Content-Type: multipart/mixed; boundary="-------------0701271854605" This is a multi-part message in MIME format. ---------------0701271854605 Content-Type: text/plain; name="07-22.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="07-22.keywords" semiclassical analysis, magnetic scattering by solenoids, total cross section, Aharonov-Bohm effect ---------------0701271854605 Content-Type: application/postscript; name="07tamura.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="07tamura.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.78 p1.4c Copyright 1996-99 ASCII Corp.(www-ptex@ascii.co.jp) %%based on dvipsk 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: 07tamura.dvi %%Pages: 47 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR12 CMMI12 CMMIB10 CMR8 CMSY10 CMEX10 CMMI8 %%+ CMSY8 CMSY6 CMR6 CMMI6 CMTI12 LASY10 %%EndComments %DVIPSCommandLine: dvipsk -D600 -t a4size -P dl 07tamura.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2007.01.28:0948 %%BeginProcSet: texc.pro %! 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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 61 /slash put dup 104 /h 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 93971def6fc0aed1bcd3e15825f528f4afa81d64383f34d8450446f639402cf7 9bdc40b3eed0bc6ccee2a6aebbf8bba094d77191d823cab967bedb48a0697e4d e725bd3bd2e84c8940ceb2d7edaf1144f526f0739cc6049a1126be1721a05e7f 703126e4ec0aa4f07c397e8c65192ff15dde5964413100fca34572a81ff2bcf1 931dbc12e0eb7da19cd1560f088e05ee5f48f5ce6bd27b6e086962bc6896370b 3da225b31236ec9b5dc478c294c68d02e38936271ec3d172a5b12bd427c41592 011f31d63fe3ef8ea6a950557feeeb6b2b348e6e7b2e1dda18f53e530cf94cd0 03eddd0d7ece019a62e7f1a1093c61e169106c8d6c947269428f5996038e76a7 35deb69ccc234873632e5336837d6c8925e13728757e2517c2905d292fb17e5b a459bf5c9af5b8c0bd97d35d6b7bb3265843668dbc80c750f6734ba2804ef608 b2f12e6f102cf42e98da6a3d94551cace64c04581fcdce2171077b87b140241a fbbfdea01fb7dcbe1a847d2084169dfc0cf62378d612f3f42437705f5d7495dd 48e87e0fdffeaddbc9c2925e0844cad2c36cbddfde473f808a2519cd571b9bcf 1253425d054dd13e597d04d82d506301af5b9b235f33ba8763ee0d1fb8586b9f 87efbd0f19849cb6ba66db8af5a25c80e3bbec0b824ae8d24cb1b60dbdc43cca f08536869df90af498d0e9a6c756b49a367dd15e9cb14149476780e634cbbb07 a901269d9a51fea9e29e62ac4142bbf1e60e753df9af187984163a57a1f7378f 5df0e88cd50852390b146ff0763bd69168457793e302831e24600226826db4b7 08cfdd64c5e6e8a5c32faa562df19d50cf943939272ea8c8f15d7528eda2896c 18c7a6bf525aef3e4ed00df6e3516ac6d87ff12a342c66f2989a6a6aa65de050 b9fef087316340aa255ed0e403749dfe0cde56fa3ae36a834b81b13bbdededf6 eaf4a2339d992bb11389a7f3c914158008227d63f54b27bf10237da1c8e33e33 6f7b43 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 49 /one 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523d98f2e44ef37ad46 282d7a587974734c2b1e24d85e2f81581a8e36a6bcfbfe9dd0920ea5cc7255dc 2040d88b37bf8afa1d04f1ec06a739f608b5fa14bac8a50bb50a12d6574847a7 cf42db3fb99524d4ac40eb874d5d228b557be3c5eede986279a04e0d5fff1fb6 72e8393e9db5a96a98000702512357b8978176cc69e6c3cf9747115422e28e80 b52f0cd73e33bfb799bbeb967ac7ed1bd961d7cd4fb14ecbfd341a322c4bebb0 aea969d33fd1cdff622d99f899dd9a21c8cb71f12cbf68997e5b9916192bedf0 c6021653ba33cd5b680d856f0863ce13a8c30889f1b00ffab149482da65a888c d570b5bd355ecc9f652c5682ffb5a87ba6c06483a78cb43fd27af7eaf14f137b c291b8e0d74a2dac9b8bb65455a2cbb9b05ca4e34f5f99fc44414c3749b9b049 6331024fb02f634ad14fc8909e01c08a7e0b3dc45e15dbdca67ab9b8b02bed02 4eb50746207b2b55517d95c8cbdcea55351544abe617130b040d22f3428f6ea0 5c10de237ed8f8a2a939304099e852a5c79065ea7bc951fb41abdd1d73629c13 8cfb1409060d9eb44121e62a086ad032d9b1de17ef1af57b5f3ce3711286a5ee f7101318e631e467f9bb5c1104762d609dcb4b72e787b68dbf4cb9a049237824 3991ce7507693804d4a0598766739c4749d2662a4495480912c7b6680b46c58f 6fbe523521ef3c3d9baca2ec31e24cf809cc37ec918fd9699aa477d7e2a26829 23d8496f7468c7a6398f2abc4ec9 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put dup 7 /minusplus put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e2851905abd26842613d8fb644512275d43f312eea72f7ea3ba90c8fda6ce 7a9dacf52f55f0dd557f8d866ed6f3d3d5e6fe7e9ee79404fbe1a285bc519ecd 7ca162f0729044aff526bfe554ed59dd9beab0f842d55be08caada6136ac9f94 4cd96ff1c2f4927d87fea4496a1d612d58eba570eef0007c665fd143e9030923 517ac31aaf6912012671dd87686f2aaab25a2adc7501663d8a1ef80cc7da7dbe 13fb5333a4618ad8b4a6c2cc8fa3d616c65848c95ac10893c62198f642f2d2f3 503204e5d5aaef2602d4953fd4b77b402232f603d83de73bb3c2d50e2416481d 92e8147eef905c280f51ecf84db66a6de0126d7b31d961386f0d80be7105cf28 b6349fbdef6efc6c1a83b5ba52ff1bb2068ec20cc03a7617a66130265dedcb48 46574b8c15ad9a2193d7d03328115d621264e2749d69e6ce6d4ddc982d577f36 465461590df040b0e08acec271e6550c2ab526bcea06a1689538e48494430464 bc473cd96cb8efcd2596d469b97ed65e5f20590cabba4187678583165075d535 981f30c2436cb6e4ed6f86c15b1114d02e0b34d71cb28620605a107712f74a8e cf45b9b558ef2deb4c84cd6671306aed6dcd5b17b411e772340d5efa82384de9 fa2cbc7850e071cfd4e4c32d59d1e0e975508792858068886a3dda363b83be8e ce4b174afdf8c1ee2ecfd8049aaf 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 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 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 b910bf03a423f0988c943911f0aae5494ef9465ab04f591e6e844b8155df1f90 584866c5dd894c23a0ef626eddbedc47c01a3f1a55a925ae47a6ae5bc8f9e674 80a0a57393f694abdcbd2e00c402b8808b0cea7f6589418179cc310304a6aafe b647f69ec3680c977db513a99eb3401b0a31d34e2eef0c5dc63b3d67bd8a8a9b 7b0c365a933cd69ef97c12e20ab727e3eb8c53319e314cb1b10a0ff1dc8824a9 23664ef52a0cff51c082ad648cb3d3c9904bfc7ac8de08b306264069fcd40bdc 8a50e98a1e29ee510aae9e5d1e543b88ef4cf9de59a6a8e4cfc3166e9a87e09a 04d5ddd2342e3aeff19ec49c31ab88dbb9f5b837b856dc03f04d784344718ac7 0be9c06df01779a2631789a0d0416dd3bde99e4208e68bee5c1c99e16b7cc198 95e4a258bb8d0f67ad5ff5e0441f6b1c9fc3523bd2b083f266cb1ba3d4b0d7f5 91f7bfcd5ae8cab3b9f1866144dd0f472764420ac2be5b3410ac0260c84f7f5f 110ac30b75f15e893dbd536fcb016f5db23cf25c68c68052555255397f8fc9d3 5563ec9e5795eec6438c40d549a538eaa41ddf2e78dfcf3ffac8fa46176278af f60b7a7994e5933e3530c7bb62d95715335ee3f3f59d7c0bfe9e1297538b659f f1d2ca6dac0aec14cae1fefa0d5be0654fe7852641e3cac322c59ca4aac7116e 9df64f2a3e0c0aa1db4538ac456d0e710936837f16084f8b3caa89b8b377d508 88fb758254c0f491051246999cc83485a944eeb78e4d307415dc8add65871e60 a38ed7bd390152ad50026843aef3c03b01b75547b180db927d34b1b495282450 c59da54d20a82c7e2d69a9b79b8ba93f6841149c19283f280738922a081c40d4 fcaefe7645219ebc65f9b578923e958b7831380332c770f5a5a20b0e48138774 209a97cff9cd143fec2789c882209734e4cf6dec67d6fb2396e95dc9df60c724 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%%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 69 /E put dup 77 /M put dup 78 /N put dup 90 /Z put dup 99 /c put dup 100 /d put dup 101 /e 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 112 /p put dup 114 /r 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 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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 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 98 /hatwide 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 10 /circlemultiply put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 28 /lessmuch put dup 29 /greatermuch put dup 33 /arrowright put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 59 /emptyset put dup 68 /D put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 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0c823923c0b6c76446b737e8a8af832eb44ddd84774ad0baf59165438713c1d5 46124fcc809de5d30be037e501bae76a1077d7d051815114cd8a24fa722cf6c1 009eb1e8da7feda6ee320031bcd61357441d768534d9855745e64960bae41080 67d64e13dc7dc2c90e80c3d719b051f21e5d6e557567946aa6f331e4f076f031 83f9a7ecab70b21d639bbd97562af5a626eeea3c625425219b1db368895d7e33 7c7ba0bba5adbec1a16a7dbada54f2ad7fb57cf4bf288ff77853a714 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 53 /five put dup 54 /six put dup 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 99 /c put dup 104 /h put dup 105 /i put dup 110 /n put dup 111 /o put dup 115 /s put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 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0563caa7deada41b503d8070d4ec23c014951898e13997fe0e35c5a203e0e946 bbde9d3daacc91f6341aacaeaf6ee4fa1a415acda19fa780e4c438433a0d367a fcff3c1c52af271b008e38f943e6bb5253c561c34ed6da9537f6223120fd48c2 eb9cd62dab8872415bffd32ba58e8066bc832d875da1d5af397dd6fb201706b5 3a21c36884f0d4e483774dbc40cd852cab125698b602de3ece2af0b415f171cd 5daed60d2e3617c7a40eabba0b0f4d729f86de7c9c68998685c86f027f403396 799af5785df476e41d229828275bb9d3f46f27f21f0aa24beabfe876109ef46c 6e21a6e6ea946032d97e6ae2c3723ad6b45d1d315d1339a33dadda5ab5a86ce5 c687520a27f6cdb7f63ba7f806446b688829264145cec55a1ea0747ea95c4675 507ea260421565877b2e2988772d5740e165a9805938a427388176e4d6f4abe1 ceb12e40bfe890b76301df58463a2bdc5124c400805344b201a4688d0e674ecd 8ca36b08afb7db768103a65a44279c07c9777f30bb578eb77346acc4d4b1f02d 03d76d5749192646b2b368df42c72639e128f2376acdcb69f2447a9a51d7891e 9df8b053772e8975a6cc58cc1d635ecd03c7343d790848d27036c82091058e15 b0306aec19141e55df45530e50ef6bc4183fc43ec7fd38ca65ed6fdc66c01e52 4768cc91f55aad5335564841088eca33ec2f141c98faf888323553c15c6d55ed 128666695046a97497b32cea70fb8cacd78922c46a3e6f80a96f1bf59277e0a6 df2edaf8c2447d787fc3305f56af898610b4f761d0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % 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 (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueID 5087392 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d78041490e364babe4b85935b8c9c7758c2dbe253653c 892b1fc2c6a01103e0b8553f847bb38d8e4fcd563ebe51cb7d5f0877af29249d b61636618fb31eeb6cbb4ea4db687fd77ed1574da8c9f9d33b592ec0e38d798c 498a205cab252f7e2f1ddb82a38f331f917b8452af11b2b93e34c1ef55ee005c e8418dbcd0fb9d4d3fa8cb388ec91f16c8864913ad3fc8960d3c424650bdd12c 4db4049367faae97c660f00021f712e9eb6366b7ce74255ff62b72396ca43287 7c77fecdc53883427c90c1c3ff7bd46e472cea9bd72eef0e1be36abb3a50a7bf 6f5d460fa2fc81466014df9ee1e15365642c2de78706dfa740e035b4f28f290d 79b8ba16e5bca13fd9c3eb7eb54006ac2c1cf0bf363b3b69e923797a95b76515 073892c75cf733da7c07da8ed1a8d1ded902f784764c6df6fcd0fd28083d88c8 4c41aeaa6c2c2c1bb10219f4feaab75ee904f4314fc0b9de5e96054f2472ad86 42140315385400686cb07a0585d922ae4b1b25ae722edc6b4afe053560fc9ac9 20a1d2fb8d0921c52c9468d34dba9bed42e3a8308742d36186ed0a3b43f690a4 dca6bb2af8bd698fb303fd68df53edc5e01912cf007dd31ca7481ce844be1258 7002d4aafb204a8075fc6df86f22249d61dd840e7ef87362d72e35f4e8ece044 95ae41ee5c02d6aafaad37141935867a8770fbd9e9ea71e77d3c935c53100566 039eb96ba3821b284b42a0e2ac4ad3181ff029ce1394c31e7694b2e7f47d34c4 190a2ec05ecb43774baeceb345230f68a967b91883e3b184d030c1183d707d1f 2cda85d6de979350243ede31995d77233c2ee1e2b00c53ee0c0fea0c527c706e 114259f991939e5a79d0eb4ef82df7fb0f7434be3b242b840f1c0dee6aa1a98c 20f395e9b93d121bb1e0e420aaaf34ecc31289bea097a288ffbc9dc85f95b752 f4561d817fa7ad9921e00b0ec4cb9ef1385d0cedcd674a9138118ad7a9e02b87 8e71ef2710a5fb847b900e2c917660d161606700958f72c0fcf42ce0752b209f e00ba3aeaf22b19a27480e0e6797cf37b07de77db58375f6c8f45d6755c15e45 eb0be8b1514781b038bfc8d4c0892015ef53dab93e4a2ef508bba2036e30fbda 1dc0803e90cd463d9eeae68b8d3fabdf0b6706f973d20bd3fa27640ef9c15c4d 081e1c458e386fc66c4a21b47b5b447cca02c179b6d9d406f26759fda215e4d2 387a1b6641d6f5454b27be1eee70ef8fb564c06a9df1c191231e30ad5bba8ff3 d22ef750bf75673e9eea30b5175d9670145d5bcd82750ca66d3a9a8290668c7c 658877a6dd0377c31f627de8f23aecc930b7a771437e72ebb36defad48d80524 b63d052d862a83b34e4857135476717d9a53bad61f9ab5a36e530dda5d5cde4c e8cf725c9bfe976d662056b6cf199cfc3ff19b2ccaba7638c2d7bb2e0d5cdf82 eceae11701d69f57da89589869d22f3b3bbfa9be4a1a579421101bf8e867c5ee 318990b8deda6e8fae2be98aff1513db3c512efc4f79bfb789c6a157009c375f d2a2dcb905a15de14202e8309cab410ce78ee34c1e7b76c6237309a7218929fe d30e9c2064ea79b07045404a4f3f7025fd95a80c13 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 13 /gamma put dup 14 /delta put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 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 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z 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 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put 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 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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 3 /Lambda put dup 5 /Pi put dup 6 /Sigma put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 22 /macron put dup 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 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98e7457ac80873047b08c15d080b09e189a6edd27778f2d6d60f11ee95c1c89c 0b70986e3c6931b6ad80fc2917c2976915084fe2bfcec0e1665a76718579d3f2 6aec26fee08d84d50f5737ce5a9cf478bfa2c22f0ed3b18845b87884f229b504 28d2af6815407270ef26f7fd9174bb40df8437457af7e435760eae9445720d30 5a775dd5ab4b40433077c130222ef7c0893ef41f0a2b2e38 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P 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 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 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (07tamura.dvi) @start /Fa 205[ 74 50[{ } 1 99.6264 /LASY10 rf /Fb 132[ 50 1[ 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 9[ 97 1[ 72 70 55 71 75 66 75 72 87 61 1[ 51 38 72 75 64 66 74 70 69 72 6[ 30 50 50 1[ 50 50 50 50 50 50 50 1[ 30 1[ 30 2[ 40 40 20[ 50 6[ 55 60 11[{ } 64 99.6264 /CMTI12 rf /Fc 151[ 36 42[ 32 26[ 29 34[{ } 3 49.8132 /CMMI6 rf /Fd 205[ 30 30 5[ 47 43[{ } 3 49.8132 /CMR6 rf /Fe 248[ 48 48 5[ 48{ } 3 49.8132 /CMSY6 rf /Ff 149[ 20 55[ 47 71 19 12[ 35 1[ 71 11[ 55 55 12[ 55 55 2[ 35 1[ 20 55{ } 13 66.4176 /CMSY8 rf /Fg 133[ 33 35 40 3[ 25 33 32 1[ 36 1[ 43 62 21 37 29 24 41 2[ 33 36 31 8[ 48 11[ 56 68 7[ 52 6[ 55 35 55 20 24[ 33 44 5[ 40 36 41 31 35 42 3[ 33 35 31 2[ 36 40 45 11[{ } 39 66.4176 /CMMI8 rf /Fh 150[ 39 39 5[ 46 7[ 46 1[ 120 18[ 51 51 2[ 73 73 14[ 73 73 6[ 67 67 6[ 66 66 10[ 44 44 61 61 50 50 3[ 28 12[{ } 22 83.022 /CMEX10 rf /Fi 141[ 83 1[ 83 1[ 50 2[ 50 28 39 39 50 50 9[ 66 66 22[ 77 8[ 50 4[ 0 3[ 66 100 9[ 77 5[ 100 3[ 100 100 1[ 77 1[ 77 2[ 77 77 9[ 77 1[ 77 77 77 3[ 77 28 77{ } 31 99.6264 /CMSY10 rf /Fj 129[ 35 10[ 28 3[ 35 39 4[ 20 39 4[ 31 4[ 35 20 1[ 20 29[ 55 1[ 20 4[ 35 35 35 35 35 35 35 4[ 55 1[ 27 27 40[{ } 22 66.4176 /CMR8 rf /Fk 173[ 87 82[{ } 1 99.6264 /CMMIB10 rf /Fl 133[ 45 48 55 70 47 56 35 46 44 1[ 49 47 58 1[ 29 51 40 33 56 47 48 45 51 42 41 51 6[ 67 57 81 92 57 66 57 60 74 77 1[ 75 78 94 66 83 54 43 81 77 63 72 81 70 74 73 51 1[ 76 49 76 27 27 18[ 64 4[ 46 61 63 61 2[ 42 55 50 55 43 48 59 57 56 1[ 45 48 43 1[ 43 51 55 62 11[{ } 76 99.6264 /CMMI12 rf /Fm 128[ 49 49 2[ 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 2[ 49 27 1[ 27 60 73 73 100 73 73 70 54 72 76 66 76 73 89 61 76 50 35 73 77 64 66 75 70 69 73 1[ 46 1[ 76 1[ 27 27 49 49 49 49 49 49 49 49 49 49 1[ 27 33 27 76 1[ 38 38 27 4[ 49 27 10[ 49 7[ 81 54 54 57 70 76 70 1[ 70 73 1[ 68 1[ 81 61{ } 94 99.6264 /CMR12 rf /Fn 134[ 59 59 81 1[ 62 44 44 46 1[ 62 56 62 93 31 59 1[ 31 62 56 34 51 62 50 62 54 12[ 78 62 84 1[ 77 84 2[ 67 2[ 42 88 2[ 74 1[ 81 1[ 85 6[ 31 56 56 56 56 56 56 56 56 56 56 1[ 31 1[ 31 31[ 62 12[{ } 47 99.6264 /CMBX12 rf /Fo 132[ 59 1[ 62 2[ 62 65 46 46 46 1[ 65 59 65 98 1[ 62 1[ 33 65 1[ 36 52 65 52 1[ 59 11[ 88 85 4[ 91 1[ 107 2[ 60 1[ 88 3[ 89 11[ 59 59 1[ 59 1[ 59 2[ 59 3[ 33 44[{ } 32 119.552 /CMR12 rf /Fp 134[ 85 1[ 117 2[ 63 64 66 2[ 81 90 134 45 2[ 45 1[ 81 49 74 90 72 90 78 12[ 112 90 5[ 153 6[ 101 2[ 117 1[ 122 6[ 45 58[{ } 24 143.462 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop Fp 130 791 a(Semiclassical) p 1089 791 a(Analysis) p 1735 791 a(for) p 1984 791 a(Magnetic) p 2693 791 a(Scattering) 80 927 y(b) l(y) p 305 927 a(Tw) l(o) p 663 927 a(Solenoidal) p 1434 927 a(Fields) p 1906 927 a(:) p 2023 927 a(T) p 2122 927 a(otal) p 2442 927 a(Cross) 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a(e) p Fm(\() p Fl(!) p Ff 878 5399 a(\000) p Fm 937 5384 a(\)) p 1005 5384 a(=) p Fl 1111 5384 a(e) p Fi 1179 5384 a(\000) p Fm 1280 5384 a(\() p Fl(e) p Fi 1385 5384 a(\001) p Fl 1435 5384 a(!) p Ff 1496 5399 a(\000) p Fm 1555 5384 a(\)) p Fl 1609 5384 a(!) p Ff 1670 5399 a(\000) p Fb 1765 5384 a(is) p 1871 5384 a(the) p 2034 5384 a(pr) p 2120 5384 a(oje) p 2240 5384 a(ction) p 2488 5384 a(of) p Fl 2604 5384 a(e) p Fb 2685 5384 a(onto) p 2908 5384 a(the) p 3071 5384 a(imp) p 3226 5384 a(act) p 3389 5384 a(line) 0 5504 y(p) p 45 5504 a(erp) p 176 5504 a(endicular) p 603 5504 a(to) p Fl 720 5504 a(!) p Ff 781 5519 a(\000) p Fb 840 5504 a(.) p Fm 1747 5753 a(3) p 90 rotate dyy eop %%Page: 4 4 4 3 bop Fm 146 407 a(W) p 238 407 a(e) p 314 407 a(mak) m(e) p 569 407 a(a) p 650 407 a(commen) m(t) p 1069 407 a(on) p 1205 407 a(ho) m(w) p 1408 407 a(the) p 1575 407 a(A{B) p 1799 407 a(quan) m(tum) p 2210 407 a(e\013ect) p 2467 407 a(is) p 2565 407 a(re\015ected) p 2955 407 a(in) p 3069 407 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m(t) 0 3728 y(realization) p 477 3728 a(with) p 699 3728 a(domain) p Fi 546 3938 a(D) p Fm 654 3938 a(=) p Fi 757 3938 a(f) p Fl(u) p Fi 890 3938 a(2) p Fl 984 3938 a(L) p Fj 1050 3897 a(2) p Fm 1118 3938 a(:) p 1173 3938 a(\() p Fi(\000) p Fl(ih) p Fi(r) p 1483 3938 a(\000) p Fl 1582 3938 a(A) p Fm(\)) p Fj 1693 3897 a(2) p Fl 1733 3938 a(u) p Fi 1816 3938 a(2) p Fl 1910 3938 a(L) p Fj 1976 3897 a(2) p Fl 2016 3938 a(;) p Fm 2200 3938 a(lim) p Ff 2106 4001 a(j) p Fg(x) p Ff(\000) p Fg(e) p Fe 2254 4010 a(\006) p Ff 2305 4001 a(j!) p Fj(0) p Fi 2447 3938 a(j) p Fl(u) p Fm(\() p Fl(x) p Fm(\)) p Fi(j) p Fl 2717 3938 a(<) p Fi 2820 3938 a(1g) p Fl(;) p Fm 0 4203 a(where) p 282 4203 a(\() p Fi(\000) p Fl(ih) p Fi(r) p 592 4203 a(\000) p Fl 692 4203 a(A) p Fm(\)) p Fj 803 4167 a(2) p Fl 843 4203 a(u) p Fm 931 4203 a(is) p 1030 4203 a(understo) s(o) s(d) p 1540 4203 a(in) p 1654 4203 a(the) p 1823 4203 a(distribution) p 2355 4203 a(sense.) p 2644 4203 a(The) p 2845 4203 a(op) s(erator) p Fl 3238 4203 a(H) p Fg 3319 4218 a(h) p Fm 3397 4203 a(can) 0 4323 y(b) s(e) p 131 4323 a(sho) m(wn) p 425 4323 a(to) p 542 4323 a(ha) m(v) m(e) p 766 4323 a(the) p 932 4323 a(follo) m(wing) p 1342 4323 a(sp) s(ectral) p 1706 4323 a(prop) s(ert) m(y) p 2103 4323 a(\([8,) p 2275 4323 a(section) p 2599 4323 a(7]\)) p 2743 4323 a(:) p Fl 2813 4323 a(H) p Fg 2894 4338 a(h) p Fm 2969 4323 a(has) p 3141 4323 a(no) p 3275 4323 a(b) s(ound) 0 4444 y(states) p 271 4444 a(and) p 455 4444 a(its) p 585 4444 a(sp) s(ectrum) p 1005 4444 a(is) p 1097 4444 a(absolutely) p 1554 4444 a(con) m(tin) m(uous.) p 2078 4444 a(W) p 2170 4444 a(e) p 2240 4444 a(can) p 2413 4444 a(further) p 2735 4444 a(sho) m(w) p 2970 4444 a(that) p 3176 4444 a(the) p 3337 4444 a(w) m(a) m(v) m(e) 0 4564 y(op) s(erator) p Fl 393 4564 a(W) p Ff 485 4579 a(\006) p Fm 544 4564 a(\() p Fl(H) p Fg 663 4579 a(h) p Fl 708 4564 a(;) p 752 4564 a(H) p Fj 833 4579 a(0) p Fg(h) p Fm 912 4564 a(\)) p 983 4564 a(exists) p 1252 4564 a(and) p 1442 4564 a(is) p 1540 4564 a(asymptotically) p 2196 4564 a(complete) 763 4774 y(Ran) p 954 4774 a(\() p Fl(W) p Fj 1084 4789 a(+) p Fm 1143 4774 a(\() p Fl(H) p Fg 1262 4789 a(h) p Fl 1307 4774 a(;) p 1351 4774 a(H) p Fj 1432 4789 a(0) p Fg(h) p Fm 1512 4774 a(\)\)) p 1615 4774 a(=) p 1719 4774 a(Ran) p 1910 4774 a(\() p Fl(W) p Ff 2040 4789 a(\000) p Fm 2099 4774 a(\() p Fl(H) p Fg 2218 4789 a(h) p Fl 2263 4774 a(;) p 2307 4774 a(H) p Fj 2388 4789 a(0) p Fg(h) p Fm 2467 4774 a(\)\)) p 2571 4774 a(=) p Fl 2674 4774 a(L) p Fj 2740 4732 a(2) p Fm 0 4983 a(for) p 155 4983 a(pair) p 360 4983 a(\() p Fl(H) p Fg 479 4998 a(h) p Fl 524 4983 a(;) p 568 4983 a(H) p Fj 649 4998 a(0) p Fg(h) p Fm 729 4983 a(\)) p 805 4983 a(with) p Fl 1032 4983 a(H) p Fj 1113 4998 a(0) p Fg(h) p Fm 1230 4983 a(=) p Fi 1343 4983 a(\000) p Fl(h) p Fj 1476 4947 a(2) p Fm 1516 4983 a(\001.) p 1684 4983 a(Hence) p 1980 4983 a(the) p 2153 4983 a(scattering) p 2609 4983 a(op) s(erator) p Fl 3007 4983 a(S) p