a(error) p 1142 2330 a(b) s(ound,) p Fe 1481 2330 a(Commun.) p 1932 2330 a(Math.) p 2216 2330 a(Phys.) p Fm 2481 2330 a(217) p Fl 2682 2330 a(\(2001\),) p 3013 2330 a(489{502.) -66 2533 y([IT2]) p 324 2533 a(Ic) m(hinose,) p 726 2533 a(T.) p 856 2533 a(and) p 1046 2533 a(T) p 1108 2533 a(am) m(ura,) p 1436 2533 a(H.:) p 1618 2533 a(Sharp) p 1900 2533 a(error) p 2138 2533 a(b) s(ound) p 2439 2533 a(on) p 2575 2533 a(norm) p 2830 2533 a(con) m(v) m(ergence) p 3369 2533 a(of) p 3480 2533 a(exp) s(o-) 324 2654 y(nen) m(tial) p 637 2654 a(pro) s(duct) p 993 2654 a(form) m(ula) p 1341 2654 a(and) p 1521 2654 a(appro) m(ximation) p 2162 2654 a(to) p 2272 2654 a(k) m(ernels) p 2588 2654 a(of) p 2689 2654 a(Sc) m(hr\177) p 2875 2654 a(odinger) p 3214 2654 a(semigroups,) 324 2774 y(Preprin) m(t.) -66 2977 y([ITTZ]) p 324 2977 a(Ic) m(hinose,) p 728 2977 a(T.;) p 889 2977 a(T) p 951 2977 a(am) m(ura,) p 1282 2977 a(H.;) p 1445 2977 a(T) p 1507 2977 a(am) m(ura,) p 1838 2977 a(Hiroshi) p 2179 2977 a(and) p 2371 2977 a(Zagrebno) m(v,) p 2877 2977 a(V.) p 3012 2977 a(A.:) p 3202 2977 a(Note) p 3440 2977 a(on) p 3578 2977 a(the) 324 3098 y(pap) s(er) p 602 3098 a(\\The) p 856 3098 a(norm) p 1115 3098 a(con) m(v) m(ergence) p 1658 3098 a(of) p 1773 3098 a(the) p 1946 3098 a(T) p 2008 3098 a(rotter{Kato) p 2549 3098 a(pro) s(duct) p 2919 3098 a(form) m(ula) p 3281 3098 a(with) p 3507 3098 a(error) 324 3218 y(b) s(ound") p 674 3218 a(b) m(y) p 809 3218 a(Ic) m(hinose) p 1183 3218 a(and) p 1373 3218 a(T) p 1435 3218 a(am) m(ura,) p Fe 1774 3218 a(Commun.) p 2225 3218 a(Math.) p 2509 3218 a(Phys.) p Fm 2775 3218 a(221) p Fl 2975 3218 a(\(2001\),) p 3306 3218 a(499{510.) -66 3421 y([K]) p 324 3421 a(Kato,) p 592 3421 a(T.:) p 766 3421 a(T) p 828 3421 a(rotter's) p 1166 3421 a(pro) s(duct) p 1528 3421 a(form) m(ula) p 1881 3421 a(for) p 2026 3421 a(an) p 2158 3421 a(arbitrary) p 2568 3421 a(pair) p 2765 3421 a(of) p 2872 3421 a(self-adjoin) m(t) p 3369 3421 a(con) m(trac-) 324 3542 y(tion) p 533 3542 a(semigroups,) p 1103 3542 a(In:) p Fe 1280 3542 a(T) p 1343 3542 a(opics) p 1599 3542 a(in) p 1727 3542 a(F) p 1784 3542 a(unctional) p 2219 3542 a(A) n(nalysis) p Fl 2617 3542 a(\(I.) p 2758 3542 a(Goh) m(b) s(erg) p 3163 3542 a(and) p 3361 3542 a(M.) p 3518 3542 a(Kac,) 324 3662 y(eds.\),) p 595 3662 a(Academic) p 1042 3662 a(Press,) p 1327 3662 a(New) p 1546 3662 a(Y) p 1611 3662 a(ork) p 1782 3662 a(1978,) p 2037 3662 a(pp.185{195.) -66 3866 y([LL]) p 324 3866 a(Lieb,) p 576 3866 a(E.) p 707 3866 a(H.) p 845 3866 a(and) p 1040 3866 a(Loss,) p 1292 3866 a(M.:) p Fe 1511 3866 a(A) n(nalysis) p Fl(,) p 1954 3866 a(Second) p 2290 3866 a(ed.,) p 2502 3866 a(Graduate) p 2941 3866 a(Studies) p 3288 3866 a(in) p 3407 3866 a(Mathe-) 324 3986 y(matics,) p 661 3986 a(V) p 726 3986 a(ol.) p 861 3986 a(14,) p 1018 3986 a(Amer.) p 1314 3986 a(Math.) p 1603 3986 a(So) s(c.,) p 1839 3986 a(Pro) m(vidence,) p 2366 3986 a(Rho) s(de) p 2674 3986 a(Island) p 2964 3986 a(2001.) -66 4189 y([RS]) p 324 4189 a(Reed,) p 589 4189 a(M.) p 729 4189 a(and) p 910 4189 a(Simon,) p 1229 4189 a(B.:) p Fe 1396 4189 a(Metho) p 1655 4189 a(ds) p 1772 4189 a(of) p 1878 4189 a(Mo) p 2010 4189 a(dern) p 2228 4189 a(Mathematic) p 2724 4189 a(al) p 2825 4189 a(Physics) p 3169 4189 a(I:) p 3264 4189 a(F) p 3321 4189 a(unctional) 324 4310 y(A) n(nalysis) p Fl(,) p 751 4310 a(Revised) p 1113 4310 a(and) p 1303 4310 a(enlarged) p 1693 4310 a(ed.,) p 1888 4310 a(Academic) p 2335 4310 a(Press,) p 2619 4310 a(New) p 2839 4310 a(Y) p 2904 4310 a(ork,) p 3101 4310 a(London) p 3455 4310 a(1980.) -66 4513 y([S]) p 324 4513 a(Stein,) p 611 4513 a(E.) p 745 4513 a(M.:) p Fe 975 4513 a(Singular) p 1370 4513 a(Inte) p 1535 4513 a(gr) p 1616 4513 a(als) p 1773 4513 a(and) p 1970 4513 a(Di\013er) p 2215 4513 a(entiability) p 2677 4513 a(Pr) p 2779 4513 a(op) p 2874 4513 a(erties) p 3149 4513 a(of) p 3271 4513 a(F) p 3328 4513 a(unctions) p Fl(,) 324 4634 y(Princeton) p 770 4634 a(Univ.) p 1035 4634 a(Press,) p 1319 4634 a(Princeton) p 1765 4634 a(1970.) -66 4837 y([T]) p 324 4837 a(T) p 386 4837 a(rotter,) p 691 4837 a(H.) p 825 4837 a(F.:) p 1002 4837 a(On) p 1165 4837 a(the) p 1334 4837 a(pro) s(duct) p 1701 4837 a(of) p 1814 4837 a(semigroups) p 2320 4837 a(of) p 2432 4837 a(op) s(erators,) p Fe 2905 4837 a(Pr) p 3007 4837 a(o) p 3052 4837 a(c.) p 3163 4837 a(A) n(mer.) p 3464 4837 a(Math.) 324 4957 y(So) p 424 4957 a(c.) p Fm 531 4957 a(10) p Fl 675 4957 a(\(1959\),) p 1006 4957 a(545{551.) 1775 5895 y(16) p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0408172206176--