Fm 3073 4983 a(\() p Fl(H) p Fg 3192 4998 a(h) p Fl 3237 4983 a(;) p 3281 4983 a(H) p Fj 3362 4998 a(0) p Fg(h) p Fm 3441 4983 a(\)) p 3516 4983 a(:) p Fl 0 5104 a(L) p Fj 66 5067 a(2) p Fi 143 5104 a(!) p Fl 280 5104 a(L) p Fj 346 5067 a(2) p Fm 425 5104 a(can) p 609 5104 a(b) s(e) p 748 5104 a(de\014ned) p 1090 5104 a(as) p 1215 5104 a(a) p 1302 5104 a(unitary) p 1652 5104 a(op) s(erator.) p 2100 5104 a(The) p 2307 5104 a(mapping) p Fl 2713 5104 a(F) p Fg 2776 5119 a(h) p Fm 2860 5104 a(de\014ned) p 3202 5104 a(b) m(y) p 3343 5104 a(\(2.2\)) 0 5224 y(decomp) s(oses) p Fl 529 5224 a(S) p Fm 595 5224 a(\() p Fl(H) p Fg 714 5239 a(h) p Fl 759 5224 a(;) p 803 5224 a(H) p Fj 884 5239 a(0) p Fg(h) p Fm 963 5224 a(\)) p 1034 5224 a(in) m(to) p 1232 5224 a(the) p 1400 5224 a(direct) p 1676 5224 a(in) m(tegral) p Fl 559 5466 a(S) p Fm 625 5466 a(\() p Fl(H) p Fg 744 5481 a(h) p Fl 788 5466 a(;) p 832 5466 a(H) p Fj 913 5481 a(0) p Fg(h) p Fm 993 5466 a(\)) p Fi 1058 5466 a(') p Fl 1163 5466 a(F) p Fg 1226 5481 a(h) p Fl 1271 5466 a(S) p Fm 1337 5466 a(\() p Fl(H) p Fg 1456 5481 a(h) p Fl 1501 5466 a(;) p 1545 5466 a(H) p Fj 1626 5481 a(0) p Fg(h) p Fm 1705 5466 a(\)) p Fl(F) p Ff 1820 5425 a(\003) p Fg 1806 5490 a(h) p Fi 1887 5466 a(') p Fh 1992 5349 a(Z) p Ff 2075 5375 a(1) p Fj 2038 5537 a(0) p Fi 2167 5466 a(\010) p Fl 2261 5466 a(S) p Fm 2327 5466 a(\() p Fl(\025) p Fm(;) p Fl 2466 5466 a(H) p Fg 2547 5481 a(h) p Fl 2591 5466 a(;) p 2635 5466 a(H) p Fj 2716 5481 a(0) p Fg(h) p Fm 2795 5466 a(\)) p Fl 2850 5466 a(d\025;) p Fm 1747 5753 a(5) p 90 rotate dyy eop %%Page: 6 6 6 5 bop Fm 0 407 a(where) p 288 407 a(the) p 463 407 a(\014bre) p Fl 691 407 a(S) p Fm 757 407 a(\() p Fl(\025) p Fm(;) p Fl 896 407 a(H) p Fg 977 422 a(h) p Fl 1021 407 a(;) p 1065 407 a(H) p Fj 1146 422 a(0) p Fg(h) p Fm 1226 407 a(\)) p 1292 407 a(:) p Fl 1346 407 a(L) p Fj 1412 366 a(2) p Fm 1452 407 a(\() p Fl(S) p Fj 1556 366 a(1) p Fm 1595 407 a(\)) p Fi 1661 407 a(!) p Fl 1788 407 a(L) p Fj 1854 366 a(2) p Fm 1894 407 a(\() p Fl(S) p Fj 1998 366 a(1) p Fm 2037 407 a(\)) p 2114 407 a(is) p 2219 407 a(called) p 2502 407 a(the) p 2676 407 a(scattering) p 3133 407 a(matrix) p 3457 407 a(at) 0 527 y(energy) p Fl 312 527 a(\025) p 396 527 a(>) p Fm 500 527 a(0) p 581 527 a(and) p 771 527 a(it) p 868 527 a(acts) p 1069 527 a(as) 581 734 y(\() p Fl(S) p Fm 685 734 a(\() p Fl(\025) p Fm(;) p Fl 824 734 a(H) p Fg 905 749 a(h) p Fl 949 734 a(;) p 993 734 a(H) p Fj 1074 749 a(0) p Fg(h) p Fm 1153 734 a(\)\() p Fl(F) p Fg 1292 749 a(h) p Fl 1337 734 a(u) p Fm(\)\() p Fl(\025;) p Fi 1586 734 a(\001) p Fm 1631 734 a(\)\)) p 1722 734 a(\() p Fl(!) p Fm 1825 734 a(\)) p 1890 734 a(=) p 1994 734 a(\() p Fl(F) p Fg 2095 749 a(h) p Fl 2140 734 a(S) p Fm 2206 734 a(\() p Fl(H) p Fg 2325 749 a(h) p Fl 2369 734 a(;) p 2413 734 a(H) p Fj 2494 749 a(0) p Fg(h) p Fm 2574 734 a(\)) p Fl(u) p Fm(\)) p 2722 734 a(\() p Fl(\025;) p 2861 734 a(!) p Fm 2926 734 a(\)) 0 940 y(on) p Fl 135 940 a(u) p Fi 219 940 a(2) p Fl 313 940 a(L) p Fj 379 904 a(2) p Fm 419 940 a(.) p 489 940 a(The) p 690 940 a(op) s(erator) p Fl 1082 940 a(S) p Fm 1148 940 a(\() p Fl(\025) p Fm(;) p Fl 1287 940 a(H) p Fg 1368 955 a(h) p Fl 1412 940 a(;) p 1456 940 a(H) p Fj 1537 955 a(0) p Fg(h) p Fm 1617 940 a(\)) p 1688 940 a(is) p 1786 940 a(unitary) p 2130 940 a(and) p 2319 940 a(tak) m(es) p 2569 940 a(the) p 2737 940 a(form) p Fl 1020 1147 a(S) p Fm 1086 1147 a(\() p Fl(\025) p Fm(;) p Fl 1225 1147 a(H) p Fg 1306 1162 a(h) p Fl 1350 1147 a(;) p 1394 1147 a(H) p Fj 1475 1162 a(0) p Fg(h) p Fm 1555 1147 a(\)) p 1620 1147 a(=) p Fl 1724 1147 a(I) p 1775 1147 a(d) p Fm 1848 1147 a(+) p Fl 1946 1147 a(T) p Fm 2017 1147 a(\() p Fl(\025) p Fm(;) p Fl 2156 1147 a(H) p Fg 2237 1162 a(h) p Fl 2281 1147 a(;) p 2325 1147 a(H) p Fj 2406 1162 a(0) p Fg(h) p Fm 2485 1147 a(\)) p 3343 1147 a(\(2.3\)) 0 1354 y(with) p Fl 216 1354 a(T) p Fm 287 1354 a(\() p Fl(\025) p Fm(;) p Fl 426 1354 a(H) p Fg 507 1369 a(h) p Fl 551 1354 a(;) p 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a(the) p 528 1594 a(amplitude) p Fl 989 1594 a(f) p Fg 1037 1609 a(h) p Fm 1081 1594 a(\() p Fl(!) p Ff 1180 1609 a(\000) p Fi 1267 1594 a(!) p Fl 1394 1594 a(!) p Fm 1459 1594 a(\)) p 1529 1594 a(at) p 1648 1594 a(energy) p Fl 1960 1594 a(E) p Fm 2070 1594 a(is) p 2168 1594 a(de\014ned) p 2504 1594 a(b) m(y) p Fl 589 1801 a(f) p Fg 637 1816 a(h) p Fm 682 1801 a(\() p Fl(!) p Ff 781 1816 a(\000) p Fi 867 1801 a(!) p Fl 994 1801 a(!) p Fm 1059 1801 a(\)) p 1124 1801 a(=) p Fl 1228 1801 a(c) p Fm(\() p Fl(E) p 1386 1801 a(=h) p Fj 1491 1760 a(2) p Fm 1530 1801 a(\)) p 1585 1801 a(\() p Fl(S) p Fm 1689 1801 a(\() p Fl(!) t(;) p 1836 1801 a(!) p Ff 1897 1816 a(\000) p Fm 1954 1801 a(;) p Fl 1998 1801 a(H) p Fg 2079 1816 a(h) p Fl 2124 1801 a(;) p 2168 1801 a(H) p Fj 2249 1816 a(0) p Fg(h) p Fm 2328 1801 a(\)) p Fi 2388 1801 a(\000) p Fl 2488 1801 a(\016) p Fm 2535 1801 a(\() p Fl(!) p Fi 2659 1801 a(\000) p Fl 2759 1801 a(!) p Ff 2820 1816 a(\000) p Fm 2879 1801 a(\)\)) p 3343 1801 a(\(2.4\)) 0 2008 y(through) p 380 2008 a(the) p 560 2008 a(k) m(ernel) p Fl 860 2008 a(S) p Fm 926 2008 a(\() p Fl(\022) s(;) p 1056 2008 a(!) p Fm 1121 2008 a(;) p Fl 1165 2008 a(H) p Fg 1246 2023 a(h) p Fl 1289 2008 a(;) p 1333 2008 a(H) p Fj 1414 2023 a(0) p Fg(;h) p Fm 1513 2008 a(\),) p 1625 2008 a(where) p Fl 1919 2008 a(c) p Fm(\() p Fl(E) p Fm 2077 2008 a(\)) p 2160 2008 a(is) p 2270 2008 a(as) p 2401 2008 a(in) p 2527 2008 a(\(1.5\).) p 2834 2008 a(If,) p 2973 2008 a(in) p 3099 2008 a(particular,) p Fl 0 2128 a(!) p Fi 92 2128 a(6) p Fm(=) p Fl 196 2128 a(!) p Ff 257 2143 a(\000) p Fm 315 2128 a(,) p 375 2128 a(then) p Fl 899 2248 a(f) p Fg 947 2263 a(h) p Fm 992 2248 a(\() p Fl(!) p Ff 1091 2263 a(\000) p Fi 1178 2248 a(!) p Fl 1305 2248 a(!) p Fm 1370 2248 a(\)) p 1435 2248 a(=) p Fl 1538 2248 a(c) p Fm(\() p Fl(E) p Fm 1696 2248 a(\)) p Fl(h) p Fj 1790 2207 a(1) p Fg(=) p Fj(2) p Fl 1901 2248 a(S) p Fm 1967 2248 a(\() p Fl(!) t(;) p 2114 2248 a(!) p Ff 2175 2263 a(\000) p Fm 2232 2248 a(;) p Fl 2276 2248 a(H) p Fg 2357 2263 a(h) p Fl 2401 2248 a(;) p 2445 2248 a(H) p Fj 2526 2263 a(0) p Fg(h) p Fm 2606 2248 a(\)) p 3343 2248 a(\(2.5\)) 0 2417 y(b) s(ecause) p 357 2417 a(of) p Fl 465 2417 a(c) p Fm(\() p Fl(E) p 623 2417 a(=h) p Fj 728 2381 a(2) p Fm 767 2417 a(\)) p 833 2417 a(=) p Fl 936 2417 a(c) p Fm(\() p Fl(E) p Fm 1094 2417 a(\)) p Fl(h) p Fj 1188 2381 a(1) p Fg(=) p Fj(2) p Fm 1298 2417 a(.) p 1368 2417 a(W) p 1460 2417 a(e) p 1532 2417 a(are) p 1691 2417 a(no) m(w) p 1890 2417 a(in) p 2001 2417 a(a) p 2078 2417 a(p) s(osition) p 2446 2417 a(to) p 2562 2417 a(pro) m(v) m(e) p 2821 2417 a(\(1.7\)) p 3051 2417 a(in) p 3161 2417 a(question.) p Fn 0 2796 a(Prop) s(osition) p 606 2796 a(2.1) p Fb 798 2796 a(We) p 975 2796 a(have) p Fl 769 3003 a(\033) p Fg 824 3018 a(h) p Fm 869 3003 a(\() p Fl(!) p Ff 968 3018 a(\000) p Fm 1027 3003 a(\)) p 1092 3003 a(=) p Fi 1196 3003 a(\000) p Fm(2\(2) p Fl(\031) p Fm 1468 3003 a(\)) p Fj 1506 2962 a(1) p Fg(=) p Fj(2) p Fl 1616 3003 a(E) p Ff 1694 2962 a(\000) p Fj(1) p Fg(=) p Fj(4) p Fl 1859 3003 a(h) p Fj 1915 2962 a(1) p Fg(=) p Fj(2) p Fm 2025 3003 a(Re) p Fh 2156 2907 a(\020) p Fl 2206 3003 a(e) p Fg 2251 2962 a(i\031) r(=) p Fj(4) p Fl 2393 3003 a(f) p Fg 2441 3018 a(h) p Fm 2486 3003 a(\() p Fl(!) p Ff 2585 3018 a(\000) p Fm 2643 3003 a(\)) p Fh 2681 2907 a(\021) p Fl 2748 3003 a(;) p Fb 0 3222 a(wher) p 196 3222 a(e) p Fl 275 3222 a(f) p Fg 323 3237 a(h) p Fm 368 3222 a(\() p Fl(!) p Ff 467 3237 a(\000) p Fm 526 3222 a(\)) p 591 3222 a(=) p Fl 695 3222 a(f) p Fg 743 3237 a(h) p Fm 788 3222 a(\() p Fl(!) p Ff 887 3237 a(\000) p Fi 973 3222 a(!) p Fl 1101 3222 a(!) p Ff 1162 3237 a(\000) p Fm 1220 3222 a(\)) p Fb 1293 3222 a(is) p 1398 3222 a(the) p 1560 3222 a(forwar) p 1832 3222 a(d) p 1916 3222 a(amplitude) p 2364 3222 a(at) p 2481 3222 a(ener) p 2662 3222 a(gy) p Fl 2789 3222 a(E) p Fb 2867 3222 a(.) 0 3481 y(Pr) p 102 3481 a(o) p 147 3481 a(of.) p Fm 354 3481 a(W) p 446 3481 a(e) p 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p Fl(s) p Fm(\)) p 2057 5504 a(=) p 2161 5504 a(0) p 2307 5504 a(on) p 2457 5504 a([2) p Fl(;) p Fi 2577 5504 a(1) p Fm(\)) p Fl(:) p Fm 3343 5504 a(\(3.9\)) 1747 5753 y(8) p 90 rotate dyy eop %%Page: 9 9 9 8 bop Fm 0 407 a(Then) p 255 407 a(w) m(e) p 398 407 a(de\014ne) p Fl 290 619 a(\021) p Fm 342 619 a(\() p Fl(x) p Fm(\)) p 501 619 a(=) p 605 619 a(\(1) p Fi 714 619 a(\000) p Fl 813 619 a(\037) p Fg 874 634 a(M) p Fm 953 619 a(\() p Fl(x) p Fm(\)\)) p Fl 1139 619 a(\021) p Fj 1187 634 a(1) p Fm 1227 619 a(\() p Fl(x) p Fm(\)) p Fl(;) p 1499 619 a(\021) p Fj 1547 634 a(1) p Fm 1614 619 a(=) p Fl 1718 619 a(\014) p 1779 619 a(\015) p Fm 1835 619 a(\() p Fl(x) p Fi 1950 619 a(\000) p Fl 2050 619 a(d) p Fj 2101 634 a(+) p Fm 2160 619 a(;) p 2207 619 a(^) p Fl 2204 619 a(e) p Fm 2248 619 a(\)) p Fi 2308 619 a(\000) p Fl 2408 619 a(\014) p 2469 619 a(\015) p Fm 2525 619 a(\() p Fl(x) p Fi 2640 619 a(\000) p Fl 2740 619 a(d) p Ff 2791 634 a(\000) p Fm 2850 619 a(;) p 2897 619 a(^) p Fl 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952 a(b) s(ecomes) 0 1072 y(a) p 81 1072 a(single) p 353 1072 a(v) p 399 1072 a(alued) p 659 1072 a(function.) p 1079 1072 a(If) p 1177 1072 a(w) m(e) p 1320 1072 a(further) p 1648 1072 a(set) 1007 1259 y(~) p Fl 984 1284 a(B) p Fg 1058 1299 a(d) p Fm 1098 1284 a(\() p Fl(x) p Fm(\)) p 1257 1284 a(=) p Fl 1361 1284 a(\037) p Fg 1422 1299 a(M) p Fm 1501 1284 a(\() p Fl(x) p Fm(\)) p Fl(B) p Fg 1706 1299 a(d) p Fm 1747 1284 a(\() p Fl(x) p Fm(\)) p 1900 1284 a(+) p 1998 1284 a(\() p Fi(r) p Fl(\037) p Fg 2180 1299 a(M) p Fm 2259 1284 a(\() p Fl(x) p Fm(\)\)) p Fl 2445 1284 a(\021) p Fj 2493 1299 a(1) p Fl 2533 1284 a(;) p Fm 0 1497 a(then) 242 1471 y(~) p Fl 219 1497 a(B) p Fg 293 1512 a(d) p Fm 362 1497 a(has) p 533 1497 a(compact) p 920 1497 a(supp) s(ort) p 1277 1497 a(in) p Fi 1388 1497 a(fj) p Fl(x) p Fi(j) p Fl 1576 1497 a(<) p 1679 1497 a(M) p 1778 1497 a(=h) p Fi(g) p Fm(,) p 1990 1497 a(and) p Fl 2177 1497 a(B) p Fg 2251 1512 a(d) p Fm 2291 1497 a(\() p Fl(x) p Fm(\)) p 2452 1497 a(admits) p 2769 1497 a(the) p 2933 1497 a(decomp) s(osition) p Fl 0 1617 a(B) p Fg 74 1632 a(d) p Fm 142 1617 a(=) 269 1592 y(~) p Fl 246 1617 a(B) p Fg 320 1632 a(d) p Fm 382 1617 a(+) p Fi 481 1617 a(r) p Fl(\021) p Fm 615 1617 a(.) p 705 1617 a(This) p 935 1617 a(is) p 1039 1617 a(sho) m(wn) p 1342 1617 a(b) m(y) p 1484 1617 a(use) p 1659 1617 a(of) p Fi 1776 1617 a(r) p Fl(\021) p Fj 1907 1632 a(1) p Fm 1986 1617 a(=) p Fl 2101 1617 a(B) p Fg 2175 1632 a(d) p Fm 2215 1617 a(\() p Fl(x) p Fm(\)) p 2385 1617 a(for) p Fi 2541 1617 a(j) p Fl(x) p Fi(j) p 2691 1617 a(\035) p Fm 2829 1617 a(1.) p 2968 1617 a(In) p 3096 1617 a(fact,) p Fl 3324 1617 a(B) p Fg 3398 1632 a(d) p Fm 3478 1617 a(is) 0 1737 y(calculated) p 461 1737 a(as) p Fl 271 1950 a(B) p Fg 345 1965 a(d) p Fm 413 1950 a(=) p Fl 517 1950 a(\037) p Fg 578 1965 a(M) p Fl 657 1950 a(B) p Fg 731 1965 a(d) p Fm 794 1950 a(+) p 892 1950 a(\(1) p Fi 1001 1950 a(\000) p Fl 1100 1950 a(\037) p Fg 1161 1965 a(M) p Fm 1240 1950 a(\)) p Fi(r) p Fl(\021) p Fj 1409 1965 a(1) p Fm 1477 1950 a(=) p Fl 1580 1950 a(\037) p Fg 1641 1965 a(M) p Fl 1720 1950 a(B) p Fg 1794 1965 a(d) p Fm 1857 1950 a(+) p Fi 1955 1950 a(r) p Fl(\021) p Fm 2112 1950 a(+) p 2210 1950 a(\() p Fi(r) p Fl(\037) p Fg 2392 1965 a(M) p Fm 2471 1950 a(\)) p Fl 2525 1950 a(\021) p Fj 2573 1965 a(1) p Fm 2641 1950 a(=) 2768 1925 y(~) p Fl 2744 1950 a(B) p Fg 2818 1965 a(d) p Fm 2859 1950 a(\() p Fl(x) p Fm(\)) p 3012 1950 a(+) p Fi 3110 1950 a(r) p Fl(\021) t(:) p Fm 0 2162 a(Th) m(us) p 247 2162 a(w) m(e) p 391 2162 a(ha) m(v) m(e) p Fl 563 2374 a(K) p Fg 646 2389 a(d) p Fm 714 2374 a(=) p Fl 817 2374 a(H) p Fm 906 2374 a(\() p Fl(B) p Fg 1018 2389 a(d) p Fm 1058 2374 a(\)) p 1124 2374 a(=) p Fl 1227 2374 a(H) p Fm 1316 2374 a(\() 1377 2349 y(~) p Fl 1354 2374 a(B) p Fg 1428 2389 a(d) p Fm 1491 2374 a(+) p Fi 1589 2374 a(r) p Fl(\021) p Fm 1724 2374 a(\)) p 1789 2374 a(=) p Fl 1893 2374 a(e) p Fg 1938 2333 a(i\021) p Fl 2004 2374 a(H) p Fm 2093 2374 a(\() 2153 2349 y(~) p Fl 2131 2374 a(B) p Fg 2205 2389 a(d) p Fm 2245 2374 a(\)) p Fl(e) p Ff 2328 2333 a(\000) p Fg(i\021) p Fm 2476 2374 a(=) p Fl 2580 2374 a(e) p Fg 2625 2333 a(i\021) p Fm 2717 2349 a(~) p Fl 2691 2374 a(K) p Fg 2774 2389 a(d) p Fl 2815 2374 a(e) p Ff 2860 2333 a(\000) p Fg(i\021) p Fm 3294 2374 a(\(3.11\)) 0 2587 y(b) m(y) p 148 2587 a(the) p 328 2587 a(gauge) p 617 2587 a(transformation.) p 1356 2587 a(The) p 1569 2587 a(op) s(erator) 2000 2561 y(~) p Fl 1974 2587 a(K) p Fg 2057 2602 a(d) p Fm 2146 2587 a(=) p Fl 2271 2587 a(H) p Fm 2360 2587 a(\() 2421 2561 y(~) p Fl 2398 2587 a(B) p Fg 2472 2602 a(d) p Fm 2512 2587 a(\)) p 2595 2587 a(has) p 2781 2587 a(the) p 2961 2587 a(same) p 3218 2587 a(forw) m(ard) 0 2707 y(scattering) p 448 2707 a(amplitude) p 905 2707 a(as) p Fl 1022 2707 a(K) p Fg 1105 2722 a(d) p Fm 1146 2707 a(.) p 1215 2707 a(It) p 1318 2707 a(is) p 1414 2707 a(kno) m(wn) p 1720 2707 a(b) m(y) p 1852 2707 a(the) p 2018 2707 a(principle) p 2416 2707 a(of) p 2524 2707 a(limiting) p 2884 2707 a(absorption) p 3364 2707 a(that) p Fl 732 2919 a(R) p Fm 807 2919 a(\() p Fl(E) p Fi 945 2919 a(\006) p Fl 1045 2919 a(i) p Fm(0;) p Fl 1171 2919 a(K) p Fg 1254 2934 a(d) p Fm 1294 2919 a(\)) p 1360 2919 a(=) p 1463 2919 a(lim) p Fg 1480 2979 a(") p Ff(#) p Fj(0) p Fm 1616 2919 a(\() p Fl(K) p Fg 1737 2934 a(d) p Fi 1799 2919 a(\000) p Fl 1899 2919 a(E) p Fi 1999 2919 a(\007) p Fl 2099 2919 a(i") p Fm(\)) p Ff 2215 2871 a(\000) p Fj(1) p Fm 2337 2919 a(:) p Fl 2392 2919 a(L) p Fj 2458 2878 a(2) p Fg 2458 2944 a(s) p Fi 2526 2919 a(!) p Fl 2653 2919 a(L) p Fj 2719 2878 a(2) p Ff 2719 2944 a(\000) p Fg(s) p Fm 0 3185 a(is) p 104 3185 a(b) s(ounded) p 508 3185 a(for) p Fl 664 3185 a(s) p 747 3185 a(>) p Fm 861 3185 a(1) p Fl(=) p Fm(2,) p 1075 3185 a(where) p Fl 1363 3185 a(L) p Fj 1429 3149 a(2) p Fg 1429 3210 a(s) p Fm 1507 3185 a(denotes) p 1866 3185 a(the) p 2040 3185 a(w) m(eigh) m(ted) p Fl 2452 3185 a(L) p Fj 2518 3149 a(2) p Fm 2597 3185 a(space) p Fl 2863 3185 a(L) p Fj 2929 3149 a(2) p Fm 2969 3185 a(\() p Fk(R) p Fj 3095 3143 a(2) p Fm 3134 3185 a(;) p Fi 3178 3185 a(h) p Fl(x) p Fi(i) p Fj 3311 3149 a(2) p Fg(s) p Fl 3399 3185 a(dx) p Fm(\)) 0 3306 y(with) p Fi 226 3306 a(h) p Fl(x) p Fi(i) p Fm 394 3306 a(=) p 504 3306 a(\(1) p 616 3306 a(+) p Fi 717 3306 a(j) p Fl(x) p Fi(j) p Fj 828 3270 a(2) p Fm 867 3306 a(\)) p Fj 905 3270 a(1) p Fg(=) p Fj(2) p Fm 1015 3306 a(.) p 1097 3306 a(W) p 1189 3306 a(e) p 1269 3306 a(use) p 1442 3306 a(the) p 1614 3306 a(auxiliary) p 2025 3306 a(op) s(erator) 2448 3281 y(~) p Fl 2422 3306 a(K) p Fg 2505 3321 a(d) p Fm 2582 3306 a(to) p 2705 3306 a(represen) m(t) p Fl 3130 3306 a(\033) p Fg 3185 3321 a(h) p Fm 3230 3306 a(\() p Fl(!) p Ff 3329 3321 a(\000) p Fm 3388 3306 a(\)) p 3462 3306 a(in) 0 3426 y(terms) p 272 3426 a(of) p Fl 383 3426 a(R) p Fm 458 3426 a(\() p Fl(E) p Fm 596 3426 a(+) p Fl 694 3426 a(i) p Fm(0;) p Fl 820 3426 a(K) p Fg 903 3441 a(d) p Fm 943 3426 a(\).) 146 3594 y(W) p 238 3594 a(e) p 314 3594 a(de\014ne) p 596 3594 a(the) p 764 3594 a(follo) m(wing) p 1176 3594 a(functions) p 1597 3594 a(:) p Fl 853 3806 a(v) p Fm 904 3806 a(\() p Fl(x) p Fj 997 3821 a(1) p Fm 1037 3806 a(\)) p 1103 3806 a(=) p Fl 1206 3806 a(\037) p Fm(\() p Fi(j) p Fl(x) p Fj 1388 3821 a(1) p Fi 1428 3806 a(j) p Fl(=) p 1500 3806 a(M) p Fm 1604 3806 a(\)) p Fl(;) p 1880 3806 a(w) p Fm 1953 3806 a(\() p Fl(x) p Fj 2046 3821 a(2) p Fm 2085 3806 a(\)) p 2151 3806 a(=) p Fl 2255 3806 a(\037) p Fm(\() p Fi(j) p Fl(x) p Fj 2437 3821 a(2) p Fi 2476 3806 a(j) p Fl(=) p 2548 3806 a(M) p Fm 2652 3806 a(\)) p 3294 3806 a(\(3.12\)) p Fl 271 4019 a(V) p Fm 350 4019 a(\() p Fl(x) p Fj 443 4034 a(1) p Fm 482 4019 a(\)) p 548 4019 a(=) p Fl 652 4019 a(v) p Fm 703 4019 a(\() p Fl(hx) p Fj 852 4034 a(1) p Fm 891 4019 a(\)) p 957 4019 a(=) p Fl 1061 4019 a(\037) p Fm(\() p Fl(h) p Fi(j) p Fl(x) p Fj 1299 4034 a(1) p Fi 1338 4019 a(j) p Fl(=) p 1410 4019 a(M) p Fm 1514 4019 a(\)) p Fl(;) p 1693 4019 a(W) p Fm 1799 4019 a(\() p Fl(x) p Fj 1892 4034 a(2) p Fm 1932 4019 a(\)) p 1997 4019 a(=) p Fl 2101 4019 a(w) p Fm 2174 4019 a(\() p Fl(hx) p Fj 2323 4034 a(2) p Fm 2362 4019 a(\)) p 2428 4019 a(=) p Fl 2531 4019 a(\037) p Fm(\() p Fl(h) p Fi(j) p Fl(x) p Fj 2769 4034 a(2) p Fi 2809 4019 a(j) p Fl(=) p 2881 4019 a(M) p Fm 2985 4019 a(\)) p 3294 4019 a(\(3.13\)) 0 4190 y(and) p Fl 191 4190 a(U) p Fm 267 4190 a(\() p Fl(x) p Fm(\)) p 428 4190 a(=) p Fl 533 4190 a(V) p Fm 611 4190 a(\() p Fl(x) p Fj 704 4205 a(1) p Fm 744 4190 a(\)) p Fl(W) p Fm 888 4190 a(\() p Fl(x) p Fj 981 4205 a(2) p Fm 1020 4190 a(\).) p 1131 4190 a(By) p 1285 4190 a(de\014nition,) p Fl 1747 4190 a(U) p Fm 1853 4190 a(=) p 1958 4190 a(1) p 2040 4190 a(on) p 2176 4190 a(supp) p Fl 2394 4190 a(\037) p Fg 2455 4205 a(M) p Fm 2534 4190 a(,) p Fl 2595 4190 a(\037) p Fg 2656 4205 a(M) p Fm 2768 4190 a(b) s(eing) p 3032 4190 a(as) p 3152 4190 a(in) p 3267 4190 a(\(3.10\).) 0 4310 y(Let) p Fl 175 4310 a(') p Fm 271 4310 a(b) s(e) p 404 4310 a(the) p 572 4310 a(outgoing) p 974 4310 a(eigenfunction) p 1573 4310 a(to) p 1692 4310 a(equation) 2116 4285 y(~) p Fl 2090 4310 a(K) p Fg 2173 4325 a(d) p Fl 2214 4310 a(') p Fm 2306 4310 a(=) p Fl 2409 4310 a(E) p 2504 4310 a(') p Fm(.) p 2639 4310 a(Since) 2917 4285 y(~) p Fl 2894 4310 a(B) p Fg 2968 4325 a(d) p Fm 3041 4310 a(has) p 3215 4310 a(supp) s(ort) 0 4431 y(in) p Fi 114 4431 a(fj) p Fl(x) p Fi(j) p Fl 302 4431 a(<) p 406 4431 a(M) p 505 4431 a(=h) p Fi(g) p Fm(,) 1405 4526 y(~) p Fl 1379 4551 a(K) p Fg 1462 4566 a(d) p Fm 1530 4551 a(=) p Fl 1634 4551 a(H) p Fm 1723 4551 a(\() 1784 4526 y(~) p Fl 1761 4551 a(B) p Fg 1835 4566 a(d) p Fm 1875 4551 a(\)) p 1940 4551 a(=) p Fl 2044 4551 a(H) p Fj 2125 4566 a(0) p Fm 3294 4551 a(\(3.14\)) 0 4722 y(o) m(v) m(er) p Fi 211 4722 a(fj) p Fl(x) p Fi(j) p Fl 405 4722 a(>) p 513 4722 a(M) p 612 4722 a(=h) p Fi(g) p Fm 802 4722 a(and) p 995 4722 a(hence) p 1269 4722 a(the) p 1440 4722 a(relation) p 1800 4722 a(remains) p 2167 4722 a(true) p 2375 4722 a(on) p 2514 4722 a(supp) p 2748 4722 a(\(1) p Fi 2857 4722 a(\000) p Fl 2957 4722 a(U) p Fm 3033 4722 a(\).) p 3150 4722 a(If) p 3251 4722 a(w) m(e) p 3397 4722 a(put) p Fl 0 4842 a(') p Fm 92 4842 a(=) p 195 4842 a(\(1) p Fi 304 4842 a(\000) p Fl 404 4842 a(U) p Fm 480 4842 a(\)) p Fl(') p Ff 582 4857 a(\000) p Fm 663 4842 a(+) p Fl 761 4842 a( ) p Fm 861 4842 a(with) p Fl 1083 4842 a(') p Ff 1147 4857 a(\000) p Fm 1234 4842 a(=) p 1337 4842 a(exp) q(\() p Fl(iE) p Fj 1635 4806 a(1) p Fg(=) p Fj(2) p Fl 1745 4842 a(x) p Fi 1823 4842 a(\001) p Fl 1873 4842 a(!) p Ff 1934 4857 a(\000) p Fm 1993 4842 a(\),) p 2090 4842 a(then) p Fl 2312 4842 a( ) p Fm 2412 4842 a(solv) m(es) p Fh 813 4971 a(\020) p Fm 889 5042 a(~) p Fl 863 5067 a(K) p Fg 946 5082 a(d) p Fi 1008 5067 a(\000) p Fl 1108 5067 a(E) p Fh 1186 4971 a(\021) p Fl 1252 5067 a( ) p Fm 1347 5067 a(=) p 1450 5067 a(\() p Fl(H) p Fj 1569 5082 a(0) p Fl 1608 5067 a(U) p Fi 1707 5067 a(\000) p Fl 1807 5067 a(U) p 1883 5067 a(H) p Fj 1964 5082 a(0) p Fm 2004 5067 a(\)) p Fl 2058 5067 a(') p Ff 2122 5082 a(\000) p Fm 2209 5067 a(=) p 2313 5067 a([) p Fl(H) p Fj 2421 5082 a(0) p Fl 2460 5067 a(;) p 2504 5067 a(U) p Fm 2580 5067 a(]) p Fl(') p Ff 2671 5082 a(\000) p Fm 0 5292 a(b) m(y) p 135 5292 a(\(3.14\).) p 455 5292 a(Hence) p Fl 745 5292 a(') p Fm 842 5292 a(is) p 940 5292 a(represen) m(ted) p 1458 5292 a(as) p Fl 861 5504 a(') p Fm 953 5504 a(=) p 1056 5504 a(\(1) p Fi 1165 5504 a(\000) p Fl 1265 5504 a(U) p Fm 1341 5504 a(\)) p Fl 1396 5504 a(') p Ff 1460 5519 a(\000) p Fm 1541 5504 a(+) p Fl 1639 5504 a(R) p Fm 1714 5504 a(\() p Fl(E) p Fm 1852 5504 a(+) p Fl 1950 5504 a(i) p Fm(0;) 2102 5479 y(~) p Fl 2076 5504 a(K) p Fg 2159 5519 a(d) p Fm 2199 5504 a(\)[) p Fl(H) p Fj 2345 5519 a(0) p Fl 2385 5504 a(;) p 2429 5504 a(U) p Fm 2505 5504 a(]) p Fl(') p Ff 2596 5519 a(\000) p Fl 2655 5504 a(:) p Fm 3294 5504 a(\(3.15\)) 1747 5753 y(9) p 90 rotate dyy eop %%Page: 10 10 10 9 bop Fm 0 407 a(Similarly) p 415 407 a(w) m(e) p 558 407 a(ha) m(v) m(e) 900 604 y(\(1) p Fi 1009 604 a(\000) p Fl 1108 604 a(U) p Fm 1184 604 a(\)) p Fl(') p Fm 1314 604 a(=) p Fl 1418 604 a(') p Ff 1482 619 a(\000) p Fi 1563 604 a(\000) p Fl 1663 604 a(R) p Fm 1738 604 a(\() p Fl(E) p Fm 1876 604 a(+) p Fl 1974 604 a(i) p Fm(0;) p Fl 2100 604 a(H) p Fj 2181 619 a(0) p Fm 2220 604 a(\)[) p Fl(H) p Fj 2366 619 a(0) p Fl 2405 604 a(;) p 2449 604 a(U) p Fm 2525 604 a(]) p Fl(';) p Fm 3294 604 a(\(3.16\)) 0 802 y(b) s(ecause) p 354 802 a([) 407 776 y(~) p Fl 381 802 a(K) p Fg 464 817 a(d) p Fl 505 802 a(;) p 549 802 a(U) p Fm 625 802 a(]) p 680 802 a(=) p 783 802 a([) p Fl(H) p Fj 891 817 a(0) p Fl 931 802 a(;) p 975 802 a(U) p Fm 1051 802 a(]) p 1104 802 a(b) m(y) p 1232 802 a(\(3.14\).) p 1550 802 a(As) p 1687 802 a(is) p 1778 802 a(w) m(ell) p 1969 802 a(kno) m(wn,) p Fl 2300 802 a(R) p Fm 2375 802 a(\() p Fl(E) p Fm 2499 802 a(+) p Fl 2583 802 a(i) p Fm(0;) p Fl 2709 802 a(H) p Fj 2790 817 a(0) p Fm 2829 802 a(\)) p 2893 802 a(has) p 3060 802 a(the) p 3221 802 a(in) m(tegral) 0 922 y(k) m(ernel) p Fl 1005 1042 a(G) p Fj 1082 1057 a(0) p Fm 1122 1042 a(\() p Fl(x;) p 1259 1042 a(y) p Fm 1311 1042 a(;) p Fl 1355 1042 a(E) p Fm 1433 1042 a(\)) p 1497 1042 a(=) p 1601 1042 a(\() p Fl(i=) p Fm(4\)) p Fl(H) p Fj 1897 991 a(\(1\)) 1889 1064 y(0) p Fm 1990 1042 a(\() p Fl(E) p Fj 2106 1001 a(1) p Fg(=) p Fj(2) p Fi 2216 1042 a(j) p Fl(x) p Fi 2322 1042 a(\000) p Fl 2421 1042 a(y) p Fi 2473 1042 a(j) p Fm(\)) 0 1221 y(and) p 190 1221 a(the) p 358 1221 a(Hank) m(el) p 686 1221 a(function) p Fl 1068 1221 a(H) p Fj 1157 1170 a(\(1\)) 1149 1242 y(0) p Fm 1250 1221 a(\() p Fl(z) p Fm 1337 1221 a(\)) p 1409 1221 a(of) p 1520 1221 a(\014rst) p 1721 1221 a(kind) p 1940 1221 a(and) p 2130 1221 a(order) p 2385 1221 a(zero) p 2591 1221 a(b) s(eha) m(v) m(es) p 2954 1221 a(lik) m(e) p Fl 343 1432 a(H) p Fj 432 1381 a(\(1\)) 424 1453 y(0) p Fm 526 1432 a(\() p Fl(z) p Fm 613 1432 a(\)) p 679 1432 a(=) p 783 1432 a(\(2) p Fl(=\031) p Fm 978 1432 a(\)) p Fj 1016 1390 a(1) p Fg(=) p Fj(2) p Fm 1142 1432 a(exp) q(\() p Fl(i) p Fm(\() p Fl(z) p Fi 1472 1432 a(\000) p Fl 1571 1432 a(\031) t(=) p Fm(4\)\)) p Fl(z) p Ff 1853 1390 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fh 2035 1335 a(\020) p Fm 2085 1432 a(1) p 2155 1432 a(+) p Fl 2253 1432 a(O) p Fm 2331 1432 a(\() p Fi(j) p Fl(z) p Fi 2446 1432 a(j) p Ff 2474 1390 a(\000) p Fj(1) p Fm 2568 1432 a(\)) p Fh 2606 1335 a(\021) p Fl 2672 1432 a(;) p Fi 2813 1432 a(j) p Fl(z) p Fi 2890 1432 a(j) p 2946 1432 a(!) p 3074 1432 a(1) p Fl(:) p Fm 0 1629 a(This) p 223 1629 a(yields) p Fl 226 1826 a(G) p Fj 303 1841 a(0) p Fm 342 1826 a(\() p Fl(x;) p 479 1826 a(y) p Fm 531 1826 a(;) p Fl 575 1826 a(E) p Fm 653 1826 a(\)) p 718 1826 a(=) p Fl 822 1826 a(c) p Fj 864 1841 a(0) p Fm 903 1826 a(\() p Fl(E) p Fm 1019 1826 a(\)) p 1074 1826 a(exp) q(\() p Fl(iE) p Fj 1372 1785 a(1) p Fg(=) p Fj(2) p Fi 1482 1826 a(j) p Fl(x) p Fi 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1678 2486 a(]) p Fl(';) p 1813 2486 a(') p Ff 1877 2501 a(\000) p Fi 1936 2486 a(i) p Fl 1991 2486 a(e) p Fg 2036 2444 a(iE) p Fd 2116 2421 a(1) p Fc(=) p Fd(2) p Ff 2212 2444 a(j) p Fg(x) p Ff(j) p Fi 2296 2486 a(j) p Fl(x) p Fi(j) p Ff 2407 2444 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fm 2593 2486 a(+) p Fl 2691 2486 a(o) p Fm(\() p Fi(j) p Fl(x) p Fi(j) p Ff 2887 2444 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fm 3052 2486 a(\)) 0 2683 y(as) p Fi 117 2683 a(j) p Fl(x) p Fi(j) p 255 2683 a(!) p 383 2683 a(1) p Fm 512 2683 a(along) p 769 2683 a(direction) p Fl 1172 2683 a(!) p Ff 1233 2698 a(\000) p Fm 1292 2683 a(.) p 1362 2683 a(W) p 1454 2683 a(e) p 1527 2683 a(insert) p 1795 2683 a(\(3.15\)) p 2074 2683 a(in) m(to) p Fl 2269 2683 a(') p Fm 2363 2683 a(in) p 2473 2683 a(the) p 2638 2683 a(scalar) p 2912 2683 a(pro) s(duct) p 3275 2683 a(on) p 3408 2683 a(the) 0 2803 y(righ) m(t) p 236 2803 a(side) p 431 2803 a(to) p 551 2803 a(obtain) p 854 2803 a(that) p Fl 235 3001 a(g) p Fg 282 3016 a(d) p Fm 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p Fl 2539 5504 a(U) p 2615 5504 a(') p Ff 2679 5519 a(\000) p Fl 2739 5504 a(;) p Fi 2783 5504 a(\000) p Fl(U) p 2936 5504 a(') p Ff 3000 5519 a(\000) p Fi 3060 5504 a(i) p Fm 3126 5504 a(=) p 3230 5504 a(0) p Fl(:) p Fm 1723 5753 a(10) p 90 rotate dyy eop %%Page: 11 11 11 10 bop Fm 0 407 a(This) p 223 407 a(yields) p 497 407 a(the) p 665 407 a(desired) p 996 407 a(represen) m(tation.) p Fa 1769 407 a(2) p Fm 146 576 a(The) p 357 576 a(function) p Fl 749 576 a(U) p Fm 825 576 a(\() p Fl(x) p Fm(\)) p 1000 576 a(tak) m(es) p 1260 576 a(the) p 1438 576 a(form) p Fl 1678 576 a(U) p Fm 1800 576 a(=) p Fl 1921 576 a(V) p Fm 1999 576 a(\() p Fl(x) p Fj 2092 591 a(1) p Fm 2132 576 a(\)) p Fl(W) p Fm 2276 576 a(\() p Fl(x) p Fj 2369 591 a(2) p Fm 2409 576 a(\).) p 2548 576 a(Hence) p 2848 576 a(the) p 3026 576 a(comm) m(utator) 0 697 y([) p Fl(H) p Fj 108 712 a(0) p Fl 147 697 a(;) p 191 697 a(U) p Fm 267 697 a(]) p 327 697 a(acts) p 528 697 a(as) 822 817 y([) p Fl(H) p Fj 930 832 a(0) p Fl 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a(M) p Fi 944 2558 a(\024) p 1070 2558 a(j) p Fl(x) p Fj 1153 2573 a(2) p Fi 1192 2558 a(j) p 1268 2558 a(\024) p Fm 1394 2558 a(2) p Fl(M) p Fi 1547 2558 a(g) p Fm(.) p 1704 2558 a(W) p 1796 2558 a(e) p 1884 2558 a(in) m(tro) s(duce) p 2329 2558 a(a) p 2423 2558 a(smo) s(oth) p 2779 2558 a(partition) p 3198 2558 a(of) p 3321 2558 a(unit) m(y) 0 2679 y(normalized) p 499 2679 a(b) m(y) p Fl 1115 2799 a(v) p Ff 1162 2814 a(\0001) p Fm 1314 2799 a(+) p Fl 1412 2799 a(v) p Ff 1459 2814 a(\000) p Fm 1540 2799 a(+) p Fl 1638 2799 a(v) p Fj 1685 2814 a(0) p Fm 1747 2799 a(+) p Fl 1845 2799 a(v) p Fj 1892 2814 a(+) p Fm 1973 2799 a(+) p Fl 2071 2799 a(v) p Fj 2118 2814 a(+) p Ff(1) p Fm 2276 2799 a(=) p 2379 2799 a(1) p 3294 2799 a(\(3.20\)) 0 2972 y(o) m(v) m(er) p 211 2972 a(the) p 381 2972 a(in) m(terv) p 624 2972 a(al) p 736 2972 a([) p Fi(\000) p Fm(2) p Fl(M) p 988 2972 a(;) p Fm 1032 2972 a(2) p Fl(M) p Fm 1185 2972 a(],) p 1275 2972 a(where) p 1559 2972 a(the) p 1729 2972 a(functions) p Fl 2152 2972 a(v) p Fj 2199 2987 a(0) p Fm 2274 2972 a(and) p Fl 2466 2972 a(v) p Ff 2513 2987 a(\0061) p Fm 2677 2972 a(are) p 2842 2972 a(nonnegativ) m(e) p 3386 2972 a(and) 0 3093 y(ha) m(v) m(e) p 225 3093 a(the) p 393 3093 a(follo) m(wing) p 805 3093 a(prop) s(erties) p 1263 3093 a(:) 354 3310 y(supp) p Fl 572 3310 a(v) p Ff 619 3325 a(\0001) p Fi 776 3310 a(\032) p Fm 881 3310 a(\() p Fi(\000) p Fm(3) p Fl(M) p 1144 3310 a(;) p 1188 3310 a(e) p Ff 1233 3325 a(\000) p Fj(1) p Fi 1350 3310 a(\000) p Fm 1450 3310 a(1) p Fl(=) p 1543 3310 a(M) p Fm 1647 3310 a(\)) p Fl(;) p 1901 3310 a(v) p Ff 1948 3325 a(\0001) p Fm 2106 3310 a(=) p 2209 3310 a(1) p 2281 3310 a(on) p 2407 3310 a([) p Fi(\000) p Fm(2) p Fl(M) p 2659 3310 a(;) p 2703 3310 a(e) p Ff 2748 3325 a(\000) p Fj(1) p Fi 2866 3310 a(\000) p Fm 2965 3310 a(2) p Fl(=) p 3058 3310 a(M) p Fm 3162 3310 a(]) 219 3456 y(supp) p Fl 436 3456 a(v) p Fj 483 3471 a(0) p Fi 551 3456 a(\032) p Fm 656 3456 a(\() p Fl(e) p Ff 739 3471 a(\000) p Fj(1) p Fm 855 3456 a(+) p 953 3456 a(1) p Fl(=) p 1046 3456 a(M) p 1145 3456 a(;) p 1189 3456 a(e) p Fj 1234 3471 a(+1) p Fi 1350 3456 a(\000) p Fm 1450 3456 a(1) p Fl(=) p 1543 3456 a(M) p Fm 1647 3456 a(\)) p Fl(;) p 1901 3456 a(v) p Fj 1948 3471 a(0) p Fm 2015 3456 a(=) p 2119 3456 a(1) p 2191 3456 a(on) p 2317 3456 a([) p Fl(e) p Ff 2389 3471 a(\000) p Fj(1) p Fm 2506 3456 a(+) p 2604 3456 a(2) p Fl(=) p 2697 3456 a(M) p 2796 3456 a(;) p 2840 3456 a(e) p Fj 2885 3471 a(+1) p Fi 3001 3456 a(\000) p Fm 3101 3456 a(2) p Fl(=) p 3194 3456 a(M) p Fm 3298 3456 a(]) 433 3601 y(supp) p Fl 651 3601 a(v) p Fj 698 3616 a(+) p Ff(1) p Fi 855 3601 a(\032) p Fm 961 3601 a(\() p Fl(e) p Fj 1044 3616 a(+1) p Fm 1160 3601 a(+) p 1258 3601 a(1) p Fl(=) p 1351 3601 a(M) p 1450 3601 a(;) p Fm 1494 3601 a(3) p Fl(M) p Fm 1647 3601 a(\)) p Fl(;) p 1901 3601 a(v) p Fj 1948 3616 a(+) p Ff(1) p Fm 2106 3601 a(=) p 2209 3601 a(1) p 2281 3601 a(on) p 2407 3601 a([) p Fl(e) p Fj 2479 3616 a(+1) p 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3179 a(=) p 682 3179 a(4) p Fl(\031) t(E) p Fj 868 3138 a(1) p Fg(=) p Fj(2) p Fl 978 3179 a(h) p Fh 1051 3083 a(D) p Fm 1102 3179 a(\005\() p Fl(L) p Fj 1279 3194 a(0) p Fm 1319 3179 a(\)) p Fl(e) p Fg 1402 3138 a(i\021) p Fl 1468 3179 a(V) p Fj 1525 3194 a(+) p Ff(1) p Fl 1654 3179 a(W) p Fj 1760 3138 a(+) p Fm 1835 3179 a(\() p Fl(@) p Fj 1924 3194 a(2) p Fl 1964 3179 a(W) p Fm 2070 3179 a(\)) p Fl 2124 3179 a(') p Ff 2188 3194 a(\000) p Fl 2247 3179 a(;) p 2291 3179 a(e) p Fg 2336 3138 a(i\021) p Fm 2417 3154 a(~) p Fl 2402 3179 a(V) p Fj 2459 3194 a(+) p Ff(1) p Fl 2589 3179 a(W) p Ff 2695 3138 a(\000) p Fm 2770 3179 a(\() p Fl(@) p Fj 2859 3194 a(2) p Fl 2899 3179 a(W) p Fm 3005 3179 a(\)) p Fl 3059 3179 a(') p Ff 3123 3194 a(\000) p Fh 3182 3083 a(E) p Fl 3249 3179 a(:) p Fm 0 3376 a(W) p 92 3376 a(e) p 171 3376 a(write) p 423 3376 a(\011) p Fj 499 3391 a(+) p Fm 594 3376 a(in) p 710 3376 a(the) p 881 3376 a(in) m(tegral) p 1239 3376 a(form) p 1472 3376 a(to) p 1595 3376 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3724 a(\)) p 2234 3671 64 4 v Fl(') p Fj 2298 3747 a(0) p Fm 2337 3724 a(\() p Fl(y) p Fm 2427 3724 a(;) p Fl 2471 3724 a(!) p Fm 2536 3724 a(\)) p Fl 2591 3724 a(d!) p Fm 0 3962 a(with) p Fl 236 3962 a(') p Fj 300 3977 a(0) p Fm 339 3962 a(\() p Fl(x) p Fm(;) p Fl 476 3962 a(!) p Fm 541 3962 a(\)) p 630 3962 a(=) p 757 3962 a(exp) q(\() p Fl(iE) p Fj 1055 3926 a(1) p Fg(=) p Fj(2) p Fl 1165 3962 a(x) p Fi 1252 3962 a(\001) p Fl 1312 3962 a(!) p Fm 1377 3962 a(\).) p 1526 3962 a(Since) p Fl 1794 3962 a(\015) p Fm 1850 3962 a(\() p Fl(x) p Fi 1975 3962 a(\000) p Fl 2084 3962 a(d) p Ff 2135 3977 a(\006) p Fm 2194 3962 a(;) p 2241 3962 a(^) p Fl 2238 3962 a(e) p Fm(\)) p Fi 2353 3962 a(\000) p Fl 2462 3962 a(\015) p Fm 2518 3962 a(\() p Fl(x) p Fi 2643 3962 a(\000) p Fl 2752 3962 a(d) p Ff 2803 3977 a(\006) p Fm 2861 3962 a(;) p Fi 2905 3962 a(\000) p Fm 2986 3962 a(^) p Fl 2982 3962 a(e) p Fm 3028 3962 a(\)) p 3117 3962 a(=) p Fi 3244 3962 a(\000) p Fl(\031) p Fm 3427 3962 a(for) p Fl 0 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5416 a(\() p Fl(I) p 2268 5416 a(d) p Fi 2340 5416 a(\000) p Fm 2448 5416 a(~) p Fl 2440 5416 a(p) p Fm(\() p Fl(D) p Fg 2608 5431 a(x) p Fm 2652 5416 a(\)\)) p Fl 2744 5416 a(e) p Ff 2789 5375 a(\000) p Fg(i\020) p Fl 2908 5416 a(U) p Ff 2984 5375 a(\000) p Fj 2974 5441 a(+) p Ff(1) p Fl 3104 5416 a(p) p Fm(\() p Fl(D) p Fg 3272 5431 a(x) p Fm 3316 5416 a(\)) p Fl(:) p Fm 1723 5753 a(16) p 90 rotate dyy eop %%Page: 17 17 17 16 bop Fm 0 407 a(Hence) p 290 407 a(w) m(e) p 434 407 a(ha) m(v) m(e) p Fl 422 619 a(R) p Fm 497 619 a(\() p Fl(E) p Fm 635 619 a(+) p Fl 733 619 a(i) p Fm(0;) p Fl 859 619 a(K) p Fg 942 634 a(d) p Fm 983 619 a(\)) p Fl(U) p Ff 1097 578 a(\000) p Fj 1087 643 a(+) p Ff(1) p Fl 1216 619 a(p) p Fm(\() p Fl(D) p Fg 1384 634 a(x) p Fm 1428 619 a(\)) p 1494 619 a(=) p Fl 1597 619 a(Q) p Fi 1697 619 a(\000) p Fl 1796 619 a(R) p Fm 1871 619 a(\() p Fl(E) p Fm 2009 619 a(+) p Fl 2107 619 a(i) p Fm(0;) p Fl 2233 619 a(K) p Fg 2316 634 a(d) p Fm 2357 619 a(\)) p 2412 619 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1023 5263 a(without) p 1395 5263 a(touc) m(hing) p 1802 5263 a(the) p 1978 5263 a(cen) m(ters) p Fl 2315 5263 a(d) p Fj 2366 5278 a(+) p Fm 2466 5263 a(and) p Fl 2664 5263 a(d) p Ff 2715 5278 a(\000) p Fm 2773 5263 a(.) p 2869 5263 a(This) p 3100 5263 a(enables) p 3451 5263 a(us) 0 5384 y(to) p 120 5384 a(rep) s(eat) p 422 5384 a(the) p 590 5384 a(same) p 835 5384 a(argumen) m(t) p 1272 5384 a(as) p 1393 5384 a(in) p 1508 5384 a(the) p 1676 5384 a(pro) s(of) p 1932 5384 a(of) p 2044 5384 a(Lemma) p 2393 5384 a(4.1,) p 2578 5384 a(and) p 2768 5384 a(w) m(e) p 2913 5384 a(get) p 3076 5384 a(the) p 3245 5384 a(desired) 0 5504 y(relation.) p 396 5504 a(W) p 488 5504 a(e) p 564 5504 a(skip) p 767 5504 a(the) p 935 5504 a(details.) p Fa 1380 5504 a(2) p Fm 1723 5753 a(17) p 90 rotate dyy eop %%Page: 18 18 18 17 bop Fm 146 407 a(The) p 350 407 a(pro) s(of) p 609 407 a(of) p 723 407 a(Lemma) p 1075 407 a(3.3) p 1236 407 a(is) p 1337 407 a(done) p 1574 407 a(b) m(y) p 1713 407 a(reducing) p 2112 407 a(it) p 2213 407 a(to) p 2336 407 a(pro) s(ofs) p 2632 407 a(of) p 2747 407 a(three) p 3000 407 a(lemmas.) p 3401 407 a(F) p 3457 407 a(or) 0 527 y(brevit) m(y) p 291 527 a(,) p 352 527 a(w) m(e) p 496 527 a(analyze) p 845 527 a(the) p 1013 527 a(b) s(eha) m(vior) p 1412 527 a(of) p 1523 527 a(only) p 1737 527 a(the) p 1905 527 a(term) 529 747 y(\010) p Ff 599 706 a(\000) p Fj 599 772 a(+) p Fm 686 747 a(=) p 790 747 a(4) p Fl(\031) t(E) p Fj 976 706 a(1) p Fg(=) p Fj(2) p Fl 1085 747 a(h) p Fh 1158 651 a(D) p Fm 1209 747 a(\005\() p Fl(K) p Fg 1403 762 a(d) p Fm 1443 747 a(\)) p Fl(e) p Fg 1526 706 a(i\021) p Fl 1592 747 a(V) p Fj 1649 762 a(+) p Fl 1708 747 a(W) p Ff 1814 706 a(\000) p Fm 1890 747 a(\() p Fl(@) p Fj 1979 762 a(2) p Fl 2019 747 a(W) p Fm 2125 747 a(\)) p Fl 2179 747 a(') p Ff 2243 762 a(\000) p Fl 2302 747 a(;) p 2346 747 a(e) p Fg 2391 706 a(i\021) p Fl 2457 747 a(V) p Fm 2552 747 a(\() p Fl(@) p Fj 2641 762 a(2) p Fl 2681 747 a(W) p Fm 2787 747 a(\)) p Fl 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3853 a(\() p Fl(@) p Fj 2790 3868 a(2) p Fl 2830 3853 a(W) p Fm 2936 3853 a(\)) p Fl 2990 3853 a(') p Ff 3054 3868 a(\000) p Fh 3113 3757 a(E) p Fl 3180 3853 a(:) p Fm 3343 3853 a(\(4.9\)) 0 4087 y(The) p 206 4087 a(asymptotic) p 712 4087 a(form) m(ula) p 1075 4087 a(of) p 1191 4087 a(\010) p Ff 1261 4051 a(\000) p Fj 1261 4112 a(+) p Fm 1358 4087 a(in) p 1477 4087 a(Lemma) p 1830 4087 a(3.3) p 1992 4087 a(is) p 2095 4087 a(obtained) p 2501 4087 a(from) p 2737 4087 a(the) p 2910 4087 a(follo) m(wing) p 3327 4087 a(three) 0 4208 y(lemmas.) p Fn 0 4486 a(Lemma) p 397 4486 a(4.3) p Fb 589 4486 a(We) p 766 4486 a(have) p Fm 990 4486 a(\000) p Fj 1051 4501 a(+) p Fm 1138 4486 a(=) p Fh 1242 4369 a(Z) p Fl 1341 4486 a(v) p Fj 1388 4501 a(+) p Fm 1447 4486 a(\() p Fl(x) p Fj 1540 4501 a(1) p Fm 1580 4486 a(\)) p Fl 1635 4486 a(dx) p Fj 1741 4501 a(1) p Fm 1802 4486 a(+) p Fl 1900 4486 a(O) p Fm 1978 4486 a(\() p Fl(h) p Fg 2072 4445 a(N) p Fm 2139 4486 a(\)) p Fb(.) p Fn 0 4896 a(Lemma) p 397 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Fg(i\014) s(\031) p Fl 2722 5138 a(h) p Fm 2801 5138 a(+) p Fl 2899 5138 a(o) p Fm(\() p Fl(h) p Fj 3040 5097 a(3) p Fg(=) p Fj(2) p Fm 3150 5138 a(\)) p Fl(:) p Fm 1723 5753 a(18) p 90 rotate dyy eop %%Page: 19 19 19 18 bop Fn 0 407 a(Lemma) p 397 407 a(4.5) p Fb 589 407 a(L) p 645 407 a(et) p Fl 757 407 a(k) p Fj 808 422 a(1) p Fb 882 407 a(b) p 922 407 a(e) p 1002 407 a(as) p 1126 407 a(in) p 1246 407 a(L) p 1302 407 a(emma) p 1591 407 a(3.3.) p 1795 407 a(Then) p 2049 407 a(we) p 2194 407 a(have) p Fm 958 627 a(\000) p Ff 1019 642 a(\000) p Fm 1106 627 a(=) p Fi 1209 627 a(\000) p Fl(k) p Fj 1337 642 a(1) p Fl 1377 627 a(e) p Fg 1422 586 a(i\031) r(=) p Fj(4) p Fl 1564 627 a(\034) p Fj 1606 642 a(+) p Fl 1665 627 a(F) p Ff 1728 642 a(\000) p Fm 1787 627 a(\() p Fl(!) p Ff 1886 642 a(\000) p Fm 1945 627 a(\)) p Fl(h) p Fj 2039 586 a(1) p Fg(=) p Fj(2) p Fm 2171 627 a(+) p Fl 2269 627 a(o) p Fm(\() p Fl(h) p Fj 2410 586 a(3) p Fg(=) p Fj(2) p Fm 2520 627 a(\)) p Fl(:) p Fm 146 905 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2773 a(\006) p Fm 657 2758 a(\() p Fl(x) p Fi 779 2758 a(\000) p Fl 886 2758 a(d) p Ff 937 2773 a(\006) p Fm 995 2758 a(;) p Fi 1039 2758 a(\006) p Fm 1120 2758 a(^) p Fl 1116 2758 a(e) p Fm 1162 2758 a(\).) p 1300 2758 a(The) p 1510 2758 a(op) s(erator) p Fl 1913 2758 a(L) p Ff 1979 2773 a(\006) p Fm 2080 2758 a(is) p 2188 2758 a(also) p 2394 2758 a(self{adjoin) m(t) p 2922 2758 a(with) p 3154 2758 a(the) p 3331 2758 a(same) 0 2878 y(domain) p 347 2878 a(as) p Fl 467 2878 a(K) p Ff 550 2893 a(\006) p Fm 609 2878 a(.) p 679 2878 a(W) p 771 2878 a(e) p 847 2878 a(pro) m(v) m(e) p 1110 2878 a(the) p 1278 2878 a(follo) m(wing) p 1690 2878 a(lemma.) p Fn 0 3156 a(Lemma) p 397 3156 a(4.6) p Fb 689 3156 a(L) p 745 3156 a(et) p 862 3156 a(the) p 1029 3156 a(notation) p 1422 3156 a(b) p 1462 3156 a(e) p 1547 3156 a(as) p 1677 3156 a(ab) p 1767 3156 a(ove.) p 1995 3156 a(Then) p Fm 2254 3156 a(\000) p 2352 3156 a(=) p 2465 3156 a(\000) p Fj 2526 3171 a(1) p Fm 2591 3156 a(+) p Fl 2693 3156 a(o) 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2940 4713 a(\() p Fi(r) p Fl(\020) p Fj 3104 4728 a(+) p Fm 3163 4713 a(\).) p Fn 0 4991 a(Lemma) p 397 4991 a(4.7) p Fb 589 4991 a(We) p 766 4991 a(have) p Fm 407 5186 a(~) p Fl 392 5211 a(V) p Fj 449 5226 a(+) p Fl 508 5211 a(W) p Fj 614 5170 a(+) p Fl 672 5211 a(R) p Fm 747 5211 a(\() p Fl(E) p Fm 886 5211 a(+) p Fl 984 5211 a(i) p Fm(0;) p Fl 1110 5211 a(K) p Fg 1193 5226 a(d) p Fm 1233 5211 a(\)) p Fl(V) p Fj 1328 5226 a(+) p Fl 1387 5211 a(W) p Ff 1493 5170 a(\000) p Fm 1579 5211 a(=) 1697 5186 y(~) p Fl 1683 5211 a(V) p Fj 1740 5226 a(+) p Fl 1798 5211 a(W) p Fj 1904 5170 a(+) p Fl 1963 5211 a(R) p Fm 2038 5211 a(\() p Fl(E) p Fm 2176 5211 a(+) p Fl 2274 5211 a(i) p Fm(0;) p Fl 2400 5211 a(L) p Fj 2466 5226 a(+) p Fm 2526 5211 a(\)) p Fl(V) p Fj 2621 5226 a(+) p Fl 2679 5211 a(W) p Ff 2785 5170 a(\000) p Fm 691 5369 a(+) 828 5344 y(~) p Fl 813 5369 a(V) p Fj 870 5384 a(+) p Fl 929 5369 a(W) p Fj 1035 5328 a(+) p Fh 1110 5272 a(\020) p Fl 1160 5369 a(R) p Fm 1235 5369 a(\() p 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p 1332 2113 a(so) p 1451 2113 a(that) p Fl 253 2333 a(K) p Fg 336 2348 a(d) p Fm 404 2333 a(=) p Fl 507 2333 a(H) p Fm 596 2333 a(\() p Fl(B) p Fj 708 2348 a(+) p Fm 789 2333 a(+) p Fl 887 2333 a(B) p Ff 961 2348 a(\000) p Fm 1020 2333 a(\)) p 1086 2333 a(=) p Fl 1189 2333 a(H) p Fm 1278 2333 a(\() p Fl(B) p Fj 1390 2348 a(+) p Fm 1471 2333 a(+) p Fi 1569 2333 a(r) p Fl(\020) p Ff 1695 2348 a(\000) p Fm 1754 2333 a(\)) p 1819 2333 a(=) p 1923 2333 a(exp) q(\() p Fl(i\020) p Ff 2186 2348 a(\000) p Fm 2245 2333 a(\)) p Fl(H) p Fm 2372 2333 a(\() p Fl(B) p Fj 2484 2348 a(+) p Fm 2542 2333 a(\)) p 2597 2333 a(exp) q(\() p Fi(\000) p Fl(i\020) p Ff 2937 2348 a(\000) p Fm 2996 2333 a(\)) p 3062 2333 a(=) p Fl 3165 2333 a(L) p Fj 3231 2348 a(+) p Fm 0 2553 a(there.) p 315 2553 a(Th) m(us) p 571 2553 a(the) p 748 2553 a(co) s(e\016cien) m (ts) p 1251 2553 a(of) p Fl 1371 2553 a(T) p Ff 1428 2568 a(\000) p Fj(1) p Fm 1564 2553 a(ha) m(v) m(e) p 1798 2553 a(supp) s(ort) p 2169 2553 a(in) p 2292 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a(i) p Fm(0;) p Fl 2809 5504 a(L) p Fj 2875 5519 a(+) p Fm 2934 5504 a(\)) p Fl(:) p Fm 1723 5753 a(22) p 90 rotate dyy eop %%Page: 23 23 23 22 bop Fm 0 407 a(The) p 205 407 a(\014rst) p 411 407 a(term) p 648 407 a(on) p 789 407 a(the) p 961 407 a(righ) m(t) p 1202 407 a(side) p 1402 407 a(just) p 1599 407 a(coincides) p 2016 407 a(with) p 2243 407 a(\000) p Fj 2304 422 a(1) p Fm 2344 407 a(.) p 2428 407 a(In) p 2554 407 a(fact,) p 2780 407 a(w) m(e) p 2928 407 a(ha) m(v) m(e) p 3157 407 a(\005\() p Fl(L) p Fj 3334 422 a(+) p Fm 3394 407 a(\)) p 3467 407 a(=) p Fl 0 527 a(e) p Fg 45 491 a(i\020) p Fe 100 500 a(\000) p Fm 157 527 a(\005\() p Fl(K) p Fj 351 542 a(+) p Fm 410 527 a(\)) p Fl(e) p Ff 493 491 a(\000) p Fg(i\020) p Fe 603 500 a(\000) p Fm 691 527 a(b) m(y) p 827 527 a(\(4.11\),) p 1136 527 a(and) p 1326 527 a(a) p 1407 527 a(simple) p 1711 527 a(computation) p 2280 527 a(yields) p Fl 861 725 a(\021) p Fi 935 725 a(\000) p Fl 1034 725 a(\020) p Ff 1077 740 a(\000) p Fm 1164 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a(\)) 0 2091 y(asso) s(ciated) p 467 2091 a(with) p 692 2091 a(self{adjoin) m(t) p 1212 2091 a(op) s(erator) p Fl 1608 2091 a(K) p Fj 1691 2106 a(+) p Fm 1782 2091 a(=) p Fl 1890 2091 a(H) p Fm 1979 2091 a(\() p Fl(B) p Fj 2091 2106 a(+) p Fm 2149 2091 a(\)) p 2222 2091 a(with) p 2447 2091 a(single) p 2721 2091 a(\014eld) p 2935 2091 a(2) p Fl(\014) p 3045 2091 a(\031) t(\016) p Fm 3151 2091 a(\() p Fl(x) p Fi 3267 2091 a(\000) p Fl 3369 2091 a(d) p Fj 3420 2106 a(+) p Fm 3478 2091 a(\),) 0 2211 y(and) p 186 2211 a(the) p 350 2211 a(k) m(ernel) p 633 2211 a(of) p 740 2211 a(\005\() p Fl(K) p Fj 934 2226 a(+) p Fm 993 2211 a(\)) p 1060 2211 a(is) p 1154 2211 a(describ) s(ed) p 1581 2211 a(in) p 1691 2211 a(terms) p 1959 2211 a(of) p 2066 2211 a(the) p 2230 2211 a(eigenfunction.) p 2865 2211 a(Th) m(us) p 3108 2211 a(w) m(e) p 3248 2211 a(require) 0 2332 y(an) p 144 2332 a(information) p 681 2332 a(on) p 825 2332 a(it) p 931 2332 a(to) p 1058 2332 a(analyze) p 1416 2332 a(the) p 1593 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3768 a(W) p 2179 3768 a(e) p 2269 3768 a(w) m(ork) p 2521 3768 a(in) p 2649 3768 a(the) p 2830 3768 a(p) s(olar) p 3096 3768 a(co) s(ordinate) 0 3889 y(system) p 325 3889 a(\() p Fl(r) m(;) p 448 3889 a(\022) p Fm 496 3889 a(\)) p 568 3889 a(to) p 689 3889 a(calculate) p 1097 3889 a(the) p 1267 3889 a(eigenfunction.) p 1908 3889 a(Let) p Fl 2085 3889 a(U) p Fm 2196 3889 a(b) s(e) p 2330 3889 a(the) p 2500 3889 a(unitary) p 2845 3889 a(op) s(erator) p 3240 3889 a(de\014ned) 0 4009 y(b) m(y) 621 4129 y(\() p Fl(U) p 735 4129 a(u) p Fm(\)\() p Fl(r) m(;) p 952 4129 a(\022) p Fm 1000 4129 a(\)) p 1066 4129 a(=) p Fl 1169 4129 a(r) p Fj 1216 4088 a(1) p Fg(=) p Fj(2) p Fl 1326 4129 a(u) p Fm(\() p Fl(r) s(\022) p Fm 1515 4129 a(\)) p 1580 4129 a(:) p Fl 1635 4129 a(L) p Fj 1701 4088 a(2) p Fi 1768 4129 a(!) p Fl 1896 4129 a(L) p Fj 1962 4088 a(2) p Fm 2001 4129 a(\(\(0) p Fl(;) p Fi 2170 4129 a(1) p Fm(\);) p Fl 2352 4129 a(dr) p Fm 2450 4129 a(\)) p Fi 2508 4129 a(\012) p Fl 2608 4129 a(L) 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a(generating) p 640 5050 a(function) p 1019 5050 a(with) p 1239 5050 a(Bessel) p 1529 5050 a(co) s(e\016cien) m(ts.) p 2059 5050 a(Hence) p Fl 2347 5050 a(') p Fj 2411 5065 a(0) p Fm 2450 5050 a(\() p Fl(x) p Fm(;) p Fl 2587 5050 a(!) p Fm 2652 5050 a(\)) p 2717 5050 a(=) p 2820 5050 a(exp) r(\() p Fl(iE) p Fj 3119 5014 a(1) p Fg(=) p Fj(2) p Fl 3229 5050 a(x) p Fi 3301 5050 a(\001) p Fl 3346 5050 a(!) p Fm 3411 5050 a(\)) p 3478 5050 a(is) 0 5171 y(expanded) p 436 5171 a(as) p Fl 627 5421 a(') p Fj 691 5436 a(0) p Fm 730 5421 a(\() p Fl(x) p Fm(;) p Fl 867 5421 a(!) p Fm 932 5421 a(\)) p 997 5421 a(=) p Ff 1167 5313 a(1) p Fh 1142 5338 a(X) p Fg 1101 5522 a(l) p Fj 1123 5522 a(=) p Ff(\0001) p Fm 1320 5421 a(exp) q(\() p Fl(i) p Fi(j) p Fl(l) p Fi 1599 5421 a(j) p Fl(\031) t(=) p Fm(2\)) p 1839 5421 a(exp\() p Fl(il) r(\015) p Fm 2145 5421 a(\() p Fl(x) p Fm(;) p Fl 2282 5421 a(!) p Fm 2347 5421 a(\)\)) p Fl(J) p Ff 2477 5436 a(j) p Fg(l) p Ff 2519 5436 a(j) p Fm 2542 5421 a(\() p 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a(\() p Fl(x) p Fm(;) p Fl 1435 5504 a(!) p Fm 1500 5504 a(\)\)) p Fl(') p Fj 1640 5519 a(0) p Fm 1679 5504 a(\() p Fl(x) p Fm(;) p Fl 1816 5504 a(!) p Fm 1881 5504 a(\)) p 1946 5504 a(=) p 2049 5504 a(exp) q(\() p Fl(i\014) p 2330 5504 a(\033) p Fi 2411 5504 a(\000) p Fl 2511 5504 a(iE) p Fj 2622 5463 a(1) p Fg(=) p Fj(2) p Fi 2732 5504 a(j) p Fl(x) p Fi(j) p Fm 2860 5504 a(cos) p Fl 3023 5504 a(\033) p Fm 3082 5504 a(\)) p 3343 5504 a(\(5.6\)) 1723 5753 y(24) p 90 rotate dyy eop %%Page: 25 25 25 24 bop Fm 0 407 a(as) p 120 407 a(the) p 288 407 a(inciden) m(t) p 659 407 a(w) m(a) m(v) m(e.) p 935 407 a(Then) p Fl 1190 407 a(') p Fj 1254 422 a(in) p Fm 1317 407 a(\() p Fl(x) p Fm(;) p Fl 1454 407 a(!) p Fm 1519 407 a(\)) p 1589 407 a(is) p 1687 407 a(expanded) p 2123 407 a(in) m(to) p 2321 407 a(the) p 2489 407 a(F) p 2545 407 a(ourier) p 2826 407 a(series) p Fl 448 684 a(') p Fj 512 699 a(in) p Fm 602 684 a(=) p 706 684 a(\(1) p Fl(=\031) p Fm 901 684 a(\)) p Ff 1021 577 a(1) p Fh 996 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3128 a(+) p Fm 1145 3113 a(;) p Fl 1189 3113 a(!) p Fm 1254 3113 a(\).) p 1361 3113 a(Ho) m(w) m(ev) m(er) p 1752 3113 a(w) m(e) p 1894 3113 a(require) p 2220 3113 a(a) p 2299 3113 a(commen) m(t) p 2717 3113 a(on) p 2851 3113 a(the) p 3017 3113 a(construction) 0 3233 y(of) p 120 3233 a(eigenfunction) p 728 3233 a(of) p Fl 848 3233 a(K) p Ff 931 3248 a(\000) p Fm 990 3233 a(.) p 1088 3233 a(T) p 1150 3233 a(o) p 1241 3233 a(de\014ne) p 1532 3233 a(it,) p 1668 3233 a(w) m(e) p 1820 3233 a(consider) p 2209 3233 a(the) p 2386 3233 a(auxiliary) p 2802 3233 a(op) s(erator) p Fl 3204 3233 a(K) p Fj 3287 3248 a(1) p Ff(\000) p Fg(\014) p Fm 3467 3233 a(=) p Fl 0 3353 a(H) p Fm 105 3353 a(\(\(1) p Fi 252 3353 a(\000) p Fl 352 3353 a(\014) p Fm 413 3353 a(\)\003\)) o(,) p 629 3353 a(0) p Fi 723 3353 a(\024) p Fm 847 3353 a(1) p Fi 925 3353 a(\000) p Fl 1032 3353 a(\014) p 1138 3353 a(<) p Fm 1260 3353 a(1,) p 1382 3353 a(and) p 1582 3353 a(denote) p 1907 3353 a(b) m(y) p 2069 3353 a(~) p Fl 2053 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4192 a(has) p 2256 4192 a(the) p 2418 4192 a(fol) p 2528 4192 a(lowing) p 2832 4192 a(pr) p 2918 4192 a(op) p 3013 4192 a(erties) p 3280 4192 a(:) p Fm 146 4362 a(\(1\)) p Fb 317 4362 a(If) p Fm 422 4362 a(1) p Fl(=c) p 592 4362 a(<) p Fi 699 4362 a(j) p Fl(x) p Fi(j) p Fl 841 4362 a(<) p 948 4362 a(c) p Fb 1026 4362 a(and) p Fi 1217 4362 a(j) p Fm 1251 4362 a(^) p Fl 1245 4362 a(x) p Fi 1324 4362 a(\000) p Fl 1425 4362 a(!) p Fi 1490 4362 a(j) p Fl 1548 4362 a(>) p Fm 1655 4362 a(1) p Fl(=c) p Fb 1831 4362 a(for) p 1989 4362 a(some) p Fl 2239 4362 a(c) p 2312 4362 a(>) p Fm 2419 4362 a(1) p Fb(,) p 2535 4362 a(then) p Fl 2754 4362 a(') p Fj 2818 4377 a(sc) p Fm 2881 4362 a(\() p Fl(x=h) p Fm(;) p Fl 3123 4362 a(!) p Fm 3188 4362 a(\)) p Fb 3262 4362 a(admits) 0 4483 y(the) p 162 4483 a(asymptotic) p 653 4483 a(exp) p 788 4483 a(ansion) p Fl 521 4784 a(') p Fj 585 4799 a(sc) p Fm 648 4784 a(\() p Fl(x=h) p Fm(;) p Fl 890 4784 a(!) p Fm 955 4784 a(\)) p 1020 4784 a(=) p Fl 1123 4784 a(h) p Fj 1179 4743 a(1) p Fg(=) p Fj(2) p Fh 1306 4613 a(0) 1306 4763 y(@) p Fg 1379 4676 a(N) p Ff 1442 4676 a(\000) p Fj(1) p Fh 1395 4701 a(X) p Fg 1394 4883 a(j) p Fj 1427 4883 a(=0) p Fl 1549 4784 a(a) p Fg 1600 4799 a(j) p Fm 1636 4784 a(\() p Fl(x;) p 1773 4784 a(!) p Fm 1838 4784 a(\)) p Fl(h) p Fg 1932 4743 a(j) p Fh 1968 4613 a(1) 1968 4763 y(A) p Fl 2058 4784 a(e) p Fg 2103 4743 a(iE) p Fd 2183 4720 a(1) p Fc(=) p Fd(2) p Ff 2279 4743 a(j) p Fg(x) p Ff(j) p Fg(=h) p Fm 2460 4784 a(+) p Fl 2558 4784 a(O) p Fm 2636 4784 a(\() p Fl(h) p Fg 2730 4743 a(N) p Fj 2793 4743 a(+1) p Fg(=) p Fj(2) p Fm 2958 4784 a(\)) p Fl(;) p Fb 0 5096 a(wher) p 196 5096 a(e) p Fl 275 5096 a(a) p Fg 326 5111 a(j) p Fm 363 5096 a(\() p Fl(x;) p 500 5096 a(!) p Fm 565 5096 a(\)) p Fb 637 5096 a(is) p 742 5096 a(smo) p 907 5096 a(oth) p 1073 5096 a(in) p Fl 1193 5096 a(!) p Fi 1285 5096 a(2) p Fl 1379 5096 a(S) p Fj 1445 5059 a(1) p Fb 1519 5096 a(and) p 1708 5096 a(in) p Fl 1828 5096 a(x) p Fb 1918 5096 a(as) p 2042 5096 a(ab) p 2132 5096 a(ove.) p Fm 146 5266 a(\(2\)) p Fb 317 5266 a(If) p Fi 420 5266 a(j) p Fl(x) p Fi(j) p Fl 558 5266 a(>) p 662 5266 a(c) p Fb 739 5266 a(for) p 894 5266 a(some) p Fl 1143 5266 a(c) p 1213 5266 a(>) p Fm 1317 5266 a(0) p Fb(,) p 1430 5266 a(then) p Fl 1647 5266 a(') p Fj 1711 5281 a(sc) p Fm 1774 5266 a(\() p Fl(x=h) p Fm(;) p Fl 2016 5266 a(!) p Fm 2081 5266 a(\)) p Fb 2153 5266 a(is) p 2258 5266 a(uniformly) p 2702 5266 a(b) p 2742 5266 a(ounde) p 2989 5266 a(d.) p Fm 1723 5753 a(25) p 90 rotate dyy eop %%Page: 26 26 26 25 bop Fb 0 407 a(Pr) p 102 407 a(o) p 147 407 a(of.) p Fm 354 407 a(\(1\)) p 576 407 a(This) p 789 407 a(is) p 877 407 a(sho) m(wn) p 1163 407 a(b) m(y) p 1288 407 a(use) p 1447 407 a(of) p 1548 407 a(the) p 1705 407 a(stationary) p 2159 407 a(phase) p 2421 407 a(metho) s(d.) p 2810 407 a(Since) p Fl 3055 407 a(\033) p Fm 3141 407 a(=) p Fl 3245 407 a(\033) p Fm 3304 407 a(\() p Fl(x) p Fm(;) p Fl 3441 407 a(!) p Fm 3506 407 a(\)) 0 527 y(de\014ned) p 336 527 a(b) m(y) p 471 527 a(\(5.5\)) p 705 527 a(is) p 803 527 a(homogeneous) p 1399 527 a(of) p 1510 527 a(degree) p 1814 527 a(zero) p 2020 527 a(as) p 2140 527 a(a) p 2221 527 a(function) p 2603 527 a(of) p Fl 2714 527 a(x) p Fm(,) p 2829 527 a(w) m(e) p 2973 527 a(ha) m(v) m(e) p Fl 275 810 a(') p Fj 339 825 a(sc) p Fm 402 810 a(\() p Fl(x=h) p Fm(;) p Fl 644 810 a(!) p Fm 709 810 a(\)) p 774 810 a(=) p 878 810 a(\() p Fi(\000) p Fm 1010 810 a(sin) p Fl 1146 810 a(\014) p 1207 810 a(\031) t(=\031) p Fm 1374 810 a(\)) p Fh 1428 664 a( ) 1494 693 y(Z) p Fm 1593 810 a(exp) q(\() p Fl(ih) p Ff 1869 769 a(\000) p Fj(1) p Fl 1964 810 a(E) p Fj 2042 769 a(1) p Fg(=) p Fj(2) p Fi 2152 810 a(j) p Fl(x) p Fi(j) p Fm 2280 810 a(cosh) p Fl 2481 810 a(t) p Fm(\)) p Fl 2661 742 a(e) p Ff 2706 706 a(\000) p Fg(\014) s(t) p 2564 786 366 4 v Fl 2564 878 a(e) p Ff 2609 849 a(\000) p Fg(t) p Fm 2716 878 a(+) p Fl 2814 878 a(e) p Fg 2859 849 a(i\033) p Fl 2957 810 a(dt) p 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2129 a(^) p Fl 949 2129 a(y) p Fi 1022 2129 a(\000) p Fl 1122 2129 a(!) p Fi 1187 2129 a(j) p Fl 1241 2129 a(>) p Fi 1345 2129 a(j) p Fl(y) p Fi 1425 2129 a(j) p Ff 1453 2093 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fm 1616 2129 a(,) p 1676 2129 a(then) p Fl 452 2379 a(I) p Fm 530 2379 a(=) p Fh 634 2262 a(Z) p Ff 680 2450 a(j) p Fg(y) p Ff 737 2450 a(j) p Fe 757 2431 a(\000) p Fd(1) p Fc(=) p Fd(2) p Fg 901 2450 a(<) p Ff(j) p Fg(t) p Ff(j) p Fg(<) p Fj(1) p Fh 1132 2283 a(\020) p Fl 1181 2379 a(e) p Ff 1226 2338 a(\000) p Fg(t) p Fm 1333 2379 a(+) p Fl 1431 2379 a(e) p Fg 1476 2338 a(i\033) p Fh 1547 2283 a(\021) p Ff 1597 2306 a(\000) p Fj(1) p Fl 1708 2379 a(e) p Fg 1753 2338 a(i) p Ff(j) p Fg(y) p Ff 1834 2338 a(j) p Fj 1865 2338 a(cosh) p Fg 2011 2338 a(t) p Fl 2057 2379 a(dt) p Fm 2165 2379 a(+) p Fl 2263 2379 a(O) p Fm 2341 2379 a(\(1\)) p Fl(;) p Fi 2704 2379 a(j) p Fl(y) p Fi 2784 2379 a(j) p 2838 2379 a(!) p 2965 2379 a(1) p Fl(:) p Fm 0 2691 a(Since) p Fi 256 2691 a(j) p Fl(@) p 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2824 a(j) p Fm 3181 2824 a(^) p Fl 3174 2824 a(y) p Fi 3247 2824 a(\000) p Fl 3347 2824 a(!) p Fi 3412 2824 a(j) p Fl 3467 2824 a(<) p Fi 0 2944 a(j) p Fl(y) p Fi 80 2944 a(j) p Ff 108 2908 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fm 271 2944 a(,) p 331 2944 a(then) p Fl 553 2944 a(I) p Fm 637 2944 a(b) s(eha) m(v) m (es) p 1000 2944 a(lik) m(e) p Fl 634 3194 a(I) p Fm 713 3194 a(=) p Fi 817 3194 a(\000) p Fh 911 3077 a(Z) p Ff 957 3266 a(j) p Fg(t) p Ff(j) p Fg(<) p Fj(1) p Fm 1116 3194 a(\() p Fl(t) p Fm 1211 3194 a(+) p Fl 1309 3194 a(i\020) p Fm 1393 3194 a(\)) p Ff 1431 3153 a(\000) p Fj(1) p Fl 1525 3194 a(e) p Fg 1570 3153 a(i) p Ff(j) p Fg(y) p Ff 1651 3153 a(j) p Fj 1682 3153 a(cosh) p Fg 1828 3153 a(t) p Fl 1874 3194 a(dt) p Fm 1982 3194 a(+) p Fl 2080 3194 a(O) p Fm 2158 3194 a(\(1\)) p Fl(;) p Fi 2521 3194 a(j) p Fl(y) p Fi 2601 3194 a(j) p 2655 3194 a(!) p 2782 3194 a(1) p Fl(;) p Fm 0 3476 a(with) p Fl 223 3476 a(\020) p Fm 301 3476 a(=) p Fl 405 3476 a(i) p Fm(\() p Fl(e) p Fg 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m(tegral) p Fh 1142 3730 a(Z) p Ff 1188 3918 a(j) p Fg(y) p Ff 1245 3918 a(j) p Fe 1265 3899 a(\000) p Fd(1) p Fc(=) p Fd(2) p Fg 1409 3918 a(<) p Ff(j) p Fg(t) p Ff(j) p Fg(<) p Fj(1) p Fl 1640 3847 a(t) p Ff 1675 3806 a(\000) p Fj(1) p Fl 1786 3847 a(e) p Fg 1831 3806 a(i) p Ff(j) p Fg(y) p Ff 1912 3806 a(j) p Fj 1944 3806 a(cosh) p Fg 2089 3806 a(t) p Fl 2135 3847 a(dt) p Fm 2249 3847 a(=) p 2352 3847 a(0) 0 4112 y(v) p 46 4112 a(anishes,) p 410 4112 a(then) p 632 4112 a(it) p 730 4112 a(follo) m(ws) p 1050 4112 a(that) p Fh 737 4239 a(Z) p Ff 783 4428 a(j) p Fg(y) p Ff 840 4428 a(j) p Fe 860 4408 a(\000) p Fd(1) p Fc(=) p Fd(2) p Fg 1004 4428 a(<) p Ff(j) p Fg(t) p Ff(j) p Fg(<) p Fj(1) p Fh 1235 4260 a(\020) p Fm 1285 4356 a(\() p Fl(t) p Fm 1380 4356 a(+) p Fl 1478 4356 a(i\020) p Fm 1562 4356 a(\)) p Ff 1600 4315 a(\000) p Fj(1) p Fi 1716 4356 a(\000) p Fl 1815 4356 a(t) p Ff 1850 4315 a(\000) p Fj(1) p Fh 1945 4260 a(\021) p Fl 2011 4356 a(e) p Fg 2056 4315 a(i) p Ff(j) p Fg(y) p Ff 2137 4315 a(j) p Fj 2168 4315 a(cosh) p Fg 2314 4315 a(t) p Fl 2360 4356 a(dt) p Fm 2474 4356 a(=) p Fl 2577 4356 a(O) p Fm 2655 4356 a(\(1\)) p Fl(:) p Fm 0 4622 a(This) p 223 4622 a(implies) p 554 4622 a(that) p Fl 805 4866 a(I) p Fm 883 4866 a(=) p Fh 987 4749 a(Z) p Ff 1033 4938 a(j) p Fg(t) p Ff(j) p Fg(<) p Ff(j) p Fg(y) p Ff 1210 4938 a(j) p Fe 1230 4918 a(\000) p Fd(1) p Fc(=) p Fd(2) p Fm 1378 4866 a(\() p Fl(t) p Fm 1473 4866 a(+) p Fl 1571 4866 a(i\020) p Fm 1655 4866 a(\)) p Ff 1693 4825 a(\000) p Fj(1) p Fl 1804 4866 a(dt) p 1907 4866 a(e) p Fg 1952 4825 a(i) p Ff(j) p Fg(y) p Ff 2033 4825 a(j) p Fm 2078 4866 a(+) p Fl 2176 4866 a(O) p Fm 2254 4866 a(\(1\)) p 2406 4866 a(=) p Fl 2509 4866 a(O) p Fm 2587 4866 a(\(1\)) p Fl(:) p Fm 0 5137 a(The) p 201 5137 a(case) p Fl 407 5137 a(\033) p Fm 494 5137 a(=) p Fl 597 5137 a(\031) p Fi 678 5137 a(\000) p Fl 778 5137 a(\016) p Fm 857 5137 a(with) p Fl 1080 5137 a(\016) p 1154 5137 a(>) p Fm 1258 5137 a(0) p 1339 5137 a(is) p 1437 5137 a(dealt) p 1681 5137 a(with) p 1903 5137 a(similarly) p 2260 5137 a(.) p 2332 5137 a(Th) m(us) p 2579 5137 a(\(2\)) p 2736 5137 a(is) p 2834 5137 a(v) m(eri\014ed.) p Fa 3311 5137 a(2) p Fm 1723 5753 a(26) p 90 rotate dyy eop %%Page: 27 27 27 26 bop Fn 0 407 a(Prop) s(osition) p 606 407 a(5.2) p Fb 798 407 a(L) p 854 407 a(et) p Fl 966 407 a(') p Fm(\() p Fl(x) p Fm(;) p Fl 1167 407 a(!) p Fm 1232 407 a(\)) p Fb 1304 407 a(b) p 1344 407 a(e) p 1423 407 a(as) p 1548 407 a(ab) p 1638 407 a(ove) p 1812 407 a(and) p 2001 407 a(let) p Fl 2138 407 a(\034) p Fm 2219 407 a(=) p Fl 2323 407 a(\034) p Fm 2376 407 a(\() p Fl(x;) p 2513 407 a(!) p Fm 2578 407 a(\)) p Fb 2651 407 a(b) p 2691 407 a(e) p 2770 407 a(de\014ne) p 3015 407 a(d) p 3099 407 a(by) p Fl 766 620 a(\034) p Fm 819 620 a(\() p Fl(x;) p 956 620 a(!) p Fm 1021 620 a(\)) p 1086 620 a(=) p Fl 1190 620 a(\015) p Fm 1246 620 a(\() p Fl(x) p Fm(;) p Fi 1383 620 a(\000) p Fl(!) p Fm 1525 620 a(\)) p Fi 1585 620 a(\000) p Fl 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p Ff(\001) p Fj(;) s(^) p Fg 1452 4684 a(e) p Fj(\)) p Fl 1517 4726 a(v) p Fj 1564 4741 a(+) p Fl 1623 4726 a(w) p Ff 1696 4684 a(\000) p Fm 1771 4726 a(\() p Fl(@) p Fj 1860 4741 a(2) p Fl 1900 4726 a(w) p Fm 1973 4726 a(\)) p Fl 2027 4726 a(') p Ff 2091 4741 a(\000) p Fm 2150 4726 a(\() p Fi(\001) p Fl(=h) p Fm(\)) p Fl(;) p 2403 4726 a(') p Fm(\() p Fi(\001) p Fl(=h) p Fm(;) p Fl 2682 4726 a(!) p Fm 2747 4726 a(\)) p Fh 2785 4629 a(E) p Fl 2850 4726 a(;) p Fm 0 4953 a(where) p Fl 275 4953 a(v) p Fj 322 4968 a(+) p Fl 381 4953 a(;) p Fm 454 4953 a(~) p Fl 450 4953 a(v) p Fj 497 4968 a(+) p Fl 556 4953 a(;) p 625 4953 a(w) p Ff 698 4917 a(\006) p Fm 782 4953 a(and) p Fl 964 4953 a(w) p Fm 1062 4953 a(are) p 1218 4953 a(as) p 1330 4953 a(in) p 1437 4953 a(sections) p 1794 4953 a(3) p 1868 4953 a(and) p 2050 4953 a(4.) p 2167 4953 a(W) p 2259 4953 a(e) p 2328 4953 a(use) p 2489 4953 a(the) p 2650 4953 a(v) p 2696 4953 a(ariables) p Fl 3047 4953 a(x) p Fm 3130 4953 a(=) p 3234 4953 a(\() 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5437 a(\(2) p Fl(\031) p Fm 1239 5437 a(\)) p Ff 1277 5396 a(\000) p Fj(1) p Fl 1371 5437 a(E) p Fj 1449 5396 a(1) p Fg(=) p Fj(2) p Fl 1559 5437 a(e) p Ff 1604 5396 a(\000) p Fg(i) p Fj(2) p Fg(\014) s(\031) p Fl 1809 5437 a(h) p Ff 1865 5396 a(\000) p Fj(1) p Fh 1976 5320 a(Z) p Fl 2075 5437 a(Y) p Fm 2154 5437 a(\() p Fl(!) p Fm 2257 5437 a(\)) p Fl(X) p Fm 2384 5437 a(\() p Fl(!) p Fm 2487 5437 a(\)) p Fl 2542 5437 a(d!) t(:) p Fm 1723 5753 a(27) p 90 rotate dyy eop %%Page: 28 28 28 27 bop Fn 0 407 a(Lemma) p 397 407 a(6.1) p Fb 589 407 a(L) p 645 407 a(et) p Fl 757 407 a(X) p Fm 846 407 a(\() p Fl(!) p Fm 949 407 a(\)) p Fb 1021 407 a(and) p Fl 1210 407 a(Y) p Fm 1289 407 a(\() p Fl(!) p Fm 1392 407 a(\)) p Fb 1464 407 a(b) p 1504 407 a(e) p 1583 407 a(as) p 1708 407 a(ab) p 1798 407 a(ove,) p 2002 407 a(and) p 2191 407 a(de\014ne) p Fl 697 639 a(Y) p Fj 754 654 a(sc) p Fm 817 639 a(\() p Fl(!) p Fm 920 639 a(\)) p 985 639 a(=) p Fh 1089 543 a(D) p Fl 1139 639 a(e) p Fg 1184 598 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1370 a(j) p Fl(!) p Fi 534 1370 a(\000) p Fl 634 1370 a(!) p Ff 695 1385 a(\000) p Fi 753 1370 a(j) p Fl 809 1370 a(<) p 912 1370 a(h) p Fj 968 1334 a(1) p Ff(\000) p Fg(") p Fb 1095 1370 a(,) p 1160 1370 a(then) p Fl 1377 1370 a(X) p Fm 1466 1370 a(\() p Fl(!) p Fm 1569 1370 a(\)) p 1633 1370 a(=) p Fl 1737 1370 a(O) p Fm 1815 1370 a(\(1\)) p Fb 1974 1370 a(and) p Fl 2163 1370 a(Y) p Fj 2220 1385 a(sc) p Fm 2283 1370 a(\() p Fl(!) p Fm 2386 1370 a(\)) p 2451 1370 a(=) p Fl 2554 1370 a(O) p Fm 2632 1370 a(\() p Fl(h) p Fg 2726 1334 a(N) p Fm 2793 1370 a(\)) p Fb(.) 0 1648 y(Pr) p 102 1648 a(o) p 147 1648 a(of.) p Fm 354 1648 a(\(1\)) p 576 1648 a(The) p 766 1648 a(fact) p 948 1648 a(that) p Fl 1148 1648 a(X) p Fm 1237 1648 a(\() p Fl(!) p Fm 1340 1648 a(\)) p 1405 1648 a(=) p Fl 1509 1648 a(O) p Fm 1587 1648 a(\(1\)) p 1732 1648 a(is) p 1820 1648 a(an) p 1945 1648 a(immediate) p 2411 1648 a(consequence) p 2951 1648 a(of) p 3051 1648 a(Prop) s(osition) 0 1768 y(5.1) p 150 1768 a(\(2\).) p 343 1768 a(T) p 405 1768 a(o) p 480 1768 a(pro) m(v) m(e) p 735 1768 a(the) p 896 1768 a(b) s(ound) p 1190 1768 a(on) p Fl 1319 1768 a(Y) p Fm 1397 1768 a(\() p Fl(!) p Fm 1500 1768 a(\),) p 1591 1768 a(w) m(e) p 1728 1768 a(use) p 1889 1768 a(Prop) s(osition) p 2407 1768 a(5.1) p 2558 1768 a(\(1\).) p 2750 1768 a(W) p 2842 1768 a(e) p 2911 1768 a(represen) m(t) p Fl 3325 1768 a(Y) p Fm 3403 1768 a(\() p Fl(!) p Fm 3506 1768 a(\)) 0 1889 y(in) p 119 1889 a(the) p 292 1889 a(in) m(tegral) p 652 1889 a(form.) p 936 1889 a(The) p 1141 1889 a(function) p Fl 1529 1889 a(\033) p Fm 1588 1889 a(\() p Fl(y) t(=h) p Fm(;) p Fl 1827 1889 a(!) p Fm 1892 1889 a(\)) p 1964 1889 a(=) p Fl 2076 1889 a(\033) p Fm 2135 1889 a(\() p Fl(y) p Fm 2225 1889 a(;) p Fl 2269 1889 a(!) p Fm 2334 1889 a(\)) p 2408 1889 a(de\014ned) p 2749 1889 a(b) m(y) p 2890 1889 a(\(5.5\)) p 3128 1889 a(is) p 3231 1889 a(smo) s(oth) 0 2009 y(o) m(v) m(er) p 209 2009 a(supp) p Fl 426 2009 a(v) p Fj 473 2024 a(+) p Fl 533 2009 a(w) p Ff 606 1973 a(\000) p Fm 664 2009 a(,) p 724 2009 a(and) p Fl 238 2229 a(') p Fm(\() p Fl(y) t(=h) p Fm(;) p Fl 541 2229 a(!) p Fm 606 2229 a(\)) p 669 2229 a(=) p Fl 773 2229 a(') p Fj 837 2244 a(in) p Fm 899 2229 a(\() p Fl(y) t(=h) p Fm(;) p Fl 1138 2229 a(!) p Fm 1203 2229 a(\)) p 1262 2229 a(+) p Fl 1360 2229 a(') p Fj 1424 2244 a(sc) p Fm 1487 2229 a(\() p Fl(y) t(=h) p Fm(;) p Fl 1726 2229 a(!) p Fm 1791 2229 a(\)) p 1854 2229 a(=) p Fl 1958 2229 a(e) p Fg 2003 2188 a(i\014) s(\033) p Fj 2112 2188 a(\() p Fg(y) p Fj 2176 2188 a(;) p Fg(!) p Fj 2242 2188 a(\)) p Fl 2275 2229 a(') p Fj 2339 2244 a(0) p Fm 2378 2229 a(\() p Fl(y) t(=h) p Fm(;) p Fl 2617 2229 a(!) p Fm 2682 2229 a(\)) p 2741 2229 a(+) p Fl 2839 2229 a(') p Fj 2903 2244 a(sc) p Fm 2966 2229 a(\() p Fl(y) t(=h) p Fm(;) p Fl 3205 2229 a(!) p Fm 3270 2229 a(\)) 0 2449 y(admits) p 320 2449 a(the) p 488 2449 a(asymptotic) p 990 2449 a(expansion) p 1443 2449 a(as) p 1563 2449 a(in) p 1677 2449 a(Prop) s(osition) p 2202 2449 a(5.1.) p 2397 2449 a(Since) p Fi 226 2669 a(jr) p Fm 354 2669 a(\() p Fl(y) p Fi 465 2669 a(\001) p Fm 515 2669 a(\() p Fl(!) p Fi 639 2669 a(\000) p Fl 739 2669 a(!) p Ff 800 2684 a(\000) p Fm 859 2669 a(\)\)) p Fi 934 2669 a(j) p Fm 990 2669 a(=) p Fi 1093 2669 a(j) p Fl(!) p Fi 1207 2669 a(\000) p Fl 1307 2669 a(!) p Ff 1368 2684 a(\000) p Fi 1427 2669 a(j) p Fl 1482 2669 a(>) p 1586 2669 a(h) p Fj 1642 2628 a(1) p Ff(\000) p Fg(") p Fl 1769 2669 a(;) p Fi 1910 2669 a(jr) p Fm(\() p Fi(j) p Fl(y) p Fi 2139 2669 a(j) p 2187 2669 a(\000) p Fl 2287 2669 a(y) p Fi 2360 2669 a(\001) p Fl 2410 2669 a(!) p Fm 2475 2669 a(\)) p Fi(j) p Fm 2568 2669 a(=) p Fi 2671 2669 a(j) p Fm 2706 2669 a(^) p Fl 2699 2669 a(y) p Fi 2772 2669 a(\000) p Fl 2872 2669 a(!) p Fi 2937 2669 a(j) p Fl 2991 2669 a(>) p 3095 2669 a(c) p 3165 2669 a(>) p Fm 3268 2669 a(0) 0 2889 y(o) m(v) m(er) p 217 2889 a(supp) p Fl 435 2889 a(v) p Fj 482 2904 a(+) p Fl 541 2889 a(w) p Ff 614 2853 a(\000) p 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a(\() p Fl(!) p Fm 753 4032 a(\)) p 818 4032 a(=) p Fh 921 3914 a(Z) p 1021 3914 a(Z) p Fm 1121 4032 a(\(\() o(1) p Fi 1267 4032 a(\000) p Fl 1367 4032 a(\037) p Fg 1428 4047 a(h) p Fm 1473 4032 a(\() p Fi(j) p Fl(\022) p Fi 1609 4032 a(\000) p Fl 1709 4032 a(!) p Fi 1774 4032 a(j) p Fm(\)\)) p 1899 4032 a(+) p Fl 1997 4032 a(\037) p Fg 2058 4047 a(h) p Fm 2102 4032 a(\() p Fi(j) p Fl(\022) p Fi 2238 4032 a(\000) p Fl 2338 4032 a(!) p Fi 2403 4032 a(j) p Fm(\)\)) p Fi 2522 4032 a(\001) p 2567 4032 a(\001) p 2612 4032 a(\001) p Fl 2672 4032 a(d) p Fi(j) p Fl(y) p Fi 2803 4032 a(j) p Fl 2848 4032 a(d\022) s(;) p Fm 0 4293 a(where) p Fl 289 4293 a(\037) p Fg 350 4308 a(h) p Fm 395 4293 a(\() p Fi(j) p Fl(\022) p Fi 509 4293 a(j) p Fm(\)) p 614 4293 a(=) p Fl 730 4293 a(\037) p Fm(\() p Fl(h) p Ff 885 4257 a(\000) p Fj(\(1) p Ff(\000) p Fg(") p Fj(\)) p Fi 1122 4293 a(j) p Fl(\022) p Fi 1198 4293 a(j) p Fm(\).) p 1355 4293 a(T) p 1417 4293 a(o) p 1505 4293 a(ev) p 1594 4293 a(aluate) p 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3054 5327 a(the) p 3223 5327 a(lemmas) 0 5447 y(b) s(elo) m(w) p 276 5447 a(as) p 396 5447 a(pro) m(v) m(ed.) 1723 5753 y(29) p 90 rotate dyy eop %%Page: 30 30 30 29 bop Fn 0 407 a(Lemma) p 397 407 a(6.2) p Fb 589 407 a(We) p 766 407 a(have) p Fm 909 622 a(\000) p Fj 970 637 a(in+) p Fm 1116 622 a(=) p Fi 1219 622 a(\000) p Fh 1313 505 a(Z) p Fl 1413 622 a(z) p Fj 1458 637 a(+) p Fm 1517 622 a(\() p Fl(x) p Fj 1610 637 a(1) p Fm 1650 622 a(\)) p Fl(v) p Fj 1735 637 a(+) p Fm 1794 622 a(\() p Fl(x) p Fj 1887 637 a(1) p Fm 1927 622 a(\)) p Fl 1982 622 a(dx) p Fj 2088 637 a(1) p Fm 2149 622 a(+) p Fl 2247 622 a(O) p Fm 2325 622 a(\() p Fl(h) p Fg 2419 581 a(N) p Fm 2486 622 a(\)) 909 839 y(\000) p Fj 970 854 a(in) p Ff(\000) p Fm 1116 839 a(=) p Fi 1219 839 a(\000) p Fl(e) p Ff 1341 798 a(\000) p Fg(i) p Fj(2) p Fg(\014) s(\031) p Fh 1563 722 a(Z) p Fl 1662 839 a(z) p Ff 1707 854 a(\000) p Fm 1767 839 a(\() p Fl(x) p Fj 1860 854 a(1) p Fm 1899 839 a(\)) p Fl(v) p Fj 1984 854 a(+) p Fm 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a(of) p 368 407 a(L) p 424 407 a(emma) p 709 407 a(6.2.) p Fm 966 407 a(W) p 1058 407 a(e) p 1130 407 a(consider) p 1505 407 a(only) p 1715 407 a(the) p 1879 407 a(b) s(eha) m(vior) p 2273 407 a(of) p 2379 407 a(\000) p Fj 2440 422 a(in+) p Fm 2586 407 a(in) p 2696 407 a(some) p 2936 407 a(details.) p 3282 407 a(Recall) 0 527 y(that) p Fl 211 527 a(!) p Fm 307 527 a(is) p 405 527 a(represen) m(ted) p 922 527 a(as) p 1041 527 a(\(6.1\),) p 1301 527 a(and) p Fl 1490 527 a(\022) p Fm 1570 527 a(ranges) p 1874 527 a(o) m(v) m(er) p 2082 527 a([) p Fi(\000) p Fm(2) p Fl(h) p Fj 2291 491 a(1) p Ff(\000) p Fg(") p Fl 2418 527 a(;) p Fm 2462 527 a(2) p Fl(h) p Fj 2567 491 a(1) p Ff(\000) p Fg(") p Fm 2694 527 a(].) p 2791 527 a(If) p Fl 2888 527 a(y) p Fi 2967 527 a(2) p Fm 3061 527 a(supp) p Fl 3279 527 a(v) p Fj 3326 542 a(+) p Fl 3385 527 a(w) p Ff 3458 491 a(\000) p Fm 3516 527 a(,) 0 648 y(then) p Fl 831 768 a(\033) p Fm 890 768 a(\() p Fl(y) p Fm 980 768 a(;) p Fl 1024 768 a(!) p Fm 1089 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s(ordinates) p 515 2177 a(\(6.1\)) p 744 2177 a(and) p 930 2177 a(\(6.2\).) p 1200 2177 a(W) p 1292 2177 a(e) p 1365 2177 a(insert) p 1633 2177 a(this) p 1819 2177 a(relation) p 2174 2177 a(in) m(to) p 2368 2177 a(the) p 2532 2177 a(term) p 2762 2177 a(\000) p Fj 2823 2192 a(0) p Fm 2891 2177 a(in) p 3002 2177 a(question) p 3386 2177 a(and) 0 2298 y(represen) m(t) p 421 2298 a(it) p 518 2298 a(in) p 632 2298 a(the) p 800 2298 a(in) m(tegral) p 1155 2298 a(form.) p 1423 2298 a(Then) p 1678 2298 a(w) m(e) p 1821 2298 a(ha) m(v) m(e) 117 2535 y(\000) p Fj 178 2550 a(0) p Fm 245 2535 a(=) p 348 2535 a(\(2) p Fl(\031) p Fm 494 2535 a(\)) p Ff 532 2494 a(\000) p Fj(1) p Fl 626 2535 a(E) p Fj 704 2494 a(1) p Fg(=) p Fj(2) p Fl 814 2535 a(e) p Ff 859 2494 a(\000) p Fg(i\014) p Fj 981 2494 a(\() p Fg(\031) p Ff 1051 2494 a(\000) p Fg(\015) p Fe 1142 2503 a(\000) p Fj 1195 2494 a(\)) p Fl 1227 2535 a(h) p Ff 1283 2494 a(\000) p Fg(") p Fh 1391 2418 a(Z) p 1491 2418 a(Z) 1590 2414 y(\024) 1634 2418 y(Z) p 1734 2418 a(Z) p Fm 1834 2535 a(exp) q(\() p Fl(ih) p Ff 2110 2494 a(\000) p Fg(") p Fl 2202 2535 a(f) p Fm 2261 2535 a(\)) p Fl(a) p 2367 2535 a(d\022) p 2481 2535 a(dy) p Fj 2580 2550 a(1) p Fh 2619 2414 a(\025) p Fl 2680 2535 a(g) p 2746 2535 a(dy) p Fj 2845 2550 a(2) p Fl 2884 2535 a(dx) p Fm 3012 2535 a(+) p Fl 3110 2535 a(o) p Fm(\() p Fl(h) p Fj 3251 2494 a(3) p Fg(=) p Fj(2) p Fm 3361 2535 a(\)) p Fl(;) p Fm 0 2790 a(where) p Fl 282 2790 a(f) p Fm 368 2790 a(=) p Fl 472 2790 a(E) p Fj 550 2754 a(1) p Fg(=) p Fj(2) p Fm 660 2790 a(\() p Fl(y) p Fj 746 2805 a(1) p Fi 807 2790 a(\000) p Fl 907 2790 a(x) p Fj 962 2805 a(1) p Fm 1001 2790 a(\)) p Fl(\022) p Fm 1120 2790 a(and) p Fl 505 2996 a(a) p Fm 584 2996 a(=) p 687 2996 a(exp) q(\() p Fl(i\014) p 968 2996 a(h) p Fj 1024 2955 a(1) p Ff(\000) p Fg(") p Fl 1151 2996 a(\022) p Fm 1199 2996 a(\)) p Fl(\037) p Fm(\() p Fi(j) p Fl(\022) p Fi 1412 2996 a(j) p Fm(\)) p Fl(v) p Fj 1525 3011 a(+) p Fm 1584 2996 a(\() p Fl(y) p Fj 1670 3011 a(1) p Fm 1709 2996 a(\)) p Fl(b) p Fm(\() p Fi(j) p Fl(x) p Fi(j) p Fl(;) p 1981 2996 a(\034) p Fm 2034 2996 a(;) p Fl 2078 2996 a(h) p Fm(\)) p 2189 2996 a(exp) q(\() p Fl(ir) p Fm 2456 2996 a(\() p Fl(y) t(=h;) p 2695 2996 a(x=h;) p 2899 2996 a(h) p Fj 2955 2955 a(1) p Ff(\000) p Fg(") p Fl 3080 2996 a(\022) p Fm 3128 2996 a(\)\)) p Fl 505 3142 a(r) p Fm 579 3142 a(=) p Fl 683 3142 a(E) p Fj 761 3100 a(1) p Fg(=) p Fj(2) p Fm 887 3142 a(\(\() p Fl(y) p Fj 1011 3157 a(1) p Fi 1072 3142 a(\000) p Fl 1172 3142 a(x) p Fj 1227 3157 a(1) p Fm 1267 3142 a(\)\(sin) p Fl 1479 3142 a(\022) p Fi 1549 3142 a(\000) p Fl 1649 3142 a(\022) p Fm 1697 3142 a(\)) p 1757 3142 a(+) p 1855 3142 a(\() p Fl(y) p Fj 1941 3157 a(2) p Fi 2002 3142 a(\000) p Fl 2102 3142 a(x) p Fj 2157 3157 a(2) p Fm 2197 3142 a(\)\(1) p Fi 2344 3142 a(\000) p Fm 2443 3142 a(cos) p Fl 2591 3142 a(\022) p Fm 2639 3142 a(\)\)) p Fl 505 3299 a(g) p Fm 583 3299 a(=) p Fl 686 3299 a(w) p Ff 759 3258 a(\000) p Fm 818 3299 a(\() p Fl(y) p Fj 904 3314 a(2) p Fm 943 3299 a(\)) p 998 3299 a(\() p Fl 1035 3299 a(@) p Fj 1086 3314 a(2) p Fl 1126 3299 a(w) p Fm 1199 3299 a(\)) p 1253 3299 a(\() p Fl(y) p Fj 1339 3314 a(2) p Fm 1378 3299 a(\)) p Fh 1433 3203 a(\020) p Fl 1482 3299 a(e) p Ff 1527 3258 a(\000) p Fg(i\014) s(\015) p Fj 1689 3258 a(\() p Fg(x) p Fj(;) s(^) p Fg 1776 3258 a(e) p Fj(\)) p Fl 1841 3299 a(z) p Fj 1886 3314 a(0) p Fm 1925 3299 a(\() p Fl(x) p Fj 2018 3314 a(1) p Fm 2058 3299 a(\)) p Fl(w) p Fj 2169 3258 a(+) p Fm 2228 3299 a(\() p Fl(x) p Fj 2321 3314 a(2) p Fm 2360 3299 a(\)) p 2415 3299 a(\() p Fl(@) p Fj 2504 3314 a(2) p Fl 2544 3299 a(w) p Fm 2617 3299 a(\)) p 2671 3299 a(\() p Fl(x) p Fj 2764 3314 a(2) p Fm 2804 3299 a(\)) p Fh 2842 3203 a(\021) p Fl 2908 3299 a(:) p Fm 0 3529 a(The) p 201 3529 a(remainder) p 661 3529 a(estimate) p Fl 1052 3529 a(o) p Fm(\() p Fl(h) p Fj 1193 3493 a(3) p Fg(=) p Fj(2) p Fm 1303 3529 a(\)) p 1373 3529 a(ab) s(o) m(v) m(e) p 1650 3529 a(comes) p 1938 3529 a(from) p 2168 3529 a(the) p 2336 3529 a(estimate) p Fl 641 3765 a(O) p Fm 719 3765 a(\() p Fl(h) p Ff 813 3724 a(\000) p Fg(") p Fm 904 3765 a(\)) p Fl(O) p Fm 1020 3765 a(\() p Fl(h) p Fj 1114 3724 a(1) p Ff(\000) p Fj(4) p Fg(") p Fm 1275 3765 a(\)) p Fi 1335 3765 a(\002) p Fh 1435 3648 a(Z) p Fl 1535 3765 a(z) p Fj 1580 3780 a(0) p Fm 1619 3765 a(\() p Fl(x) p Fj 1712 3780 a(1) p Fm 1752 3765 a(\)) p Fl 1807 3765 a(dx) p Fj 1913 3780 a(1) p Fm 1980 3765 a(=) p Fl 2084 3765 a(O) p Fm 2162 3765 a(\() p Fl(h) p Fj 2256 3724 a(2) p Ff(\000) p Fj(6) p Fg(") p Fm 2417 3765 a(\)) p 2483 3765 a(=) p Fl 2586 3765 a(o) p Fm(\() p Fl(h) p Fj 2727 3724 a(3) p Fg(=) p Fj(2) p Fm 2837 3765 a(\)) p Fl(:) p Fm 0 4001 a(If) p 98 4001 a(w) m(e) p 241 4001 a(tak) m(e) p 452 4001 a(accoun) m(t) p 813 4001 a(of) p 924 4001 a(the) p 1092 4001 a(prop) s(ert) m(y) p 1490 4001 a(of) p Fl 1601 4001 a(b) p Fm(\() p Fi(j) p Fl(x) p Fi(j) p Fl(;) p 1835 4001 a(\034) p Fm 1888 4001 a(;) p Fl 1932 4001 a(h) p Fm(\)) p 2059 4001 a(in) p 2173 4001 a(Prop) s(osition) p 2698 4001 a(5.2,) p 2882 4001 a(then) p 3104 4001 a(w) m(e) p 3248 4001 a(obtain) 219 4237 y(\000) p Fj 280 4252 a(0) p Fm 347 4237 a(=) p Fl 451 4237 a(e) p Ff 496 4196 a(\000) p Fg(i\014) p Fj 618 4196 a(\() p Fg(\031) p Ff 688 4196 a(\000) p Fg(\015) p Fe 779 4205 a(\000) p Fj 832 4196 a(\)) p Fh 880 4120 a(Z) p Fl 979 4237 a(e) p Ff 1024 4196 a(\000) p Fg(i\014) s(\015) p Fj 1186 4196 a(\() p Fg(x) p Fj(;) s(^) p Fg 1273 4196 a(e) p Fj(\)) p Fl 1338 4237 a(b) p Fm(\() p Fi(j) p Fl(x) p Fi(j) p Fl(;) p 1572 4237 a(\034) p Fj 1614 4252 a(0) p Fm 1654 4237 a(;) p Fl 1698 4237 a(h) p Fm(\)) p Fl(z) p Fj 1837 4252 a(0) p Fm 1876 4237 a(\() p Fl(x) p Fj 1969 4252 a(1) p Fm 2009 4237 a(\)) p Fl(w) p Fj 2120 4196 a(+) p Fm 2178 4237 a(\() p Fl(x) p Fj 2271 4252 a(2) p Fm 2311 4237 a(\)) p 2366 4237 a(\() p Fl(@) p Fj 2455 4252 a(2) p Fl 2495 4237 a(w) p Fm 2568 4237 a(\)) p 2622 4237 a(\() p Fl(x) p Fj 2715 4252 a(2) p Fm 2754 4237 a(\)) p Fl 2809 4237 a(dx) p Fm 2937 4237 a(+) p Fl 3035 4237 a(o) p Fm(\() p Fl(h) p Fj 3176 4196 a(3) p Fg(=) p Fj(2) p Fm 3286 4237 a(\)) 0 4473 y(b) m(y) p 128 4473 a(the) p 289 4473 a(stationary) p 745 4473 a(phase) p 1010 4473 a(metho) s(d,) p 1386 4473 a(where) p Fl 1660 4473 a(\034) p Fj 1702 4488 a(0) p Fm 1770 4473 a(=) p Fl 1873 4473 a(\034) p Fm 1926 4473 a(\() p Fl(x;) p 2063 4473 a(!) p Ff 2124 4488 a(\000) p Fm 2184 4473 a(\)) p 2249 4473 a(=) p Fl 2353 4473 a(\027) p Fm 2407 4473 a(.) p 2475 4473 a(By) p 2621 4473 a(Prop) s(osition) p 3139 4473 a(5.2) p 3289 4473 a(again,) 0 4594 y(w) m(e) p 144 4594 a(ha) m(v) m(e) p Fl 822 4714 a(') p Fm(\() p Fl(x=h) p Fm(;) p Fl 1128 4714 a(!) p Ff 1189 4729 a(\000) p Fm 1248 4714 a(\)) p 1313 4714 a(=) p Fl 1417 4714 a(b) p Fm(\() p Fi(j) p Fl(x) p Fi(j) p Fl(;) p 1651 4714 a(\034) p Fj 1693 4729 a(0) p Fm 1733 4714 a(;) p Fl 1777 4714 a(h) p Fm(\)) p Fl(') p Ff 1935 4729 a(\000) p Fm 1993 4714 a(\() p Fl(x=h) p Fm(\)) p 2252 4714 a(+) p Fl 2350 4714 a(O) p Fm 2428 4714 a(\() p Fl(h) p Fj 2522 4673 a(1) p Ff(\000) p Fj(4) p Fg(") p Fm 2683 4714 a(\)) 0 4883 y(for) p Fl 154 4883 a(x) p Fi 247 4883 a(2) p Fm 350 4883 a(supp) p Fl 568 4883 a(z) p Fj 613 4898 a(+) p Fl 672 4883 a(w) p Fj 745 4846 a(+) p Fm 804 4883 a(,) p 870 4883 a(and) p 1065 4883 a(hence) p Fl 1341 4883 a(b) p Fm(\() p Fi(j) p Fl(x) p Fi(j) p Fl(;) p 1575 4883 a(\034) p Fj 1617 4898 a(0) p Fm 1657 4883 a(;) p Fl 1701 4883 a(h) p Fm(\)) p 1832 4883 a(=) p Fl 1945 4883 a(') p Fm(\() p Fl(x=h) p Fm(;) p Fl 2251 4883 a(!) p Ff 2312 4898 a(\000) p Fm 2370 4883 a(\)) p 2408 4830 64 4 v Fl(') p Ff 2472 4906 a(\000) p Fm 2531 4883 a(\() p Fl(x=h) p Fm(\)) p 2793 4883 a(+) p Fl 2895 4883 a(O) p Fm 2973 4883 a(\() p Fl(h) p Fj 3067 4846 a(1) p Ff(\000) p Fj(4) p Fg(") p Fm 3228 4883 a(\).) p 3353 4883 a(This) 0 5003 y(pro) m(v) m(es) p 301 5003 a(the) p 469 5003 a(lemma.) p Fa 919 5003 a(2) p Fb 0 5169 a(Pr) p 102 5169 a(o) p 147 5169 a(of) p 262 5169 a(of) p 376 5169 a(L) p 432 5169 a(emma) p 721 5169 a(6.5.) p Fm 978 5169 a(W) p 1070 5169 a(e) p 1146 5169 a(w) m(ork) p 1385 5169 a(in) p 1498 5169 a(the) p 1666 5169 a(co) s(ordinate) p 2146 5169 a(system) p 2470 5169 a(\(6.2\).) p 2741 5169 a(Then) p 2995 5169 a(w) m(e) p 3139 5169 a(ha) m(v) m(e) p Fl 684 5438 a(\033) p Fm 771 5438 a(=) p Fl 874 5438 a(\033) p Fm 933 5438 a(\() p Fl(x) p Fm(;) p Fl 1070 5438 a(!) p Ff 1131 5453 a(\000) p Fm 1190 5438 a(\)) p 1256 5438 a(=) p Fl 1359 5438 a(\015) p Fm 1415 5438 a(\() p Fl(x) p Fm(;) p Fl 1552 5438 a(!) p Ff 1613 5453 a(\000) p Fm 1672 5438 a(\)) p Fi 1732 5438 a(\000) p Fl 1832 5438 a(\031) p Fm 1919 5438 a(=) p Fh 2022 5291 a(\() p Fl 2130 5377 a(\027) p Fi 2207 5377 a(\000) p Fl 2307 5377 a(\031) t(;) p 2573 5377 a(\027) p 2655 5377 a(>) p Fm 2759 5377 a(0) p Fl 2131 5497 a(\027) p Fm 2208 5497 a(+) p Fl 2306 5497 a(\031) t(;) p 2573 5497 a(\027) p 2655 5497 a(<) p Fm 2759 5497 a(0) 3343 5438 y(\(6.3\)) 1723 5753 y(32) p 90 rotate dyy eop %%Page: 33 33 33 32 bop Fm 0 407 a(and) p 197 407 a(hence) p Fl 475 407 a(e) p Fg 520 371 a(i\033) p Fm 630 407 a(=) p Fi 746 407 a(\000) p Fl(e) p Fg 868 371 a(i\027) p Fm 936 407 a(.) p 1027 407 a(W) p 1119 407 a(e) p 1202 407 a(also) p 1405 407 a(ha) m(v) m(e) p Fl 1637 407 a(\015) p Fm 1693 407 a(\() p Fl(x) p Fm(;) p 1834 407 a(^) p Fl 1830 407 a(e) p Fm(\)) p 1953 407 a(=) p Fl 2068 407 a(\027) p Fm 2150 407 a(+) p Fl 2252 407 a(\015) p Ff 2303 422 a(\000) p Fm 2402 407 a(with) p Fl 2631 407 a(\015) p Ff 2682 422 a(\000) p Fm 2780 407 a(=) p Fl 2896 407 a(\015) p Fm 2952 407 a(\() p Fl(!) p Ff 3051 422 a(\000) p Fm 3109 407 a(;) p 3157 407 a(^) p Fl 3153 407 a(e) p Fm(\).) p 3328 407 a(If) p 3432 407 a(w) m(e) 0 527 y(insert) p 272 527 a(the) p 440 527 a(represen) m(tation) p 1077 527 a(\(5.7\)) p 1310 527 a(for) p Fl 1459 527 a(') p Fj 1523 542 a(sc) p Fm 1586 527 a(\() p Fl(x=h) p Fm(;) p Fl 1828 527 a(!) p Ff 1889 542 a(\000) p Fm 1948 527 a(\),) p 2045 527 a(then) p 2268 527 a(\000) p Fj 2329 542 a(sc) p Fm 2425 527 a(tak) m(es) p 2674 527 a(the) p 2842 527 a(form) 541 769 y(\000) p Fj 602 784 a(sc) p Fm 693 769 a(=) p 796 769 a(\(sin) p Fl 971 769 a(\014) p 1032 769 a(\031) t(=\031) p Fm 1199 769 a(\)) p Fl(e) p Ff 1282 728 a(\000) p Fg(i\014) s(\031) p Fh 1467 652 a(Z) p Ff 1550 678 a(1) p Fj 1513 841 a(0) p Fh 1641 648 a(\024) 1685 652 y(Z) p 1784 652 a(Z) p Fm 1884 769 a(exp) q(\() p Fl(ih) p Ff 2160 728 a(\000) p Fj(1) p Fl 2255 769 a(f) p Fm 2314 769 a(\)) p Fl(g) p 2418 769 a(d\027) p 2540 769 a(dt) p Fh 2626 648 a(\025) p Fi 2686 769 a(j) p Fl(x) p Fi(j) p Fl 2814 769 a(d) p Fi(j) p Fl(x) p Fi(j) p Fl(;) p Fm 0 1023 a(where) p Fl 282 1023 a(f) p Fm 368 1023 a(=) p Fl 472 1023 a(E) p Fj 550 986 a(1) p Fg(=) p Fj(2) p Fi 660 1023 a(j) p Fl(x) p Fi(j) p Fm(\() p Fl(t) p Fj 844 986 a(2) p Fm 905 1023 a(+) p Fl 1003 1023 a(\027) p Fj 1057 986 a(2) p Fm 1097 1023 a(\)) p Fl(=) p Fm(2) p 1265 1023 a(and) p Fl 603 1256 a(g) p Fm 681 1256 a(=) p Fl 784 1256 a(e) p Fg 829 1215 a(i\027) p Fl 897 1256 a(e) p Ff 942 1215 a(\000) p Fg(\014) p Fj 1040 1215 a(\() p Fg(t) p Fj(+) p Fg(i\027) p Fj 1210 1215 a(\)) p Fh 1259 1160 a(\020) p Fl 1308 1256 a(e) p Ff 1353 1215 a(\000) p Fg(t) p Fi 1460 1256 a(\000) p Fl 1560 1256 a(e) p Fg 1605 1215 a(i\027) p Fh 1672 1160 a(\021) p Ff 1722 1183 a(\000) p Fj(1) p Fm 1837 1256 a(~) p Fl 1833 1256 a(v) p Fj 1880 1271 a(+) p Fl 1939 1256 a(w) p Fj 2012 1215 a(+) p Fm 2087 1256 a(\() p Fl(@) p Fj 2176 1271 a(2) p Fl 2216 1256 a(w) p Fm 2289 1256 a(\)) p 2343 1256 a(exp) q(\() p Fl(ih) p Ff 2619 1215 a(\000) p Fj(1) p Fl 2714 1256 a(r) p Fm 2761 1256 a(\() p Fl(x;) p 2898 1256 a(t;) p 2977 1256 a(\027) p Fm 3031 1256 a(\)\)) p Fl 603 1439 a(r) p Fm 677 1439 a(=) p Fl 781 1439 a(E) p Fj 859 1398 a(1) p Fg(=) p Fj(2) p Fi 969 1439 a(j) p Fl(x) p Fi(j) p Fh 1097 1343 a(\020) p Fm 1146 1439 a(\(cosh) p Fl 1385 1439 a(t) p Fi 1442 1439 a(\000) p Fm 1542 1439 a(1) p Fi 1613 1439 a(\000) p Fl 1712 1439 a(t) p Fj 1747 1398 a(2) p Fl 1787 1439 a(=) p Fm(2\)) p Fi 1945 1439 a(\000) p Fm 2044 1439 a(\(cos) p Fl 2230 1439 a(\027) p Fi 2306 1439 a(\000) p Fm 2406 1439 a(1) p 2477 1439 a(+) p Fl 2575 1439 a(\027) p Fj 2629 1398 a(2) p Fl 2669 1439 a(=) p Fm(2\)) p Fh 2805 1343 a(\021) p Fl 2870 1439 a(:) p Fm 0 1656 a(W) p 92 1656 a(e) p 168 1656 a(denote) p 482 1656 a(b) m(y) p Fl 617 1656 a(I) p Fj 660 1671 a(sc) p Fm 723 1656 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p 942 1656 a(the) p 1110 1656 a(in) m(tegral) p 1464 1656 a(in) p 1578 1656 a(the) p 1746 1656 a(brac) m(k) m(et) p 2089 1656 a(and) p 2279 1656 a(represen) m(t) p 2699 1656 a(it) p 2796 1656 a(in) p 2910 1656 a(the) p 3078 1656 a(p) s(olar) p 3329 1656 a(co) s(or-) 0 1776 y(dinates) p 337 1776 a(\() p Fl(t;) p 454 1776 a(\027) p Fm 508 1776 a(\)) p 574 1776 a(=) p 677 1776 a(\() p Fl(\032) p Fm 782 1776 a(cos) p Fl 929 1776 a(\026;) p 1032 1776 a(\032) p Fm 1099 1776 a(sin) p Fl 1235 1776 a(\026) p Fm(\).) p 1402 1776 a(If) p 1499 1776 a(w) m(e) p 1643 1776 a(write) p Fh 77 1914 a(\020) p Fl 127 2010 a(e) p Ff 172 1969 a(\000) p Fg(t) p Fi 279 2010 a(\000) p Fl 378 2010 a(e) p Fg 423 1969 a(i\027) p Fh 491 1914 a(\021) p Ff 540 1937 a(\000) p Fj(1) p Fm 662 2010 a(=) p 766 2010 a(\() p Fl(t) p Fi 861 2010 a(\000) p Fl 961 2010 a(i\027) p Fm 1048 2010 a(\)) p Ff 1086 1969 a(\000) p Fj(1) p Fh 1197 1914 a(\020) p Fm 1247 2010 a(\() p Fl(t) p Fi 1342 2010 a(\000) p Fl 1442 2010 a(i\027) p Fm 1529 2010 a(\)) p Fl(=) p Fm(\() p Fl(e) p Ff 1699 1969 a(\000) p Fg(t) p Fi 1806 2010 a(\000) p Fl 1906 2010 a(e) p Fg 1951 1969 a(i\027) p Fm 2018 2010 a(\)) p Fh 2056 1914 a(\021) p Fm 2133 2010 a(=) p Fl 2237 2010 a(\032) p Ff 2287 1969 a(\000) p Fj(1) p Fl 2382 2010 a(e) p Fg 2427 1969 a(i\026) p Fh 2514 1914 a(\020) p Fm 2564 2010 a(\() p Fl(t) p Fi 2659 2010 a(\000) p Fl 2759 2010 a(i\027) p Fm 2846 2010 a(\)) p Fl(=) p Fm(\() p Fl(e) p Ff 3016 1969 a(\000) p Fg(t) p Fi 3123 2010 a(\000) p Fl 3222 2010 a(e) p Fg 3267 1969 a(i\027) p Fm 3335 2010 a(\)) p Fh 3373 1914 a(\021) p Fl 3439 2010 a(;) p Fm 0 2227 a(then) p Fl 222 2227 a(I) p Fj 265 2242 a(sc) p Fm 329 2227 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p 548 2227 a(tak) m(es) p 798 2227 a(the) p 966 2227 a(form) p Fl 632 2478 a(I) p Fj 675 2493 a(sc) p Fm 766 2478 a(=) p Fh 869 2361 a(Z) p Fj 952 2388 a(2) p Fg(\031) p Fj 915 2550 a(0) p Fh 1051 2357 a(\024) 1095 2361 y(Z) p Ff 1178 2388 a(1) p Fj 1141 2550 a(0) p Fm 1269 2478 a(exp) q(\() p Fl(ih) p Ff 1545 2437 a(\000) p Fj(1) p Fl 1640 2478 a(E) p Fj 1718 2437 a(1) p Fg(=) p Fj(2) p Fi 1828 2478 a(j) p Fl(x) p Fi(j) p Fl(\032) p Fj 1989 2437 a(2) p Fl 2029 2478 a(=) p Fm(2\)) p Fl(a) p 2233 2478 a(d\032) p Fh 2334 2357 a(\025) p Fl 2393 2478 a(d\026) p Fm 2525 2478 a(+) p Fl 2623 2478 a(o) p Fm(\() p Fl(h) p Fj 2764 2437 a(3) p Fg(=) p Fj(2) p Fm 2874 2478 a(\)) 0 2732 y(uniformly) p 439 2732 a(in) p Fi 548 2732 a(j) p Fl(x) p Fi(j) p Fm 686 2732 a(\() p Fl(x) p Fi 807 2732 a(2) p Fm 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a(and) p 466 3297 a(that) p 680 3297 a(it) p 780 3297 a(has) p 957 3297 a(the) p 1127 3297 a(limit) p 1363 3297 a(\() p Fl(t) p Fi 1458 3297 a(\000) p Fl 1558 3297 a(i\027) p Fm 1645 3297 a(\)) p Fl(=) p Fm(\() p Fl(e) p Ff 1815 3256 a(\000) p Fg(t) p Fi 1922 3297 a(\000) p Fl 2022 3297 a(e) p Fg 2067 3256 a(i\027) p Fm 2134 3297 a(\)) p Fi 2200 3297 a(!) p 2327 3297 a(\000) p Fl(e) p Ff 2449 3256 a(\000) p Fg(i) p Fj(2) p Fg(\026) p Fm 2646 3297 a(as) p Fl 2768 3297 a(\032) p Fi 2850 3297 a(!) p Fm 2982 3297 a(0.) p 3109 3297 a(Hence) p Fl 3401 3297 a(b) p Fm 3478 3297 a(is) 0 3417 y(of) p 111 3417 a(the) p 279 3417 a(form) p Fl 509 3417 a(b) p Fm 579 3417 a(=) p Fl 682 3417 a(e) p Ff 727 3381 a(\000) p Fg(i) p Fj(2) p Fg(\026) p Fi 910 3417 a(\002) p Fm 1010 3417 a(\(smo) s(oth) p 1393 3417 a(function\)) p 1813 3417 a(and) p 2002 3417 a(is) p 2100 3417 a(expanded) p 2537 3417 a(as) p Fl 223 3694 a(b) p Fm 292 3694 a(=) p Fl 396 3694 a(e) p Ff 441 3652 a(\000) p Fg(i) p Fj(2) p Fg(\026) p Fh 618 3547 a( ) p Fl 684 3694 a(b) p Fj 725 3709 a(0) p Fm 787 3694 a(+) p Fh 885 3597 a(\020) p Fl 935 3694 a(b) p Fj 976 3709 a(+) p Fl 1035 3694 a(e) p Fg 1080 3652 a(i\026) p Fm 1173 3694 a(+) p Fl 1271 3694 a(b) p Ff 1312 3709 a(\000) p Fl 1372 3694 a(e) p Ff 1417 3652 a(\000) p Fg(i\026) p Fh 1543 3597 a(\021) p Fl 1609 3694 a(\032) p Fm 1681 3694 a(+) p Fh 1779 3547 a( ) p Fj 1892 3586 a(2) p Fh 1849 3611 a(X) p Fg 1845 3795 a(k) p Fj 1884 3795 a(=0) p Fl 1990 3694 a(b) p Fj 2031 3709 a(2) p Fg(k) p Fm 2126 3694 a(cos) p Fg 2257 3652 a(k) p Fl 2316 3694 a(\026) p Fm 2392 3694 a(sin) p Fj 2511 3652 a(2) p Ff(\000) p Fg(k) p Fl 2661 3694 a(\026) p Fh 2720 3547 a(!) p Fl 2802 3694 a(\032) p Fj 2852 3652 a(2) p Fm 2914 3694 a(+) p Fl 3012 3694 a(O) p Fm 3090 3694 a(\() p Fl(\032) p Fj 3178 3652 a(3) p Fm 3217 3694 a(\)) p Fh 3255 3547 a(!) p Fm 0 3965 a(in) p 119 3965 a(a) p 205 3965 a(neigh) m(b) s(orho) s(o) s(d) p 822 3965 a(of) p Fl 937 3965 a(\032) p Fm 1024 3965 a(=) p 1135 3965 a(0) p 1221 3965 a(b) m(y) p 1361 3965 a(the) p 1534 3965 a(T) p 1596 3965 a(a) m(ylor) p 1845 3965 a(series,) p 2139 3965 a(where) p 2426 3965 a(all) p 2566 3965 a(the) p 2739 3965 a(co) s(e\016cien) m(ts) p 3237 3965 a(dep) s(end) 0 4086 y(on) p Fi 137 4086 a(j) p Fl(x) p Fi(j) p Fm 282 4086 a(only) p 455 4086 a(.) p 531 4086 a(If) p 630 4086 a(w) m(e) p 775 4086 a(apply) p 1045 4086 a(the) p 1214 4086 a(stationary) p 1680 4086 a(phase) p 1953 4086 a(metho) s(d) p 2310 4086 a(to) p 2431 4086 a(the) p 2600 4086 a(in) m(tegral) p 2957 4086 a(in) p Fl 3072 4086 a(\032) p Fm(,) p 3184 4086 a(then) p 3408 4086 a(the) 0 4206 y(stationary) p 462 4206 a(p) s(oin) m(t) p Fl 716 4206 a(\032) p Fm 794 4206 a(=) p 897 4206 a(0) p 977 4206 a(is) p 1074 4206 a(the) p 1240 4206 a(endp) s(oin) m(t) p 1645 4206 a(of) p 1755 4206 a(the) p 1921 4206 a(in) m(tegral.) p 2313 4206 a(Th) m(us) p 2559 4206 a(w) m(e) p 2701 4206 a(ha) m(v) m(e) p 2925 4206 a(to) p 3042 4206 a(tak) m(e) p 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Fj(3) p Fg(") p Fm 2843 4531 a(\)) 0 4759 y(for) p Fi 149 4759 a(j) p Fl(\032) p Fi(j) p Fl 282 4759 a(<) p Fm 386 4759 a(2) p Fl(h) p Fj 491 4723 a(\(1) p Ff(\000) p Fg(") p Fj(\)) p Fg(=) p Fj(2) p Fm 743 4759 a(.) p 814 4759 a(All) p 974 4759 a(the) p 1142 4759 a(in) m(tegrals) p 1535 4759 a(b) s(elo) m(w) p Fh 9 4877 a(Z) p Fl 108 4994 a(e) p Ff 153 4953 a(\000) p Fg(i\026) p Fl 296 4994 a(d\026;) p Fh 477 4877 a(Z) p Fl 576 4994 a(b) p Ff 617 5009 a(\000) p Fl 677 4994 a(e) p Ff 722 4953 a(\000) p Fg(i) p Fj(2) p Fg(\026) p Fl 899 4994 a(d\026;) p Fh 1080 4877 a(Z) p Fl 1180 4994 a(e) p Ff 1225 4953 a(\000) p Fg(i\026) p Fm 1367 4994 a(cos) p Fg 1498 4953 a(k) p Fl 1557 4994 a(\026) p Fm 1633 4994 a(sin) p Fj 1752 4953 a(2) p Ff(\000) p Fg(k) p Fl 1901 4994 a(\026) p 1977 4994 a(d\026;) p Fh 2157 4877 a(Z) p Fl 2257 4994 a(e) p Ff 2302 4953 a(\000) p Fg(i\026) p Fm 2444 4994 a(cos) p Fj 2575 4953 a(4) p Fl 2631 4994 a(\026) p 2707 4994 a(d\026;) p Fh 2887 4877 a(Z) p Fl 2987 4994 a(e) p Ff 3032 4953 a(\000) p Fg(i\026) p Fm 3174 4994 a(sin) p Fj 3294 4953 a(4) p Fl 3350 4994 a(\026) p 3426 4994 a(d\026) p Fm 0 5229 a(o) m(v) m(er) p 209 5229 a(the) p 377 5229 a(in) m(terv) p 620 5229 a(al) p 729 5229 a(\(0) p Fl(;) p Fm 860 5229 a(2) p Fl(\031) p Fm 968 5229 a(\)) p 1037 5229 a(v) p 1083 5229 a(anish.) p 1377 5229 a(On) p 1539 5229 a(the) p 1707 5229 a(other) p 1962 5229 a(hand,) p 2233 5229 a(the) p 2401 5229 a(in) m(tegral) p Fh 927 5349 a(Z) p Ff 1010 5375 a(1) p Fj 973 5537 a(0) p Fl 1101 5466 a(O) p Fm 1179 5466 a(\() p Fl(\032) p Fj 1267 5425 a(3) p Fm 1306 5466 a(\)) p Fl(\037) p Fg 1405 5481 a(h) p Fm 1450 5466 a(\() p Fl(\032) p Fm(\)) p Fl 1593 5466 a(d\032) p Fm 1721 5466 a(=) p Fl 1825 5466 a(O) p Fm 1903 5466 a(\() p Fl(h) p Fj 1997 5425 a(2) p Ff(\000) p Fj(2) p Fg(") p Fm 2158 5466 a(\)) p 2224 5466 a(=) p Fl 2328 5466 a(o) p Fm(\() p Fl(h) p Fj 2469 5425 a(3) p Fg(=) p Fj(2) p Fm 2579 5466 a(\)) 1723 5753 y(33) p 90 rotate dyy eop %%Page: 34 34 34 33 bop Fm 0 407 a(can) p 175 407 a(b) s(e) p 303 407 a(dealt) p 543 407 a(with) p 761 407 a(as) p 877 407 a(a) p 954 407 a(remainder) p 1411 407 a(term.) p 1681 407 a(Th) m(us) p 1924 407 a(the) p 2088 407 a(in) m(tegral) p 2438 407 a(asso) s(ciated) p 2899 407 a(with) p Fl 3117 407 a(b) p Fj 3158 422 a(+) p Fl 3217 407 a(e) p Fg 3262 371 a(i\026) p Fm 3362 407 a(only) 0 527 y(mak) m(es) p 296 527 a(a) p 380 527 a(con) m(tribution) p 938 527 a(to) p 1060 527 a(the) p 1231 527 a(leading) p 1570 527 a(term.) p 1849 527 a(W) p 1941 527 a(e) p 2020 527 a(no) m(w) p 2226 527 a(calculate) p 2635 527 a(the) p 2806 527 a(term) p Fl 3042 527 a(b) p Fj 3083 542 a(+) p Fm 3142 527 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\).) p 3408 527 a(W) p 3500 527 a(e) 0 648 y(can) p 179 648 a(expand) p 521 648 a(~) p Fl 518 648 a(v) p Fj 565 663 a(+) p Fl 624 648 a(;) p 700 648 a(w) p Fj 773 611 a(+) p Fm 864 648 a(and) p Fl 1054 648 a(@) p Fj 1105 663 a(2) p Fl 1145 648 a(w) p Fm 1249 648 a(as) p 1369 648 a(follo) m(ws) p 1690 648 a(:) p 1764 648 a(~) p Fl 1760 648 a(v) p Fj 1807 663 a(+) p Fm 1866 648 a(\() p Fl(x) p Fj 1959 663 a(1) p Fm 1999 648 a(\)) p 2065 648 a(=) p 2172 648 a(~) p Fl 2168 648 a(v) p Fj 2215 663 a(+) p Fm 2274 648 a(\() p Fi(\000j) p Fl(x) p Fi(j) p Fm 2517 648 a(sin) p Fl 2654 648 a(\027) p Fm 2708 648 a(\)) p 2774 648 a(=) p 2877 648 a(1) p 2948 648 a(+) p Fl 3046 648 a(O) p Fm 3124 648 a(\() p Fl(\032) p Fj 3212 611 a(2) p Fm 3251 648 a(\),) p Fl 131 845 a(w) p Fj 204 804 a(+) p Fm 263 845 a(\() p Fl(x) p Fj 356 860 a(2) p Fm 396 845 a(\)) p 461 845 a(=) p Fl 565 845 a(w) p Fj 638 804 a(+) p Fm 696 845 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm 862 845 a(cos) p Fl 1009 845 a(\027) p Fm 1063 845 a(\)) p 1129 845 a(=) p Fl 1232 845 a(w) p Fj 1305 804 a(+) p Fm 1364 845 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p 1573 845 a(+) p Fl 1671 845 a(O) p Fm 1749 845 a(\() p Fl(\032) p Fj 1837 804 a(2) p Fm 1876 845 a(\)) p Fl(;) p Fm 2055 845 a(\() p Fl(@) p Fj 2144 860 a(2) p Fl 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1240 a(\() p Fl(\032) p Fj 2981 1199 a(2) p Fm 3020 1240 a(\)) p Fl 652 1414 a(e) p Ff 697 1373 a(\000) p Fg(\014) p Fj 795 1373 a(\() p Fg(t) p Fj(+) p Fg(i\027) p Fj 965 1373 a(\)) p Fm 1025 1414 a(=) p 1128 1414 a(1) p Fi 1199 1414 a(\000) p Fl 1299 1414 a(\014) p Fm 1360 1414 a(\() p Fl(t) p Fm 1455 1414 a(+) p Fl 1553 1414 a(i\027) p Fm 1640 1414 a(\)) p 1701 1414 a(+) p Fl 1799 1414 a(O) p Fm 1877 1414 a(\() p Fl(\032) p Fj 1965 1373 a(2) p Fm 2004 1414 a(\)) p 2069 1414 a(=) p 2173 1414 a(1) p Fi 2244 1414 a(\000) p Fl 2343 1414 a(\014) p 2404 1414 a(e) p Fg 2449 1373 a(i\026) p Fl 2520 1414 a(\032) p Fm 2592 1414 a(+) p Fl 2690 1414 a(O) p Fm 2768 1414 a(\() p Fl(\032) p Fj 2856 1373 a(2) p Fm 2895 1414 a(\)) 0 1611 y(and) p 190 1611 a(that) 0 1809 y(\() p Fl(t) p Fi 77 1809 a(\000) p Fl 158 1809 a(i\027) p Fm 245 1809 a(\)\() p Fl(e) p Ff 366 1768 a(\000) p Fg(t) p Fi 456 1809 a(\000) p Fl 537 1809 a(e) p Fg 582 1768 a(i\027) p Fm 650 1809 a(\)) p Ff 688 1768 a(\000) p Fj(1) p 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p Fm(\)) p 1289 2204 a(=) p 1393 2204 a(\() p Fl(\014) p Fi 1514 2204 a(\000) p Fm 1613 2204 a(1) p Fl(=) p Fm(2\)) p Fl(w) p Fj 1871 2163 a(+) p Fm 1929 2204 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)\() p Fl(@) p Fj 2205 2219 a(2) p Fl 2245 2204 a(w) p Fm 2318 2204 a(\)\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p Fl(:) p Fm 0 2401 a(Hence) p 290 2401 a(the) p 458 2401 a(leading) p 794 2401 a(term) p 1027 2401 a(comes) p 1315 2401 a(from) p 1545 2401 a(the) p 1713 2401 a(in) m(tegral) 417 2631 y(2) p 483 2631 a(sin) p Fl 619 2631 a(\014) p 680 2631 a(\031) t(e) p Ff 784 2589 a(\000) p Fg(i\014) s(\031) p Fh 969 2513 a(Z) p Ff 1052 2540 a(1) p Fj 1015 2702 a(0) p Fh 1143 2509 a(\024) 1187 2513 y(Z) p Ff 1270 2540 a(1) p Fj 1233 2702 a(0) p Fm 1361 2631 a(exp) q(\() p Fl(ih) p Ff 1637 2589 a(\000) p Fj(1) p Fl 1732 2631 a(E) p Fj 1810 2589 a(1) p Fg(=) p Fj(2) p Fi 1920 2631 a(j) p Fl(x) p Fi(j) p Fl(\032) p Fj 2081 2589 a(2) p Fl 2121 2631 a(=) p Fm(2\)) p Fl(\037) p Fg 2318 2646 a(h) p Fm 2362 2631 a(\() p Fl(\032) p Fm(\)) p Fl(\032) p 2555 2631 a(d\032) p Fh 2656 2509 a(\025) p Fl 2717 2631 a(b) p Fj 2758 2646 a(+) p Fm 2817 2631 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p Fi(j) p Fl(x) p Fi(j) p Fl 3132 2631 a(d) p Fi(j) p Fl(x) p Fi(j) p Fm 612 2858 a(=) p 762 2858 a(2) p Fl(i) p Fm(\() p Fl(\014) p Fi 965 2858 a(\000) p Fm 1064 2858 a(1) p Fl(=) p Fm(2\)) p 1266 2858 a(sin) p Fl 1401 2858 a(\014) p 1462 2858 a(\031) t(E) p Ff 1599 2817 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fl 1764 2858 a(e) p Ff 1809 2817 a(\000) p Fg(i\014) s(\031) p Fl 1978 2858 a(h) p Fh 2051 2741 a(Z) p Ff 2134 2767 a(1) p Fj 2097 2929 a(0) p Fl 2225 2858 a(w) p Fj 2298 2817 a(+) p Fm 2357 2858 a(\() p Fl(@) p Fj 2446 2873 a(2) p Fl 2486 2858 a(w) p Fm 2559 2858 a(\)) p Fl 2614 2858 a(d) p Fi(j) p Fl(x) p Fi(j) p Fm 2796 2858 a(+) p Fl 2894 2858 a(o) p Fm(\() p Fl(h) p Fj 3035 2817 a(3) p Fg(=) p Fj(2) p Fm 3145 2858 a(\)) 612 3054 y(=) p Fi 762 3054 a(\000) p Fl(ik) p Fj 923 3069 a(0) p Fl 963 3054 a(e) p Ff 1008 3012 a(\000) p Fg(i\014) s(\031) p Fl 1177 3054 a(h) p Fm 1255 3054 a(+) p Fl 1353 3054 a(o) p Fm(\() p Fl(h) p Fj 1494 3012 a(3) p Fg(=) p Fj(2) p Fm 1604 3054 a(\)) p Fl(:) p Fm 0 3251 a(This) p 223 3251 a(completes) p 673 3251 a(the) p 841 3251 a(pro) s(of) p 1096 3251 a(of) p 1207 3251 a(the) p 1375 3251 a(lemma.) p Fa 1825 3251 a(2) p Fn 146 3490 a(7.) p 271 3490 a(Scattering) p 808 3490 a(b) m(y) p 964 3490 a(single) p 1277 3490 a(solenoidal) p 1794 3490 a(\014eld) p Fm 146 3697 a(The) p 347 3697 a(calculation) p 841 3697 a(of) p 953 3697 a(the) p 1121 3697 a(third) p 1365 3697 a(term) p 1599 3697 a(of) p 1710 3697 a(the) p 1879 3697 a(asymptotic) p 2381 3697 a(form) m(ula) p 2739 3697 a(relies) p 2990 3697 a(on) p 3126 3697 a(the) p 3294 3697 a(repre-) 0 3817 y(sen) m(tation) p 422 3817 a(for) p 573 3817 a(scattering) p 1024 3817 a(amplitudes) p 1525 3817 a(b) m(y) p 1662 3817 a(single) p 1935 3817 a(solenoidal) p 2387 3817 a(\014eld) p 2600 3817 a(in) p 2715 3817 a(terms) p 2988 3817 a(of) p 3101 3817 a(resolv) m(en) m(ts.) 0 3937 y(W) p 92 3937 a(e) p 168 3937 a(here) p 379 3937 a(mak) m(e) p 634 3937 a(a) p 715 3937 a(quic) m(k) p 973 3937 a(review) p 1279 3937 a(on) p 1414 3937 a(it) p 1512 3937 a(without) p 1875 3937 a(detailed) p 2244 3937 a(pro) s(of.) 146 4101 y(W) p 238 4101 a(e) p 307 4101 a(use) p 469 4101 a(the) p 630 4101 a(notation) p Fl 1014 4101 a(W) p Ff 1106 4116 a(\006) p Fm 1165 4101 a(\() p Fl(H) r(;) p 1330 4101 a(K) p Fm 1420 4101 a(\)) p 1483 4101 a(and) p Fl 1666 4101 a(S) p Fm 1732 4101 a(\() p Fl(H) r(;) p 1897 4101 a(K) p Fm 1987 4101 a(\)) p 2050 4101 a(with) p 2266 4101 a(the) p 2427 4101 a(same) p 2664 4101 a(meanings) p 3086 4101 a(ascrib) s(ed) p 3462 4101 a(in) 0 4222 y(section) p 320 4222 a(2.) p 437 4222 a(W) p 529 4222 a(e) p 599 4222 a(consider) p 974 4222 a(the) p 1136 4222 a(self{adjoin) m(t) p 1648 4222 a(op) s(erator) p Fl 2035 4222 a(H) p Fg 2116 4237 a(\013h) p Fm 2233 4222 a(de\014ned) p 2563 4222 a(b) m(y) p 2693 4222 a(\(1.3\)) p 2920 4222 a(with) p 3137 4222 a(b) s(oundary) 0 4342 y(condition) p 428 4342 a(\(1.4\).) p 699 4342 a(Let) p Fl 874 4342 a(U) p Fj 940 4357 a(1) p Fm 1012 4342 a(b) s(e) p 1145 4342 a(as) p 1265 4342 a(in) p 1378 4342 a(\(3.2\)) p 1611 4342 a(and) p 1801 4342 a(let) 1959 4317 y(~) p Fl 1942 4342 a(U) p Fj 2008 4357 a(2) p Fm 2080 4342 a(b) s(e) p 2213 4342 a(de\014ned) p 2549 4342 a(b) m(y) p Fh 997 4456 a(\020) p Fm 1063 4527 a(~) p Fl 1047 4552 a(U) p Fj 1113 4567 a(2) p Fl 1152 4552 a(f) p Fh 1211 4456 a(\021) p Fm 1277 4552 a(\() p Fl(x) p Fm(\)) p 1436 4552 a(=) p 1540 4552 a(exp) q(\() p Fl(i) p Fm([) p Fl(\013) q(=h) p Fm(]) p Fl(\015) p Fm 2038 4552 a(\() p Fl(x) p Fm(\)\)) p Fi 2229 4552 a(\002) p Fl 2329 4552 a(f) p Fm 2388 4552 a(\() p Fl(x) p Fm(\)) p Fl(;) p Fm 0 4762 a(where) p Fl 282 4762 a(\015) p Fm 338 4762 a(\() p Fl(x) p Fm(\)) p 497 4762 a(=) p Fl 600 4762 a(\015) p Fm 673 4762 a(\() p 717 4762 a(^) p Fl 711 4762 a(x) p Fm(\)) p 837 4762 a(denotes) p 1190 4762 a(the) p 1358 4762 a(azim) m(uth) p 1734 4762 a(angle) p 1989 4762 a(from) p 2219 4762 a(the) p Fl 2387 4762 a(x) p Fj 2442 4777 a(1) p Fm 2515 4762 a(axis.) p 2751 4762 a(Then) p 3006 4762 a(w) m(e) p 3149 4762 a(obtain) p Fl 638 4976 a(K) p Fg 721 4991 a(\014) p Fm 796 4976 a(:=) p Fh 926 4880 a(\020) p Fl 976 4976 a(U) p Fj 1042 4991 a(1) p Fm 1098 4951 a(~) p Fl 1082 4976 a(U) p Fj 1148 4991 a(2) p Fh 1187 4880 a(\021) p Ff 1237 4903 a(\003) p Fl 1293 4976 a(H) p Fg 1374 4991 a(\013h) p Fh 1481 4880 a(\020) p Fl 1530 4976 a(U) p Fj 1596 4991 a(1) p Fm 1652 4951 a(~) p Fl 1636 4976 a(U) p Fj 1702 4991 a(2) p Fh 1742 4880 a(\021) p Fm 1819 4976 a(=) p Fl 1922 4976 a(H) p Fm 2011 4976 a(\() p Fl(\014) p Fm 2110 4976 a(\003\)) p 2243 4976 a(=) p 2346 4976 a(\() p Fi(\000) p Fl(i) p Fi(r) p 2600 4976 a(\000) p Fl 2700 4976 a(\014) p Fm 2761 4976 a(\003\)) p Fj 2866 4928 a(2) p Fm 0 5186 a(with) p Fl 223 5186 a(\014) p Fm 314 5186 a(=) p Fl 419 5186 a(\013) q(=h) p Fi 610 5186 a(\000) p Fm 710 5186 a([) p Fl(\013) q(=h) p Fm(].) p 1006 5186 a(This) p 1230 5186 a(op) s(erator) p 1624 5186 a(is) p 1724 5186 a(also) p 1921 5186 a(self{adjoin) m(t) p 2440 5186 a(under) p 2717 5186 a(\(1.4\).) p 2992 5186 a(According) p 3457 5186 a(to) 0 5307 y(notation) p 390 5307 a(\(3.5\),) p 650 5307 a(w) m(e) p 794 5307 a(set) 719 5479 y(~) p Fl 691 5504 a(W) p Fj 783 5519 a(+) p Fm 869 5504 a(=) p Fl 973 5504 a(W) p Fj 1065 5519 a(+) p Fm 1124 5504 a(\() p Fl(H) p Fj 1243 5519 a(0) p Fl 1282 5504 a(;) p 1326 5504 a(H) p Fj 1407 5519 a(0) p Fm 1446 5504 a(;) 1507 5479 y(~) p Fl 1490 5504 a(U) p Fj 1556 5519 a(2) p Fm 1596 5504 a(\)) p Fl(;) p Fm 1901 5479 a(~) p Fl 1872 5504 a(W) p Ff 1964 5519 a(\000) p Fm 2051 5504 a(=) p Fl 2155 5504 a(W) p Ff 2247 5519 a(\000) p Fm 2306 5504 a(\() p Fl(H) p Fj 2425 5519 a(0) p Fl 2464 5504 a(;) p 2508 5504 a(H) p Fj 2589 5519 a(0) p Fm 2628 5504 a(;) 2688 5479 y(~) p Fl 2672 5504 a(U) p Ff 2748 5463 a(\003) p Fj 2738 5529 a(2) p Fm 2788 5504 a(\)) p Fl(;) p Fm 3343 5504 a(\(7.1\)) 1723 5753 y(34) p 90 rotate dyy eop %%Page: 35 35 35 34 bop Fm 0 407 a(Then) p 255 407 a(w) m(e) p 398 407 a(get) p 561 407 a(the) p 729 407 a(relation) p Fl 954 613 a(S) p Fm 1020 613 a(\() p Fl(H) p Fg 1139 628 a(\013h) p Fl 1229 613 a(;) p 1273 613 a(H) p Fj 1354 628 a(0) p Fg(h) p Fm 1433 613 a(\)) p 1499 613 a(=) p Fl 1602 613 a(U) p Fj 1668 628 a(1) p Fm 1737 588 a(~) p Fl 1708 613 a(W) p Fj 1800 628 a(+) p Fl 1859 613 a(S) p Fm 1925 613 a(\() p Fl(K) p Fg 2046 628 a(\014) p Fl 2093 613 a(;) p 2137 613 a(H) p Fj 2218 628 a(0) p Fm 2257 613 a(\)) 2323 588 y(~) p Fl 2295 613 a(W) p Ff 2387 628 a(\000) p Fl 2446 613 a(U) p Ff 2522 572 a(\003) p Fj 2512 638 a(1) p Fl 2562 613 a(:) p Fm 3343 613 a(\(7.2\)) 0 820 y(The) p 202 820 a(existence) p 619 820 a(of) 760 795 y(~) p Fl 731 820 a(W) p Ff 823 835 a(\006) p Fm 916 820 a(follo) m(ws) p 1238 820 a(as) p 1360 820 a(a) p 1442 820 a(consequence) p 1995 820 a(of) p 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2078 a(F) p Ff 1086 2037 a(\003) p Fm 1152 2078 a(=) p 1256 2078 a(exp) q(\() p Fl(i) p Fm([) p Fl(\013) q(=h) p Fm(]) p Fl(\015) p Fm 1754 2078 a(\() p Fl(!) p Fm 1857 2078 a(\)\)) p Fi(\002) p Fm 2037 2078 a(=) p 2141 2078 a(exp) q(\() p Fl(i) p Fm([) p Fl(\013) q(=h) p Fm(]) p Fl(!) p Fm 2648 2078 a(\)) p Fi(\002) p Fm 0 2284 a(on) p Fl 134 2284 a(L) p Fj 200 2248 a(2) p Fm 240 2284 a(\(\(0) p Fl(;) p Fi 409 2284 a(1) p Fm(\);) p Fl 591 2284 a(d\025) p Fm(\)) p Fi 753 2284 a(\012) p Fl 850 2284 a(L) p Fj 916 2248 a(2) p Fm 955 2284 a(\() p Fl(S) p Fj 1059 2248 a(1) p Fm 1099 2284 a(\),) p 1195 2284 a(where) p 1475 2284 a(the) p 1641 2284 a(p) s(osition) p 2011 2284 a(v) m(ector) p Fl 2302 2284 a(!) p Fm 2397 2284 a(on) p Fl 2531 2284 a(S) p Fj 2597 2248 a(1) p Fm 2667 2284 a(is) p 2764 2284 a(iden) m(ti\014ed) p 3187 2284 a(with) p 3408 2284 a(the) 0 2405 y(azim) m(uth) p 385 2405 a(angle) p Fl 647 2405 a(\015) p Fm 703 2405 a(\() p Fl(!) p Fm 806 2405 a(\).) p 938 2405 a(Since) p 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1500 3073 a(0) p Fg(h) p Fm 1580 3058 a(\)) p 1659 3058 a(and) p Fl 1858 3058 a(S) p Fm 1924 3058 a(\() p Fl(E) p Fm 2040 3058 a(;) p Fl 2084 3058 a(K) p Fg 2167 3073 a(\014) p Fl 2214 3058 a(;) p 2258 3058 a(H) p Fj 2339 3073 a(0) p Fm 2378 3058 a(\)) p 2457 3058 a(at) p 2585 3058 a(energy) p Fl 2906 3058 a(E) p Fm 3025 3058 a(resp) s(ectiv) m(ely) p 3513 3058 a(.) 0 3179 y(Then) p 255 3179 a(it) p 352 3179 a(follo) m(ws) p 673 3179 a(from) p 903 3179 a(\(7.2\)) p 1136 3179 a(that) p Fl 428 3385 a(S) p Fm 494 3385 a(\() p Fl(\022) s(;) p 624 3385 a(!) p Fm 689 3385 a(;) p Fl 733 3385 a(H) p Fg 814 3400 a(\013h) p Fl 902 3385 a(;) p 946 3385 a(H) p Fj 1027 3400 a(0) p Fg(h) p Fm 1107 3385 a(\)) p 1173 3385 a(=) p 1276 3385 a(\() p Fi(\000) p Fm(1\)) p Fj 1478 3344 a([) p Fg(\013=h) p Fj(]) p Fl 1643 3385 a(e) p Fg 1688 3344 a(i) p Fj([) p Fg(\013=h) p Fj(]\() p Fg(\022) p Ff 1935 3344 a(\000) p Fg(!) p Fj 2036 3344 a(\)) p Fl 2068 3385 a(S) p Fm 2134 3385 a(\() p Fl(\022) s(;) p 2264 3385 a(!) p Fm 2329 3385 a(;) p Fl 2373 3385 a(K) p Fg 2456 3400 a(\014) p Fl 2502 3385 a(;) p 2546 3385 a(H) p Fj 2627 3400 a(0) p Fm 2665 3385 a(\)) p Fl(;) p 2845 3385 a(\022) p Fi 2921 3385 a(6) p Fm(=) p Fl 3024 3385 a(!) t(:) p Fm 0 3592 a(If) p 104 3592 a(0) p Fi 191 3592 a(\024) p Fl 308 3592 a(\014) p 407 3592 a(<) p Fm 521 3592 a(1,) p 638 3592 a(then) p 867 3592 a(the) p 1041 3592 a(k) m(ernel) p 1335 3592 a(for) p 1490 3592 a(scattering) p 1947 3592 a(b) m(y) p 2089 3592 a(single) p 2367 3592 a(\014eld) p 2585 3592 a(has) p 2765 3592 a(b) s(een) p 3002 3592 a(kno) m(wn) p 3317 3592 a(to) p 3443 3592 a(b) s(e) 0 3712 y(explicitly) p 423 3712 a(calculated) p 883 3712 a(as) p Fl 929 3919 a(S) p Fm 995 3919 a(\() p Fl(\022) s(;) p 1125 3919 a(!) p Fm 1190 3919 a(;) p Fl 1234 3919 a(K) p Fg 1317 3934 a(\014) p Fl 1363 3919 a(;) p 1407 3919 a(H) p Fj 1488 3934 a(0) p Fm 1527 3919 a(\)) p 1592 3919 a(=) p 1696 3919 a(\() p Fl(i=\031) p Fm 1875 3919 a(\)) p 1930 3919 a(sin) p Fl 2082 3919 a(\014) p 2143 3919 a(\031) t(F) p Fj 2265 3934 a(0) p Fm 2304 3919 a(\() p Fl(\022) p Fi 2413 3919 a(\000) p Fl 2512 3919 a(!) p Fm 2577 3919 a(\)) 0 4125 y(b) m(y) p 138 4125 a(the) p 309 4125 a(early) p 553 4125 a(w) m(orks) p 833 4125 a([2,) p 971 4125 a(3,) p 1083 4125 a(15],) p 1271 4125 a(as) p 1393 4125 a(already) p 1740 4125 a(men) m(tioned) p 2217 4125 a(in) p 2334 4125 a(In) m(tro) s(duction,) p 2931 4125 a(where) p Fl 3216 4125 a(F) p Fj 3279 4140 a(0) p Fm 3318 4125 a(\() p Fl(\022) p Fm 3404 4125 a(\)) p 3478 4125 a(is) 0 4246 y(as) p 119 4246 a(in) p 233 4246 a(\(1.5\).) p 503 4246 a(W) p 595 4246 a(e) p 671 4246 a(recall) p 931 4246 a(\(see) p 1126 4246 a(\(2.4\)\)) p 1396 4246 a(that) p 1607 4246 a(the) p 1775 4246 a(amplitude) p Fl 2235 4246 a(f) p Fg 2283 4261 a(h) p Fm 2328 4246 a(\() p Fl(!) p Fi 2458 4246 a(!) p Fl 2585 4246 a(\022) p Fm 2633 4246 a(;) p Fl 2677 4246 a(\013) p Fm 2740 4246 a(\)) p 2809 4246 a(for) p 2958 4246 a(the) p 3125 4246 a(scattering) 0 4366 y(from) p 230 4366 a(inciden) m(t) p 602 4366 a(direction) p Fl 1008 4366 a(!) p Fm 1105 4366 a(to) p 1224 4366 a(\014nal) p 1441 4366 a(one) p Fl 1620 4366 a(\022) p Fm 1700 4366 a(at) p 1820 4366 a(energy) p Fl 2131 4366 a(E) p Fm 2242 4366 a(is) p 2340 4366 a(de\014ned) p 2676 4366 a(b) m(y) p Fl 906 4573 a(f) p Fg 954 4588 a(h) p Fm 999 4573 a(\() p Fl(!) p Fi 1129 4573 a(!) p Fl 1256 4573 a(\022) p Fm 1304 4573 a(;) p Fl 1348 4573 a(\013) p Fm 1411 4573 a(\)) p 1476 4573 a(=) p Fl 1580 4573 a(c) p Fm(\() p Fl(E) p 1738 4573 a(=h) p Fj 1843 4532 a(2) p Fm 1882 4573 a(\)) p Fl(S) p Fm 1986 4573 a(\() p Fl(\022) s(;) p 2116 4573 a(!) p Fm 2181 4573 a(;) p Fl 2225 4573 a(H) p Fg 2306 4588 a(\013h) p Fl 2395 4573 a(;) p 2439 4573 a(H) p Fj 2520 4588 a(0) p Fg(h) p Fm 2599 4573 a(\)) 0 4779 y(for) p 154 4779 a(pair) p 360 4779 a(\() p Fl(H) p Fg 479 4794 a(\013h) p Fl 569 4779 a(;) p 613 4779 a(H) p Fj 694 4794 a(0) p Fg(h) p Fm 773 4779 a(\),) p 877 4779 a(where) p Fl 1164 4779 a(c) p Fm(\() p Fl(E) p Fm 1322 4779 a(\)) p 1397 4779 a(is) p 1501 4779 a(as) p 1625 4779 a(in) p 1744 4779 a(\(1.5\).) p 2030 4779 a(Similarly) p 2450 4779 a(the) p 2623 4779 a(amplitude) p Fl 3089 4779 a(g) p Fg 3136 4794 a(\014) p Fm 3183 4779 a(\() p Fl(!) p Fi 3321 4779 a(!) p Fl 3457 4779 a(\022) p Fm 3505 4779 a(\)) 0 4900 y(for) p 149 4900 a(pair) p 350 4900 a(\() p Fl 387 4900 a(K) p Fg 470 4915 a(\014) p Fl 518 4900 a(;) p 562 4900 a(H) p Fj 643 4915 a(0) p Fm 682 4900 a(\)) p 752 4900 a(is) p 850 4900 a(de\014ned) p 1186 4900 a(b) m(y) p Fl 1058 5106 a(g) p Fg 1105 5121 a(\014) p Fm 1152 5106 a(\() p Fl(!) p Fi 1282 5106 a(!) p Fl 1409 5106 a(\022) p Fm 1457 5106 a(\)) p 1523 5106 a(=) p Fl 1627 5106 a(c) p Fm(\() p Fl(E) p Fm 1785 5106 a(\)) p Fl(S) p Fm 1889 5106 a(\() p Fl(\022) s(;) p 2019 5106 a(!) p Fm 2084 5106 a(;) p Fl 2128 5106 a(K) p Fg 2211 5121 a(\014) p Fl 2256 5106 a(;) p 2300 5106 a(H) p Fj 2381 5121 a(0) p Fm 2420 5106 a(\)) p Fl(:) p Fm 0 5313 a(Th) m(us) p 254 5313 a(w) m(e) p 404 5313 a(obtain) p 715 5313 a(the) p 889 5313 a(follo) m(wing) p 1308 5313 a(relation) p 1673 5313 a(b) s(et) m(w) m(een) p Fl 2056 5313 a(f) p Fg 2104 5328 a(h) p Fm 2149 5313 a(\() p Fl(\022) p Fi 2274 5313 a(!) p Fl 2413 5313 a(!) p Fm 2478 5313 a(;) p Fl 2522 5313 a(\013) p Fm 2585 5313 a(\)) p 2661 5313 a(and) p Fl 2858 5313 a(g) p Fg 2905 5328 a(\014) p Fm 2952 5313 a(\() p Fl(\022) p Fi 3077 5313 a(!) p Fl 3216 5313 a(!) p Fm 3281 5313 a(\),) p 3386 5313 a(and) 0 5433 y(hence) p 271 5433 a(\(1.5\)) p 504 5433 a(follo) m(ws) p 824 5433 a(immediately) p 1337 5433 a(.) 1723 5753 y(35) p 90 rotate dyy eop %%Page: 36 36 36 35 bop Fn 0 407 a(Prop) s(osition) p 606 407 a(7.1) p Fb 798 407 a(L) p 854 407 a(et) p 966 407 a(the) p 1128 407 a(notation) p 1516 407 a(b) p 1556 407 a(e) p 1636 407 a(as) p 1760 407 a(ab) p 1850 407 a(ove.) p 2064 407 a(Then) p 2318 407 a(we) p 2463 407 a(have) p Fl 724 617 a(f) p Fg 772 632 a(h) p Fm 817 617 a(\() p Fl(!) p Fi 947 617 a(!) p Fl 1074 617 a(\022) p Fm 1122 617 a(;) p Fl 1166 617 a(\013) p Fm 1229 617 a(\)) p 1294 617 a(=) p 1398 617 a(\() p Fi(\000) p Fm(1\)) p Fj 1600 576 a([) p Fg(\013=h) p Fj(]) p Fl 1764 617 a(e) p Fg 1809 576 a(i) p Fj([) p Fg(\013=h) p Fj(]\() p Fg(\022) p Ff 2056 576 a(\000) p Fg(!) p Fj 2157 576 a(\)) p Fl 2189 617 a(h) p Fj 2245 576 a(1) p Fg(=) p Fj(2) p Fl 2355 617 a(g) p Fg 2402 632 a(\014) p Fm 2449 617 a(\() p Fl(!) p Fi 2579 617 a(!) p Fl 2706 617 a(\022) p Fm 2754 617 a(\)) p Fl(:) p Fn 0 882 a(Remark) p 438 882 a(7.1.) p Fm 710 882 a(W) p 802 882 a(e) p 889 882 a(recall) p 1160 882 a(that) p Fl 1383 882 a(f) p Fg 1431 897 a(h) p Fm 1476 882 a(\() p Fl(!) p Fi 1625 882 a(!) p Fl 1771 882 a(\022) p Fm 1819 882 a(;) p Fi 1863 882 a(\006) p Fl(\013) q(;) p 2047 882 a(e) p Ff 2092 897 a(\006) p Fm 2151 882 a(\)) p 2233 882 a(denotes) p 2597 882 a(the) p 2776 882 a(amplitude) p 3248 882 a(for) p 3408 882 a(the) 0 1002 y(scattering) p 462 1002 a(b) m(y) p 610 1002 a(\014eld) p Fi 833 1002 a(\006) p Fm(2) p Fl(\031) t(\013) q(\016) p Fm 1128 1002 a(\() p Fl(x) p Fi 1252 1002 a(\000) p Fl 1360 1002 a(e) p Ff 1405 1017 a(\006) p Fm 1464 1002 a(\).) p 1609 1002 a(Let) p Fl 1795 1002 a(K) p Ff 1878 1017 a(\006) p Fm 1986 1002 a(=) p Fl 2110 1002 a(H) p Fm 2199 1002 a(\() p Fl(B) p Ff 2311 1017 a(\006) p Fm 2369 1002 a(\)) p 2452 1002 a(b) s(e) p 2597 1002 a(de\014ned) p 2945 1002 a(b) m(y) p 3092 1002 a(\(4.10\)) p 3386 1002 a(and) 0 1123 y(let) p Fl 146 1123 a(g) p Ff 193 1138 a(\006) p Fm 252 1123 a(\() p Fl(\022) p Fi 375 1123 a(!) p Fl 512 1123 a(!) p Fm 577 1123 a(\)) p 652 1123 a(denote) p 972 1123 a(the) p 1146 1123 a(scattering) p 1602 1123 a(amplitude) p 2068 1123 a(for) p 2223 1123 a(pair) p 2429 1123 a(\() p Fl(K) p Ff 2550 1138 a(\006) p Fl 2609 1123 a(;) p 2653 1123 a(H) p Fj 2734 1138 a(0) p Fm 2773 1123 a(\).) p 2898 1123 a(Then) p 3158 1123 a(the) p 3331 1123 a(same) 0 1243 y(argumen) m(t) p 436 1243 a(as) p 556 1243 a(used) p 779 1243 a(to) p 898 1243 a(pro) m(v) m(e) p 1161 1243 a(Prop) s(osition) p 1686 1243 a(7.1) p 1843 1243 a(enables) p 2185 1243 a(us) p 2310 1243 a(to) p 2429 1243 a(get) p Fl 644 1454 a(f) p Fg 692 1469 a(h) p Fm 737 1454 a(\() p Fl(!) p Fi 867 1454 a(!) p Fl 994 1454 a(\022) p Fm 1042 1454 a(;) p Fl 1086 1454 a(\013) q(;) p 1193 1454 a(e) p Fj 1238 1469 a(+) p Fm 1296 1454 a(\)) p 1362 1454 a(=) p 1466 1454 a(\() p Fi(\000) p Fm(1\)) p Fj 1668 1412 a([) p Fg(\013=h) p Fj(]) p Fl 1832 1454 a(e) p Fg 1877 1412 a(i) p Fj([) p Fg(\013=h) p Fj(]\() p Fg(\022) p Ff 2124 1412 a(\000) p Fg(!) p Fj 2225 1412 a(\)) p Fl 2257 1454 a(h) p Fj 2313 1412 a(1) p Fg(=) p Fj(2) p Fl 2423 1454 a(g) p Fj 2470 1469 a(+) p Fm 2529 1454 a(\() p Fl(!) p Fi 2659 1454 a(!) p Fl 2786 1454 a(\022) p Fm 2834 1454 a(\)) p Fl(:) p Fm 0 1664 a(If) p 98 1664 a(w) m(e) p 241 1664 a(write) p Fi 490 1664 a(\000) p Fl(\014) p Fm 661 1664 a(as) p Fi 781 1664 a(\000) p Fl(\014) p Fm 947 1664 a(=) p Fi 1050 1664 a(\000) p Fl(\013) q(=h) p Fi 1317 1664 a(\000) p Fm 1417 1664 a(\() p Fi(\000) p Fm([) p Fl(\013) q(=h) p Fm(]\),) p 1852 1664 a(then) p 2074 1664 a(w) m(e) p 2218 1664 a(also) p 2413 1664 a(ha) m(v) m(e) p Fl 578 1875 a(f) p Fg 626 1890 a(h) p Fm 671 1875 a(\() p Fl(!) p Fi 800 1875 a(!) p Fl 928 1875 a(\022) p Fm 976 1875 a(;) p Fi 1020 1875 a(\000) p Fl(\013) q(;) p 1204 1875 a(e) p Ff 1249 1890 a(\000) p Fm 1308 1875 a(\)) p 1373 1875 a(=) p 1477 1875 a(\() p Fi(\000) p Fm(1\)) p Fj 1679 1833 a([) p Fg(\013=h) p Fj(]) p Fl 1844 1875 a(e) p Ff 1889 1833 a(\000) p Fg(i) p Fj([) p Fg(\013=h) p Fj(]\() p Fg(\022) p Ff 2191 1833 a(\000) p Fg(!) p Fj 2292 1833 a(\)) p Fl 2323 1875 a(h) p Fj 2379 1833 a(1) p Fg(=) p Fj(2) p Fl 2490 1875 a(g) p Ff 2537 1890 a(\000) p Fm 2595 1875 a(\() p Fl(!) p Fi 2725 1875 a(!) p Fl 2852 1875 a(\022) p Fm 2900 1875 a(\)) p Fl(:) p Fn 0 2253 a(Remark) p 412 2253 a(7.2.) p Fm 684 2253 a(As) p 818 2253 a(is) p 905 2253 a(easily) p 1163 2253 a(seen,) p 1393 2253 a(the) p 1550 2253 a(scattering) p 1990 2253 a(matrix) p Fl 2296 2253 a(S) p Fm 2362 2253 a(\() p Fl(\025) p Fm(;) p Fl 2501 2253 a(H) p Fg 2582 2268 a(\013h) p Fl 2672 2253 a(;) p 2716 2253 a(H) p Fj 2797 2268 a(0) p Fg(h) p Fm 2876 2253 a(\)) p 2936 2253 a(is) p 3023 2253 a(indep) s(enden) m(t) 0 2373 y(of) p 114 2373 a(energy) p Fl 429 2373 a(\025) p Fm 521 2373 a(as) p 643 2373 a(a) p 728 2373 a(function) p 1113 2373 a(with) p 1338 2373 a(v) p 1384 2373 a(alues) p 1631 2373 a(in) p 1748 2373 a(b) s(ounded) p 2149 2373 a(op) s(erators) p 2583 2373 a(from) p Fl 2817 2373 a(L) p Fj 2883 2337 a(2) p Fm 2922 2373 a(\() p Fl(S) p Fj 3026 2337 a(1) p Fm 3065 2373 a(\)) p 3139 2373 a(in) m(to) p 3340 2373 a(itself) 0 2493 y(for) p 158 2493 a(the) p 335 2493 a(self{adjoin) m(t) p 862 2493 a(op) s(erator) p Fl 1263 2493 a(H) p Fg 1344 2508 a(\013h) p Fm 1476 2493 a(de\014ned) p 1821 2493 a(b) m(y) p 1965 2493 a(\(1.3\)) p 2207 2493 a(with) p 2438 2493 a(\(1.4\).) p 2735 2493 a(This) p 2967 2493 a(means) p 3274 2493 a(that) p 3495 2493 a(a) 0 2614 y(system) p 321 2614 a(of) p 429 2614 a(single) p 698 2614 a(\014eld) p 907 2614 a(do) s(es) p 1124 2614 a(not) p 1295 2614 a(ha) m(v) m(e) p 1518 2614 a(an) m(y) p 1699 2614 a(resonances) p 2180 2614 a(under) p 2454 2614 a(b) s(oundary) p 2890 2614 a(condition) p 3316 2614 a(\(1.4\).) 146 2902 y(W) p 238 2902 a(e) p 316 2902 a(represen) m(t) p Fl 739 2902 a(g) p Fg 786 2917 a(\014) p Fm 833 2902 a(\() p Fl(!) p Fi 967 2902 a(!) p Fl 1097 2902 a(\022) p Fm 1145 2902 a(\)) p 1218 2902 a(in) p 1334 2902 a(terms) p 1608 2902 a(of) p Fl 1721 2902 a(R) p Fm 1796 2902 a(\() p Fl(E) p Fm 1936 2902 a(+) p Fl 2035 2902 a(i) p Fm(0;) p Fl 2161 2902 a(K) p Fg 2244 2917 a(\014) p Fm 2291 2902 a(\).) p 2406 2902 a(The) p 2609 2902 a(prop) s(osition) p 3123 2902 a(b) s(elo) m(w) p 3402 2902 a(has) 0 3022 y(b) s(een) p 240 3022 a(v) m(eri\014ed) p 590 3022 a(as) p 720 3022 a([10,) p 913 3022 a(Lemma) p 1271 3022 a(3.2].) p 1521 3022 a(The) p 1731 3022 a(deriv) p 1939 3022 a(ation) p 2198 3022 a(is) p 2305 3022 a(based) p 2586 3022 a(on) p 2731 3022 a(the) p 2908 3022 a(analysis) p 3285 3022 a(in) p 3408 3022 a(the) 0 3142 y(phase) p 272 3142 a(space) p 532 3142 a(and) p 722 3142 a(is) p 820 3142 a(due) p 1004 3142 a(to) p 1123 3142 a(the) p 1291 3142 a(idea) p 1497 3142 a(dev) m(elop) s(ed) p 1950 3142 a(in) p 2064 3142 a([7,) p 2199 3142 a(19].) p Fn 0 3407 a(Prop) s(osition) p 606 3407 a(7.2) p Fb 798 3407 a(L) p 854 3407 a(et) p Fl 964 3407 a(j) p Ff 1004 3422 a(\006) p Fm 1064 3407 a(\() p Fl(x) p Fm(;) p Fl 1201 3407 a(!) p Fm 1266 3407 a(\)) p Fb 1336 3407 a(b) p 1376 3407 a(e) p 1455 3407 a(de\014ne) p 1700 3407 a(d) p 1782 3407 a(by) p 1907 3407 a(\(4.1\).) p 2191 3407 a(Set) p Fl 2356 3407 a( ) p Fm 2423 3407 a(\() p Fl(x) p Fm(\)) p 2582 3407 a(=) p 2686 3407 a(1) p Fi 2754 3407 a(\000) p Fl 2850 3407 a(\037) p Fm(\(2) p Fl(h) p Fg 3054 3371 a(") p Fi 3091 3407 a(j) p Fl(x) p Fi(j) p Fm(\)) p Fb(,) p 3303 3407 a(wher) p 3499 3407 a(e) p Fl 0 3527 a(\037) p Fi 89 3527 a(2) p Fl 183 3527 a(C) p Ff 260 3491 a(1) p Fj 253 3552 a(0) p Fm 335 3527 a([0) p Fl(;) p Fi 455 3527 a(1) p Fm(\)) p Fb 627 3527 a(is) p 731 3527 a(a) p 816 3527 a(cut{o\013) p 1140 3527 a(function) p 1523 3527 a(with) p 1735 3527 a(pr) p 1821 3527 a(op) p 1916 3527 a(erty) p 2116 3527 a(\(3.9\).) p 2400 3527 a(Then) p 2654 3527 a(we) p 2798 3527 a(have) p Fl 109 3738 a(g) p Fg 156 3753 a(\014) p Fm 203 3738 a(\() p Fl(!) p Fi 333 3738 a(!) p Fl 460 3738 a(\022) p Fm 508 3738 a(\)) p 574 3738 a(=) p 677 3738 a(\() p Fl(ic) p Fm(\() p Fl(E) p Fm 906 3738 a(\)) p Fl(=) p Fm(4) p Fl(\031) p Fm 1101 3738 a(\)) p Fi 1155 3738 a(h) p Fm(\() p Fl(R) p Fm 1307 3738 a(\() p Fl(E) p Fm 1445 3738 a(+) p Fl 1543 3738 a(i) p Fm(0;) p Fl 1669 3738 a(K) p Fg 1752 3753 a(\014) p Fm 1799 3738 a(\)) p Fl(Q) p Fj 1914 3753 a(1) p Fl 1954 3738 a(') p Fj 2018 3753 a(0) p Fm 2057 3738 a(\() p Fl(!) p Fm 2160 3738 a(\)) p Fl(;) p 2242 3738 a(Q) p Fj 2319 3753 a(2) p Fl 2358 3738 a(') p Fj 2422 3753 a(0) p Fm 2461 3738 a(\() p Fl(\022) p Fm 2547 3738 a(\)) p Fi(i) p Fm 2646 3738 a(+) p Fl 2744 3738 a(O) p Fm 2822 3738 a(\() p Fl(h) p Fg 2916 3697 a(N) p Fm 2983 3738 a(\)) p Fl(;) p 3164 3738 a(!) p Fi 3256 3738 a(6) p Fm(=) p Fl 3359 3738 a(\022) s(;) p Fb 0 3948 a(for) p 156 3948 a(any) p Fl 342 3948 a(N) p Fi 459 3948 a(\035) p Fm 586 3948 a(1) p Fb(,) p 699 3948 a(wher) p 895 3948 a(e) p Fl 975 3948 a(') p Fj 1039 3963 a(0) p Fm 1078 3948 a(\() p Fl(!) p Fm 1181 3948 a(\)) p 1246 3948 a(=) p 1349 3948 a(exp) r(\() p Fl(iE) p Fj 1648 3912 a(1) p Fg(=) p Fj(2) p Fl 1758 3948 a(x) p Fi 1835 3948 a(\001) p Fl 1885 3948 a(!) p Fm 1950 3948 a(\)) p Fb 2022 3948 a(and) p Fl 476 4159 a(Q) p Fj 553 4174 a(1) p Fm 620 4159 a(=) p 724 4159 a(exp) q(\() p Fl(ij) p Fj 984 4174 a(+) p Fm 1044 4159 a(\() p Fl(x) p Fm(;) p Fl 1181 4159 a(!) p Fm 1246 4159 a(\)\)[) p Fl( ) t(;) p 1460 4159 a(H) p Fj 1541 4174 a(0) p Fm 1579 4159 a(]) p Fl(;) p 1849 4159 a(Q) p Fj 1926 4174 a(2) p Fm 1993 4159 a(=) p 2097 4159 a(exp) q(\() p Fl(ij) p Fj 2357 4174 a(+) p Fm 2416 4159 a(\() p Fl(x) p Fm(;) p Fi 2553 4159 a(\000) p Fl(\022) p Fm 2678 4159 a(\)\)[) p Fl( ) t(;) p 2892 4159 a(H) p Fj 2973 4174 a(0) p Fm 3013 4159 a(]) p Fl(:) p Fm 146 4423 a(W) p 238 4423 a(e) p 314 4423 a(apply) p 583 4423 a(the) p 751 4423 a(ab) s(o) m(v) m(e) p 1027 4423 a(prop) s(osition) p 1540 4423 a(to) p Fl 1659 4423 a(g) p Ff 1706 4438 a(\006) p Fm 1792 4423 a(=) p Fl 1896 4423 a(g) p Ff 1943 4438 a(\006) p Fm 2002 4423 a(\() p Fl(!) p Fi 2132 4423 a(!) p Fl 2259 4423 a(\022) p Fm 2307 4423 a(\)) p 2377 4423 a(to) p 2497 4423 a(obtain) p Fl 440 4634 a(g) p Ff 487 4649 a(\006) p Fm 573 4634 a(=) p 677 4634 a(\() p Fl(ic) p Fm(\() p Fl(E) p Fm 906 4634 a(\)) p Fl(=) p Fm(4) p Fl(\031) p Fm 1101 4634 a(\)) p Fi 1155 4634 a(h) p Fl(R) p Fm 1269 4634 a(\() p Fl(E) p Fm 1407 4634 a(+) p Fl 1505 4634 a(i) p Fm(0;) p Fl 1631 4634 a(K) p Ff 1714 4649 a(\006) p 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Fl(x) p Fi 2550 5055 a(\000) p Fl 2649 5055 a(d) p Ff 2700 5070 a(\006) p Fm 2759 5055 a(;) p Fi 2803 5055 a(\000) p Fl(\022) p Fm 2928 5055 a(\)\)[) p Fl( ) p Ff 3094 5070 a(\006) p Fl 3154 5055 a(;) p 3198 5055 a(H) p Fj 3279 5070 a(0) p Fm 3318 5055 a(]) 0 5266 y(with) p Fl 222 5266 a( ) p Ff 285 5281 a(\006) p Fm 372 5266 a(=) p 476 5266 a(1) p Fi 547 5266 a(\000) p Fl 646 5266 a(\037) p Fm(\(2) p Fl(h) p Fg 850 5229 a(") p Fi 887 5266 a(j) p Fl(x) p Fi 992 5266 a(\000) p Fl 1092 5266 a(d) p Ff 1143 5281 a(\006) p Fi 1202 5266 a(j) p Fm(\).) p Fn 146 5504 a(8.) p 271 5504 a(Pro) s(of) p 580 5504 a(of) p 708 5504 a(Lemma) p 1105 5504 a(4.5) p 1285 5504 a(:) p 1366 5504 a(calculation) p 1930 5504 a(of) p 2057 5504 a(third) p 2340 5504 a(term) p Fm 1723 5753 a(36) p 90 rotate dyy eop %%Page: 37 37 37 36 bop Fm 146 407 a(In) p 261 407 a(this) p 443 407 a(section) p 761 407 a(w) m(e) p 897 407 a(pro) m(v) m(e) p 1152 407 a(Lemma) p 1493 407 a(4.5.) p 1686 407 a(As) p 1822 407 a(a) p 1896 407 a(result,) p 2188 407 a(the) p 2349 407 a(third) p 2585 407 a(term) p 2810 407 a(of) p 2914 407 a(the) p 3074 407 a(asymptotic) 0 527 y(form) m(ula) p 365 527 a(is) p 471 527 a(calculated) p 939 527 a(and) p 1136 527 a(also) p 1340 527 a(the) p 1515 527 a(pro) s(of) p 1778 527 a(of) p 1896 527 a(Lemma) p 2252 527 a(3.3) p 2417 527 a(is) p 2522 527 a(completed) p 2996 527 a(for) p 3153 527 a(\010) p Ff 3223 491 a(\000) p Fj 3223 552 a(+) p Fm 3282 527 a(.) p 3375 527 a(The) 0 648 y(calculation) p 493 648 a(is) p 592 648 a(based) p 864 648 a(on) p 999 648 a(an) p 1135 648 a(idea) p 1341 648 a(similar) p 1662 648 a(to) p 1782 648 a(that) p 1993 648 a(used) p 2216 648 a(to) p 2336 648 a(pro) m(v) m(e) p 2599 648 a([10,) p 2783 648 a(Theorem) p 3196 648 a(1.1]) p 3380 648 a(\(see) 0 768 y(the) p 169 768 a(argumen) m(t) p 606 768 a(in) p 721 768 a([10,) p 907 768 a(sections) p 1272 768 a(4) p 1354 768 a(and) p 1545 768 a(5]\).) p 1732 768 a(W) p 1824 768 a(e) p 1901 768 a(giv) m(e) p 2103 768 a(only) p 2318 768 a(a) p 2400 768 a(rather) p 2694 768 a(sk) m(etc) m(h) m(y) p 3040 768 a(pro) s(of) p 3296 768 a(of) p 3408 768 a(the) 0 888 y(lemma.) p Fb 0 1055 a(Pr) p 102 1055 a(o) p 147 1055 a(of) p 274 1055 a(of) p 402 1055 a(L) p 458 1055 a(emma) p 759 1055 a(4.5.) p Fm 1016 1055 a(Let) p 1205 1055 a(\000) p Ff 1266 1070 a(\000) p Fm 1371 1055 a(b) s(e) p 1518 1055 a(de\014ned) p 1868 1055 a(b) m(y) p 2017 1055 a(\(4.9\).) p 2329 1055 a(The) p 2543 1055 a(aim) p 2747 1055 a(is) p 2859 1055 a(to) p 2992 1055 a(establish) p 3408 1055 a(the) 0 1176 y(asymptotic) p 502 1176 a(form) m(ula) 958 1384 y(\000) p Ff 1019 1399 a(\000) p Fm 1106 1384 a(=) p Fi 1209 1384 a(\000) p Fl(k) p Fj 1337 1399 a(1) p Fl 1377 1384 a(e) p Fg 1422 1343 a(i\031) r(=) p Fj(4) p Fl 1564 1384 a(\034) p Fj 1606 1399 a(+) p Fl 1665 1384 a(F) p Ff 1728 1399 a(\000) p Fm 1787 1384 a(\() p Fl(!) p Ff 1886 1399 a(\000) p Fm 1945 1384 a(\)) p Fl(h) p Fj 2039 1343 a(1) p Fg(=) p Fj(2) p Fm 2171 1384 a(+) p Fl 2269 1384 a(o) p Fm(\() p Fl(h) p Fj 2410 1343 a(3) p Fg(=) p Fj(2) p Fm 2520 1384 a(\)) p Fl(;) p Fm 0 1592 a(where) p Fl 282 1592 a(k) p Fj 333 1607 a(1) p Fm 400 1592 a(=) p 503 1592 a(\(2) p Fl(\031) p Fm 649 1592 a(\)) p Fj 687 1556 a(1) p Fg(=) p Fj(2) p Fi 797 1592 a(j) p Fl(e) p Fi(j) p Ff 898 1556 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fl 1062 1592 a(E) p Ff 1140 1556 a(\000) p Fj(1) p Fg(=) p Fj(4) p Fm 1338 1592 a(and) p Fl 202 1801 a(\034) p Fj 244 1816 a(+) p Fm 331 1801 a(=) p 434 1801 a(exp) q(\() p Fl(i) p Fm(2\() p Fl(\013) q(=h) p Fm(\)\() p Fl(\031) p Fi 1066 1801 a(\000) p Fl 1165 1801 a(\015) p Fm 1221 1801 a(\() t(^) p Fl 1259 1801 a(e) p Fm 1305 1801 a(;) p Fl 1349 1801 a(!) p Ff 1410 1816 a(\000) p Fm 1468 1801 a(\)\)) p 1572 1801 a(=) p 1675 1801 a(exp) q(\() p Fl(i) p Fm(2\() p Fl(\013) q(=h) p Fm(\)\() p Fl(\015) p Ff 2277 1816 a(\000) p Fi 2357 1801 a(\000) p Fl 2457 1801 a(\031) p Fm 2516 1801 a(\)\)) p Fl(;) p 2733 1801 a(\015) p Ff 2784 1816 a(\000) p Fm 2870 1801 a(=) p Fl 2974 1801 a(\015) p Fm 3030 1801 a(\() p Fl(!) p Ff 3129 1816 a(\000) p Fm 3188 1801 a(;) p 3235 1801 a(^) p Fl 3232 1801 a(e) p Fm(\)) p Fl(:) p Fm 0 2009 a(The) p 195 2009 a(particle) p 543 2009 a(starting) p 901 2009 a(from) p 1127 2009 a(supp) p Fl 1344 2009 a(V) p Fj 1401 2024 a(+) p Fl 1460 2009 a(W) p Ff 1566 1973 a(\000) p Fm 1652 2009 a(at) p 1767 2009 a(v) m(elo) s(cit) m(y) p 2122 2009 a(2) p Fl(E) p Fj 2249 1973 a(1) p Fg(=) p Fj(2) p Fl 2359 2009 a(!) p Ff 2420 2024 a(\000) p Fm 2506 2009 a(mo) m(v) m(es) p 2792 2009 a(lik) m(e) p 2965 2009 a(a) p 3042 2009 a(free) p 3224 2009 a(particle) 0 2129 y(for) p Fl 149 2129 a(t) p 212 2129 a(<) p Fm 315 2129 a(0,) p 424 2129 a(and) p 614 2129 a(it) p 711 2129 a(nev) m(er) p 971 2129 a(passes) p 1266 2129 a(o) m(v) m(er) p 1474 2129 a(supp) 1707 2104 y(~) p Fl 1692 2129 a(V) p Ff 1749 2144 a(\000) p Fl 1808 2129 a(W) p Fj 1914 2093 a(+) p Fm 1972 2129 a(.) p 2043 2129 a(Hence) p 2333 2129 a(w) m(e) p 2476 2129 a(see) p 2634 2129 a(that) 32 2347 y(\000) p Ff 93 2362 a(\000) p Fm 180 2347 a(=) p Fi 283 2347 a(\000) p Fm(2) p Fl(iE) p Fj 520 2306 a(1) p Fg(=) p Fj(2) p Fl 631 2347 a(h) p Fh 704 2251 a(D) p Fl 754 2347 a(R) p Fm 829 2347 a(\() p Fl(E) p Fm 967 2347 a(+) p Fl 1065 2347 a(i) p Fm(0;) p Fl 1191 2347 a(K) p Fg 1274 2362 a(d) p Fm 1315 2347 a(\)) p Fl(e) p Fg 1398 2306 a(i\021) p Fl 1464 2347 a(V) p Fj 1521 2362 a(+) p Fl 1580 2347 a(W) p Ff 1686 2306 a(\000) p Fm 1761 2347 a(\() p Fl(@) p Fj 1850 2362 a(2) p Fl 1890 2347 a(W) p Fm 1996 2347 a(\)) p Fl 2050 2347 a(') p Ff 2114 2362 a(\000) p Fl 2173 2347 a(;) p 2217 2347 a(e) p Fg 2262 2306 a(i\021) p Fm 2343 2322 a(~) p Fl 2328 2347 a(V) p Ff 2385 2362 a(\000) p Fl 2444 2347 a(W) p Fj 2550 2306 a(+) p Fm 2625 2347 a(\() p Fl(@) p Fj 2714 2362 a(2) p Fl 2754 2347 a(W) p Fm 2860 2347 a(\)) p Fl 2914 2347 a(') p Ff 2978 2362 a(\000) p Fh 3037 2251 a(E) p Fm 3110 2347 a(+) p Fl 3208 2347 a(O) p Fm 3286 2347 a(\() p Fl(h) p Fg 3380 2306 a(N) p Fm 3446 2347 a(\)) p Fl(:) p Fm 0 2556 a(W) p 92 2556 a(e) p 168 2556 a(pro) s(ceed) p 528 2556 a(with) p 751 2556 a(the) p 919 2556 a(argumen) m(t,) p 1382 2556 a(accepting) p 1815 2556 a(a) p 1897 2556 a(series) p 2158 2556 a(of) p 2269 2556 a(the) p 2437 2556 a(lemmas) p 2790 2556 a(b) s(elo) m(w) p 3066 2556 a(as) p 3186 2556 a(pro) m(v) m(ed.) p Fn 0 2817 a(Lemma) p 397 2817 a(8.1) p Fb 589 2817 a(L) p 645 2817 a(et) p Fm 766 2791 a(~) p Fl 757 2817 a(\020) p Fm 807 2817 a(\() p Fl(x) p Fm(\)) p Fb 974 2817 a(b) p 1014 2817 a(e) p 1093 2817 a(de\014ne) p 1338 2817 a(d) p 1422 2817 a(by) p Fm 886 2999 a(~) p Fl 877 3026 a(\020) p Fm 927 3026 a(\() p Fl(x) p Fm(\)) p 1086 3026 a(=) p Fl 1190 3026 a(j) p Fj 1230 3041 a(+) p Fm 1289 3026 a(\() p Fl(x) p Fi 1405 3026 a(\000) p Fl 1504 3026 a(d) p Fj 1555 3041 a(+) p Fm 1614 3026 a(;) p Fl 1658 3026 a(!) p Ff 1719 3041 a(\000) p Fm 1778 3026 a(\)) p 1838 3026 a(+) p Fl 1936 3026 a(j) p Ff 1976 3041 a(\000) p Fm 2035 3026 a(\() p Fl(x) p Fi 2151 3026 a(\000) p Fl 2250 3026 a(d) p Ff 2301 3041 a(\000) p Fm 2360 3026 a(;) p Fi 2404 3026 a(\000) p Fl(!) p Ff 2542 3041 a(\000) p Fm 2601 3026 a(\)) p Fl(;) p Fm 3343 3026 a(\(8.1\)) p Fb 0 3234 a(wher) p 196 3234 a(e) p Fl 275 3234 a(j) p Ff 315 3249 a(\006) p Fb 409 3234 a(is) p 514 3234 a(de\014ne) p 759 3234 a(d) p 843 3234 a(by) p 970 3234 a(\(4.1\).) p 1254 3234 a(Then) p 1508 3234 a(we) p 1652 3234 a(have) p Fm 190 3417 a(~) p Fl 175 3442 a(V) p Ff 232 3457 a(\000) p Fl 291 3442 a(W) p Fj 397 3401 a(+) p Fl 456 3442 a(R) p Fm 531 3442 a(\() p Fl(E) p Fm 669 3442 a(+) p Fl 767 3442 a(i) p Fm(0;) p Fl 893 3442 a(K) p Fg 976 3457 a(d) p Fm 1016 3442 a(\)) p Fl(e) p Fg 1099 3401 a(i\021) p Fl 1165 3442 a(U) p Ff 1241 3401 a(\000) p Fj 1231 3467 a(+) p Fl 1301 3442 a(p) p Fm(\() p Fl(D) p Fg 1469 3457 a(x) p Fm 1513 3442 a(\)) p 1578 3442 a(=) p Fl 374 3610 a(e) p Ff 419 3569 a(\000) p Fg(i\014) s(\031) p Fm 603 3585 a(~) p Fl 588 3610 a(V) p Ff 645 3625 a(\000) p Fl 704 3610 a(W) p Fj 810 3569 a(+) p Fl 869 3610 a(R) p Fm 944 3610 a(\() p Fl(E) p Fm 1082 3610 a(+) p Fl 1180 3610 a(i) p Fm(0;) p Fl 1306 3610 a(K) p Fg 1389 3625 a(d) p Fm 1430 3610 a(\)) p Fl(e) p Fg 1513 3569 a(i) p Fj 1543 3552 a(~) p Fg 1537 3569 a(\020) p Fm 1576 3610 a([) p Fl( ) p Fj 1666 3625 a(+) p Fl 1726 3610 a(;) p 1770 3610 a(H) p Fj 1851 3625 a(0) p Fm 1890 3610 a(]) p Fl(R) p Fm 1992 3610 a(\() p Fl(E) p Fm 2130 3610 a(+) p Fl 2228 3610 a(i) p Fm(0;) p Fl 2354 3610 a(H) p Fj 2435 3625 a(0) p Fm 2474 3610 a(\)) p Fl(U) p Ff 2588 3569 a(\000) p Fj 2578 3635 a(+) p Fl 2648 3610 a(p) p Fm(\() p Fl(D) p Fg 2816 3625 a(x) p Fm 2860 3610 a(\)) p 2920 3610 a(+) p Fl 3018 3610 a(O) p Fg 3093 3625 a(p) p Fm 3132 3610 a(\() p Fl(h) p Fg 3226 3569 a(N) p Fm 3293 3610 a(\)) p Fl(X) p Ff 3412 3625 a(\000) p Fg(N) p Fb 0 3819 a(with) p Fl 212 3819 a(U) p Ff 288 3782 a(\000) p Fj 278 3843 a(+) p Fm 375 3819 a(=) p Fl 479 3819 a(V) p Fj 536 3834 a(+) p Fl 595 3819 a(W) p 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a(;) p 1743 4195 a(H) p Fj 1824 4210 a(0) p Fm 1862 4195 a(]) p Fl(R) p Fm 1964 4195 a(\() p Fl(E) p Fi 2103 4195 a(\000) p Fl 2202 4195 a(i) p Fm(0;) p Fl 2328 4195 a(H) p Fj 2409 4210 a(0) p Fm 2448 4195 a(\)) p Fl(U) p Fj 2562 4154 a(+) p Ff 2552 4220 a(\000) p Fl 2622 4195 a(p) p Fm(\() p Fl(D) p Fg 2790 4210 a(x) p Fm 2834 4195 a(\)) p 2894 4195 a(+) p Fl 2992 4195 a(O) p Fg 3067 4210 a(p) p Fm 3106 4195 a(\() p Fl(h) p Fg 3200 4154 a(N) p Fm 3267 4195 a(\)) p Fl(X) p Ff 3386 4210 a(\000) p Fg(N) p Fb 0 4414 a(with) p Fl 213 4414 a(U) p Fj 289 4378 a(+) p Ff 279 4439 a(\000) p Fm 378 4414 a(=) 499 4389 y(~) p Fl 484 4414 a(V) p Ff 541 4429 a(\000) p Fl 600 4414 a(W) p Fj 706 4378 a(+) p Fm 781 4414 a(\() p Fl(@) p Fj 870 4429 a(2) p Fl 910 4414 a(W) p Fm 1016 4414 a(\)) p Fb(,) p 1120 4414 a(wher) p 1316 4414 a(e) p Fl 1396 4414 a( ) p Ff 1459 4429 a(\006) p Fm 1519 4414 a(\() p Fl(x) p Fm(\)) p 1680 4414 a(=) p 1786 4414 a(1) p Fi 1857 4414 a(\000) p Fl 1958 4414 a(\037) p Fm(\(2) p Fl(h) p Fg 2162 4378 a(") p Fi 2199 4414 a(j) p Fl(x) p Fi 2305 4414 a(\000) p Fl 2405 4414 a(d) p Ff 2456 4429 a(\006) p Fi 2515 4414 a(j) p Fm(\)) p Fb 2617 4414 a(and) p Fl 2807 4414 a(p) p Fm(\() p Fl(\030) p Fm 2942 4414 a(\)) p Fb 3015 4414 a(is) p 3121 4414 a(de\014ne) p 3366 4414 a(d) p 3451 4414 a(by) 0 4534 y(\(4.4\).) p Fn 0 4891 a(Lemma) p 397 4891 a(8.2) p Fb 589 4891 a(We) p 766 4891 a(have) p Fl 375 5099 a(s) p Fj 421 5114 a(+) p Fl 480 5099 a(R) p Fm 555 5099 a(\() p Fl(E) p Fm 693 5099 a(+) p Fl 791 5099 a(i) p Fm(0;) p Fl 917 5099 a(H) p Fj 998 5114 a(0) p Fm 1037 5099 a(\)) p Fl(V) p Fj 1132 5114 a(+) p Fl 1191 5099 a(W) p Ff 1297 5058 a(\000) p Fm 1372 5099 a(\() p Fl(@) p Fj 1461 5114 a(2) p Fl 1501 5099 a(W) p Fm 1607 5099 a(\)) p Fl 1661 5099 a(') p Ff 1725 5114 a(\000) p Fm 1812 5099 a(=) p Fl 1915 5099 a(s) p Fj 1961 5114 a(+) p Fh 2037 5003 a(\020) p Fm 2087 5099 a(\() p Fl(i=) p Fm(2\)) p Fl 2310 5099 a(E) p Ff 2388 5058 a(\000) p Fj(1) p Fg(=) p 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m(elo) s(cit) m(y) p 2102 5045 a(2) p Fl(E) p Fj 2229 5009 a(1) p Fg(=) p Fj(2) p Fl 2338 5045 a(!) p Ff 2399 5060 a(\000) p Fm 2490 5045 a(mo) m(v) m(es) p 2779 5045 a(lik) m(e) p 2957 5045 a(a) p 3038 5045 a(free) p 3224 5045 a(particle) 0 5166 y(for) p 148 5166 a(all) p Fl 283 5166 a(t) p Fm(,) p Fi 377 5166 a(\0001) p Fl 582 5166 a(<) p 685 5166 a(t) p 748 5166 a(<) p Fi 852 5166 a(1) p Fm(,) p 1010 5166 a(without) p 1372 5166 a(touc) m(hing) p 1770 5166 a(the) p 1937 5166 a(cen) m(ters) p Fl 2264 5166 a(d) p Ff 2315 5181 a(\006) p Fm 2374 5166 a(.) p 2444 5166 a(Hence) p 2733 5166 a(w) m(e) p 2876 5166 a(can) p 3054 5166 a(sho) m(w) p 3295 5166 a(in) p 3408 5166 a(the) 0 5286 y(same) p 244 5286 a(w) m(a) m(y) p 442 5286 a(as) p 562 5286 a(in) p 676 5286 a(the) p 844 5286 a(pro) s(of) p 1099 5286 a(of) p 1210 5286 a(Lemma) p 1558 5286 a(3.1) p 1715 5286 a(that) 522 5487 y(4) p Fl(\031) t(E) p Fj 708 5446 a(1) p Fg(=) p Fj(2) p Fl 818 5487 a(h) p Fh 891 5391 a(D) p Fm 942 5487 a(\005\() p Fl(K) p Fg 1136 5502 a(d) p Fm 1176 5487 a(\)) p Fl(e) p Fg 1259 5446 a(i\021) p Fh 1342 5391 a(\020) p Fl 1391 5487 a(@) p Fj 1447 5446 a(2) 1442 5512 y(1) p Fl 1488 5487 a(V) p Fh 1566 5391 a(\021) p Fl 1632 5487 a(W) p 1738 5487 a(') p Ff 1802 5502 a(\000) p Fl 1861 5487 a(;) p 1905 5487 a(e) p Fg 1950 5446 a(i\021) p Fl 2016 5487 a(V) p Fm 2111 5487 a(\() p Fl(@) p Fj 2200 5502 a(2) p Fl 2240 5487 a(W) p Fm 2346 5487 a(\)) p Fl 2400 5487 a(') p Ff 2464 5502 a(\000) p Fh 2523 5391 a(E) p Fm 2601 5487 a(=) p Fl 2705 5487 a(o) p Fm(\() p Fl(h) p Fj 2846 5446 a(3) p Fg(=) p Fj(2) p Fm 2956 5487 a(\)) p Fl(:) p Fm 1723 5753 a(40) p 90 rotate dyy eop %%Page: 41 41 41 40 bop Fm 0 424 a(Since) p 255 424 a(the) p 423 424 a(in) m(tegral) p Fh 778 307 a(Z) p Fl 877 424 a(w) p Ff 950 383 a(\006) p Fh 1025 328 a(\020) p Fl 1075 424 a(@) p Fj 1131 383 a(2) 1126 449 y(2) p Fl 1171 424 a(w) p Fh 1244 328 a(\021) p Fl 1327 424 a(dx) p Fj 1433 439 a(2) p Fm 1500 424 a(=) p 1603 424 a(0) 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Fl 599 4410 a(') p Fm 695 4410 a(admits) p 1016 4410 a(the) p 1184 4410 a(decomp) s(osition) p Fl 1826 4410 a(') p Fm 1918 4410 a(=) p Fl 2021 4410 a(') p Fj 2085 4425 a(in) p Fm 2170 4410 a(+) p Fl 2268 4410 a(') p Fj 2332 4425 a(sc) p Fm 2396 4410 a(,) p 2455 4410 a(where) p Fl 418 4616 a(') p Fj 482 4631 a(in) p Fm 545 4616 a(\() p Fl(x) p Fm(;) p Fl 682 4616 a(!) p Fm 747 4616 a(\)) p 812 4616 a(=) p Fl 915 4616 a(e) p Ff 960 4575 a(\000) p Fg(i\015) p Fj 1079 4575 a(\() p Fg(x) p Fj(;) p Fg(!) p Fj 1212 4575 a(\)) p Fl 1244 4616 a(e) p Fg 1289 4575 a(i) p Fj(\(1) p Ff(\000) p Fg(\014) p Fj 1473 4575 a(\)) p Fg(\033) p Fj 1542 4575 a(\() p Fg(x) p Fj(;) p Fg(!) p Fj 1675 4575 a(\)) p Fl 1709 4616 a(') p Fj 1773 4631 a(0) p Fm 1812 4616 a(\() p Fl(x) p Fm(;) p Fl 1949 4616 a(!) p Fm 2014 4616 a(\)) p Fl(;) p 2193 4616 a(\033) p Fm 2252 4616 a(\() p Fl(x) p Fm(;) p Fl 2389 4616 a(!) p Fm 2454 4616 a(\)) p 2519 4616 a(=) p Fl 2622 4616 a(\015) p Fm 2678 4616 a(\() p Fl(x) p Fm(;) p Fl 2815 4616 a(!) p Fm 2880 4616 a(\)) p Fi 2940 4616 a(\000) p Fl 3039 4616 a(\031) t(;) p Fm 0 4822 a(and) p Fl 190 4822 a(') p Fj 254 4837 a(sc) p Fm 317 4822 a(\() p Fl(x) p Fm(;) p Fl 454 4822 a(!) p Fm 519 4822 a(\)) p 584 4822 a(=) p Fl 687 4822 a(e) p Ff 732 4786 a(\000) p Fg(i\015) p Fj 851 4786 a(\() p Fg(x) p Fj(;) p Fg(!) p Fj 984 4786 a(\)) p Fm 1032 4822 a(~) p Fl 1017 4822 a(') p Fj 1081 4837 a(sc) p Fm 1144 4822 a(\() p Fl(x) p Fm(;) p Fl 1281 4822 a(!) p Fm 1346 4822 a(\).) p 1454 4822 a(If) p Fl 1551 4822 a(y) p Fi 1630 4822 a(2) p Fm 1724 4822 a(supp) p Fl 1942 4822 a(v) p Ff 1989 4837 a(\000) p Fl 2048 4822 a(w) p Ff 2121 4786 a(\000) p Fm 2179 4822 a(,) p 2239 4822 a(then) p Fl 804 5028 a(e) p Fg 849 4987 a(i\021) p Fe 908 4996 a(\000) p Fj 961 4987 a(\() p Fg(y) r(=h) p Fj(;) s(^) p Fg 1121 4987 a(e) p Fj(\)) p 1185 4975 64 4 v Fl 1185 5028 a(') p Fj 1249 5051 a(in) p Fm 1312 5028 a(\() p Fl(y) t(=h) p Fm(;) p Fl 1551 5028 a(!) p Ff 1612 5043 a(\000) p Fm 1670 5028 a(\)) p 1735 5028 a(=) p Fl 1839 5028 a(e) p Fg 1884 4987 a(i) p Fj(\(\(1) p Ff(\000) p Fg(\014) p Fj 2095 4987 a(\)) p Fg(\031) p Ff 2165 4987 a(\000) p Fg(\014) s(\015) p Fe 2299 4996 a(\000) p Fj 2353 4987 a(\)) p 2384 4975 V Fl 2384 5028 a(') p Ff 2448 5051 a(\000) p Fm 2507 5028 a(\() p Fl(y) t(=h) p Fm(\)) 0 5234 y(with) p Fl 222 5234 a(\015) p Ff 273 5249 a(\000) p Fm 360 5234 a(=) p Fl 463 5234 a(\015) p Fm 519 5234 a(\() p Fl(!) p Ff 618 5249 a(\000) p Fm 677 5234 a(;) p 724 5234 a(^) p Fl 721 5234 a(e) p Fm(\).) p 874 5234 a(Th) m(us) p 1121 5234 a(the) p 1289 5234 a(second) p 1604 5234 a(term) p 1837 5234 a(comes) p 2125 5234 a(from) p 2355 5234 a(the) p 2523 5234 a(in) m(tegral) p Fl 425 5470 a(I) p Fm 503 5470 a(=) p Fl 607 5470 a(e) p Fg 652 5429 a(i) p Fj(\(\(1) p Ff(\000) p Fg(\014) p Fj 863 5429 a(\)) p Fg(\031) p Ff 933 5429 a(\000) p Fg(\014) s(\015) p Fe 1067 5438 a(\000) p Fj 1121 5429 a(\)) p Fh 1169 5353 a(Z) p Fl 1269 5470 a(e) p Fg 1314 5429 a(i\014) s(\015) p Fj 1421 5429 a(\() p Fg(x) p Fj(;) s(^) p Fg 1508 5429 a(e) p Fj(\)) p Fl 1572 5470 a(') p Fj 1636 5485 a(sc) p Fm 1700 5470 a(\() p Fl(x=h) p Fm(;) p Fl 1942 5470 a(!) p Ff 2003 5485 a(\000) p Fm 2061 5470 a(\)) t(~) p Fl 2099 5470 a(v) p Ff 2146 5485 a(\000) p Fl 2206 5470 a(w) p Fj 2279 5429 a(+) p Fm 2354 5470 a(\() p Fl(@) p Fj 2443 5485 a(2) p Fl 2482 5470 a(w) p Fm 2555 5470 a(\)) p 2609 5417 V Fl 2609 5470 a(') p Ff 2673 5493 a(\000) p Fm 2732 5470 a(\() p Fl(x=h) p Fm(\)) p Fl 2985 5470 a(dx:) p Fm 1723 5753 a(41) p 90 rotate dyy eop %%Page: 42 42 42 41 bop Fm 0 407 a(W) p 92 407 a(e) p 168 407 a(rewrite) p 499 407 a(it) p 596 407 a(as) p Fl 100 620 a(I) p Fm 234 620 a(=) p Fl 393 620 a(e) p Fg 438 579 a(i) p Fj(\(\(1) p Ff(\000) p Fg(\014) p Fj 649 579 a(\)) p Fg(\031) p Ff 719 579 a(\000) p Fg(\014) s(\015) p Fe 853 588 a(\000) p Fj 907 579 a(\)) p Fl 939 620 a(e) p Fg 984 579 a(i\015) p Fe 1044 588 a(\000) p Fh 1117 503 a(Z) p Fl 1217 620 a(e) p Ff 1262 579 a(\000) p Fg(i) p Fj(\(1) p Ff(\000) p Fg(\014) p Fj 1501 579 a(\)) p Fg(\015) p Fj 1568 579 a(\() p Fg(x) p Fj(;) s(^) p Fg 1655 579 a(e) p Fj 1689 579 a(\)) p Fm 1736 620 a(~) p Fl 1720 620 a(') p Fj 1784 635 a(sc) p Fm 1848 620 a(\() p Fl(x=h) p Fm(;) p Fl 2090 620 a(!) p Ff 2151 635 a(\000) p Fm 2209 620 a(\)) t(~) p Fl 2247 620 a(v) p Ff 2294 635 a(\000) p Fl 2354 620 a(w) p Fj 2427 579 a(+) p Fm 2502 620 a(\() p Fl 2539 620 a(@) p Fj 2590 635 a(2) p Fl 2630 620 a(w) p Fm 2703 620 a(\)) p 2757 567 64 4 v Fl 2757 620 a(') p Ff 2821 644 a(\000) p Fm 2880 620 a(\() p Fl(x=h) p Fm(\)) p Fl 3133 620 a(dx) p Fm 234 845 a(=) p Fl 393 845 a(e) p Ff 438 804 a(\000) p Fg(i) p Fj(2) p Fg(\014) s(\031) p Fh 659 724 a(\024) p Fl 703 845 a(e) p Ff 748 804 a(\000) p Fg(i) p Fj(\(1) p Ff(\000) p Fg(\014) p Fj 987 804 a(\)\() p Fg(\031) p Ff 1084 804 a(\000) p Fg(\015) p Fe 1175 813 a(\000) p Fj 1229 804 a(\)) p Fh 1277 728 a(Z) p Fl 1377 845 a(e) p Ff 1422 804 a(\000) p Fg(i) p Fj(\(1) p Ff(\000) p Fg(\014) p Fj 1661 804 a(\)) p Fg(\015) p Fj 1728 804 a(\() p Fg(x) p Fj(;) s(^) p Fg 1815 804 a(e) p Fj 1849 804 a(\)) p Fm 1896 845 a(~) p Fl 1880 845 a(') p Fj 1944 860 a(sc) p Fm 2008 845 a(\() p Fl(x=h) p Fm(;) p Fl 2250 845 a(!) p Ff 2311 860 a(\000) p Fm 2369 845 a(\)) t(~) p Fl 2407 845 a(v) p Ff 2454 860 a(\000) p Fl 2513 845 a(w) p Fj 2586 804 a(+) p Fm 2661 845 a(\() p Fl(@) p Fj 2750 860 a(2) p Fl 2790 845 a(w) p Fm 2863 845 a(\)) p 2917 792 V Fl 2917 845 a(') p Ff 2981 869 a(\000) p Fm 3040 845 a(\() p Fl(x=h) p Fm(\)) p Fl 3293 845 a(dx) p Fh 3399 724 a(\025) p Fm 0 1090 a(and) p 194 1090 a(w) m(e) p 342 1090 a(apply) p 615 1090 a(Lemma) p 968 1090 a(6.5) p 1130 1090 a(with) p Fl 1356 1090 a(\014) p Fm 1454 1090 a(replaced) p 1843 1090 a(b) m(y) p 1983 1090 a(1) p Fi 2057 1090 a(\000) p Fl 2160 1090 a(\014) p Fm 2258 1090 a(to) p 2382 1090 a(the) p 2554 1090 a(in) m(tegral) p 2914 1090 a(in) p 3032 1090 a(the) p 3205 1090 a(brac) m(k) m(et.) 0 1211 y(Then) p Fl 255 1211 a(I) p Fm 338 1211 a(has) p 512 1211 a(the) p 680 1211 a(leading) p 1016 1211 a(term) p Fl 402 1424 a(e) p Ff 447 1383 a(\000) p Fg(i) p Fj(2) p Fg(\014) s(\031) p Fh 668 1328 a(\020) p Fi 717 1424 a(\000) p Fm(2) p Fl(i) p Fm(\(\(1) p Fi 1024 1424 a(\000) p Fl 1123 1424 a(\014) p Fm 1184 1424 a(\)) p Fi 1244 1424 a(\000) p Fm 1344 1424 a(1) p Fl(=) p Fm(2\)) p 1546 1424 a(sin) o(\(1) p Fi 1773 1424 a(\000) p Fl 1873 1424 a(\014) p Fm 1934 1424 a(\)) p Fl(\031) t(e) p Ff 2076 1383 a(\000) p Fg(i) p Fj(\(1) p Ff(\000) p Fg(\014) p Fj 2315 1383 a(\)) p Fg(\031) p Fh 2390 1328 a(\021) p Fl 2456 1424 a(h) p Fm 2540 1424 a(=) p Fi 2643 1424 a(\000) p Fl(ik) p Fj 2804 1439 a(0) p Fl 2844 1424 a(e) p Ff 2889 1383 a(\000) p Fg(i\014) s(\031) p Fl 3058 1424 a(h:) p Fm 0 1651 a(This) p 223 1651 a(is) p 321 1651 a(just) p 514 1651 a(the) p 682 1651 a(second) p 997 1651 a(term) p 1230 1651 a(obtained) p 1631 1651 a(from) p 1861 1651 a(\010) p Ff 1931 1615 a(\000) 1931 1676 y(\000) p Fm 1991 1651 a(.) p Fn 146 1890 a(10.) p 332 1890 a(App) s(endix) p 852 1890 a(:) p 943 1890 a(Pro) s(of) p 1257 1890 a(of) p 1390 1890 a(Prop) s(osition) p 2001 1890 a(5.2.) p Fm 2273 1890 a(W) p 2365 1890 a(e) p 2445 1890 a(end) p 2633 1890 a(the) p 2806 1890 a(pap) s(er) p 3084 1890 a(b) m(y) p 3224 1890 a(pro) m(ving) 0 2010 y(Prop) s(osition) p 525 2010 a(5.2) p 682 2010 a(whic) m(h) p 961 2010 a(remains) p 1325 2010 a(unpro) m(v) m(ed.) p Fb 0 2178 a(Pr) p 102 2178 a(o) p 147 2178 a(of) p 271 2178 a(of) p 394 2178 a(Pr) p 496 2178 a(op) p 591 2178 a(osition) p 921 2178 a(5.2.) p Fm 1178 2178 a(W) p 1270 2178 a(e) p 1356 2178 a(b) s(egin) p 1629 2178 a(b) m(y) p 1774 2178 a(recalling) p 2174 2178 a(the) p 2352 2178 a(notation:) p 2799 2178 a(the) p 2977 2178 a(eigenfunction) p Fl 0 2299 a(') p Fm(\() p Fl(x) p Fm(;) p Fl 201 2299 a(!) p Fm 266 2299 a(\)) p 336 2299 a(under) p 612 2299 a(consideration) p 1209 2299 a(admits) p 1529 2299 a(the) p 1697 2299 a(decomp) s(osition) p Fl 2340 2299 a(') p Fm 2431 2299 a(=) p Fl 2535 2299 a(') p Fj 2599 2314 a(in) p Fm 2684 2299 a(+) p Fl 2782 2299 a(') p Fj 2846 2314 a(sc) p Fm 2909 2299 a(,) p 2969 2299 a(where) p Fl 489 2512 a(') p Fj 553 2527 a(in) p Fm 616 2512 a(\() p Fl(x) p Fm(;) p Fl 753 2512 a(!) p Fm 818 2512 a(\)) p 883 2512 a(=) p 987 2512 a(exp) q(\() p Fl(i\014) p 1268 2512 a(\033) p Fm 1327 2512 a(\)) p Fl(') p Fj 1429 2527 a(0) p Fm 1468 2512 a(\() p Fl(x) p Fm(;) p Fl 1605 2512 a(!) p Fm 1670 2512 a(\)) p 1735 2512 a(=) p 1839 2512 a(exp) q(\() p Fl(i\014) p 2120 2512 a(\033) p Fm 2179 2512 a(\)) p 2234 2512 a(exp\() p Fl(iE) p Fj 2531 2471 a(1) p Fg(=) p Fj(2) p Fl 2641 2512 a(x) p Fi 2719 2512 a(\001) p Fl 2769 2512 a(!) p Fm 2834 2512 a(\)) p Fl 489 2720 a(') p Fj 553 2735 a(sc) p Fm 617 2720 a(\() p Fl(x) p Fm(;) p Fl 754 2720 a(!) p Fm 819 2720 a(\)) p 884 2720 a(=) p Fi 987 2720 a(\000) p Fm 1074 2652 a(sin) p Fl 1211 2652 a(\014) p 1272 2652 a(\031) p 1074 2697 256 4 v 1173 2788 a(\031) p Fh 1374 2603 a(Z) p Fm 1473 2720 a(exp) q(\() p Fl(ih) p Ff 1749 2679 a(\000) p Fj(1) p Fl 1844 2720 a(E) p Fj 1922 2679 a(1) p Fg(=) p Fj(2) p Fi 2032 2720 a(j) p Fl(x) p Fi(j) p Fm 2160 2720 a(cosh) p Fl 2361 2720 a(t) p Fm(\)) p Fh 2451 2574 a( ) p Fl 2623 2652 a(e) p Ff 2668 2616 a(\000) p Fg(\014) s(t) p 2526 2697 366 4 v Fl 2526 2788 a(e) p Ff 2571 2759 a(\000) p Fg(t) p Fm 2678 2788 a(+) p Fl 2776 2788 a(e) p Fg 2821 2759 a(i\033) p Fh 2902 2574 a(!) p Fl 3001 2720 a(dt) p 3104 2720 a(e) p Fg 3149 2679 a(i\033) p Fm 0 2995 a(with) p Fl 232 2995 a(\033) p Fm 335 2995 a(=) p Fl 455 2995 a(\033) p Fm 514 2995 a(\() p Fl(x) p Fm(;) p Fl 651 2995 a(!) p Fm 716 2995 a(\)) p 797 2995 a(=) p Fl 917 2995 a(\015) p Fm 973 2995 a(\() p Fl(x) p Fm(;) p Fl 1110 2995 a(!) p Fm 1175 2995 a(\)) p Fi 1241 2995 a(\000) p Fl 1347 2995 a(\031) p Fm 1448 2995 a(\(see) p 1654 2995 a(\(5.6\)) p 1896 2995 a(and) p 2096 2995 a(\(5.7\)\).) p 2433 2995 a(F) p 2489 2995 a(or) p 2618 2995 a(brevit) m(y) p 2909 2995 a(,) p 2982 2995 a(w) m(e) p 3135 2995 a(pro) m(v) m(e) p 3408 2995 a(the) 0 3116 y(prop) s(osition) p 526 3116 a(for) p 688 3116 a(the) p 869 3116 a(case) p Fl 1089 3116 a(!) p Fm 1203 3116 a(=) p Fl 1329 3116 a(!) p Ff 1390 3131 a(\000) p Fm 1499 3116 a(=) p 1625 3116 a(\(0) p Fl(;) p Fm 1756 3116 a(1\),) p 1919 3116 a(and) p 2121 3116 a(w) m(e) p 2278 3116 a(write) p Fl 2541 3116 a(') p Fm(\() p Fl(x) p Fm(\)) p 2782 3116 a(for) p Fl 2944 3116 a(') p Fm(\() p Fl(x) p Fm(;) p Fl 3145 3116 a(!) p Ff 3206 3131 a(\000) p Fm 3265 3116 a(\)) p 3348 3116 a(\(and) 0 3236 y(similarly) p 399 3236 a(for) p Fl 548 3236 a(') p Fj 612 3251 a(in) p Fm 707 3236 a(and) p Fl 897 3236 a(') p Fj 961 3251 a(sc) p Fm 1024 3236 a(\).) p 1133 3236 a(W) p 1225 3236 a(e) p 1301 3236 a(w) m(ork) p 1539 3236 a(in) p 1653 3236 a(the) p 1821 3236 a(co) s(ordinate) p 2300 3236 a(system) p 2624 3236 a(\(6.2\)) p 2857 3236 a(:) p Fl 580 3449 a(x) p Fm 663 3449 a(=) p 767 3449 a(\() p Fl(x) p Fj 860 3464 a(1) p Fl 899 3449 a(;) p 943 3449 a(x) p Fj 998 3464 a(2) p Fm 1038 3449 a(\)) p 1104 3449 a(=) p 1207 3449 a(\() p Fi(\000j) p Fl(x) p Fi(j) p Fm 1450 3449 a(sin) p Fl 1586 3449 a(\027) q(;) p Fi 1679 3449 a(j) p Fl(x) p Fi(j) p Fm 1807 3449 a(cos) p Fl 1954 3449 a(\027) p Fm 2008 3449 a(\)) p Fl(;) p 2285 3449 a(\027) p Fm 2367 3449 a(=) p Fl 2471 3449 a(\015) p Fm 2527 3449 a(\() p Fl(x) p Fm(\)) p Fi 2680 3449 a(\000) p Fl 2780 3449 a(\031) t(=) p Fm(2) p Fl(:) p Fm 0 3663 a(Then) p Fl 817 3783 a(\034) p Fm 870 3783 a(\() p Fl(x;) p 1007 3783 a(!) p Ff 1068 3798 a(\000) p Fm 1127 3783 a(\)) p 1193 3783 a(=) p Fl 1296 3783 a(\015) p Fm 1352 3783 a(\() p Fl(x) p Fm 1473 3783 a(:) p Fi 1528 3783 a(\000) p Fl(!) p Ff 1666 3798 a(\000) p Fm 1725 3783 a(\)) p Fi 1785 3783 a(\000) p Fl 1885 3783 a(\031) p Fm 1972 3783 a(=) p Fl 2075 3783 a(\015) p Fm 2131 3783 a(\() p Fl(x) p Fm(\)) p Fi 2285 3783 a(\000) p Fl 2384 3783 a(\031) t(=) p Fm(2) p 2568 3783 a(=) p Fl 2672 3783 a(\027) p Fm 0 3955 a(and) p 190 3955 a(it) p 287 3955 a(follo) m(ws) p 608 3955 a(b) m(y) p 743 3955 a(assumption) p 1259 3955 a(that) p Fi 759 4168 a(j) p Fl(\027) p Fi 841 4168 a(j) p 896 4168 a(\024) p Fl 1002 4168 a(c) p 1061 4168 a(h) p Fj 1117 4127 a(1) p Ff(\000) p Fg(") p Fl 1243 4168 a(;) p Fi 1482 4168 a(j) p Fl(x) p Fj 1565 4183 a(1) p Fi 1605 4168 a(j) p 1660 4168 a(\024) p Fl 1765 4168 a(c) p 1824 4168 a(h) p Fj 1880 4127 a(1) p Ff(\000) p Fg(") p Fl 2007 4168 a(;) p Fm 2246 4168 a(1) p Fl(=c) p 2413 4168 a(<) p 2516 4168 a(x) p Fj 2571 4183 a(2) p Fl 2639 4168 a(<) p 2742 4168 a(c) p Fm 3294 4168 a(\(10.1\)) 0 4381 y(for) p 153 4381 a(some) p 401 4381 a(constan) m(t) p Fl 799 4381 a(c) p 875 4381 a(>) p Fm 985 4381 a(1.) p 1116 4381 a(W) p 1208 4381 a(e) p 1288 4381 a(also) p 1488 4381 a(recall) p 1752 4381 a(the) p 1924 4381 a(relation) p 2285 4381 a(\(6.3\)) p 2522 4381 a(:) p Fl 2601 4381 a(\033) p Fm 2694 4381 a(=) p Fl 2804 4381 a(\033) p Fm 2863 4381 a(\() p Fl(x) p Fm(;) p Fl 3000 4381 a(!) p Ff 3061 4396 a(\000) p Fm 3120 4381 a(\)) p 3193 4381 a(=) p Fl 3303 4381 a(\027) p Fi 3382 4381 a(\000) p Fl 3484 4381 a(\031) p Fm 0 4501 a(or) p Fl 136 4501 a(\033) p Fm 250 4501 a(=) p Fl 381 4501 a(\027) p Fm 469 4501 a(+) p Fl 578 4501 a(\031) p Fm 686 4501 a(according) p 1141 4501 a(as) p Fl 1277 4501 a(\027) p 1387 4501 a(>) p Fm 1518 4501 a(0) p 1616 4501 a(or) p Fl 1752 4501 a(\027) p 1862 4501 a(<) p Fm 1993 4501 a(0,) p 2122 4501 a(so) p 2258 4501 a(that) p Fl 2485 4501 a(e) p Fg 2530 4465 a(i\033) p Fm 2657 4501 a(=) p Fi 2788 4501 a(\000) p Fl(e) p Fg 2910 4465 a(i\027) p Fm 2978 4501 a(.) p 3098 4501 a(By) p 3267 4501 a(\(10.1\),) p Fl 0 4622 a(e) p Fg 45 4586 a(i\014) s(\027) p Fm 183 4622 a(=) p 287 4622 a(1) p 358 4622 a(+) p Fl 456 4622 a(O) p Fm 534 4622 a(\() p Fl(h) p Fj 628 4586 a(1) p Ff(\000) p Fg(") p Fm 754 4622 a(\),) p 851 4622 a(and) p 1041 4622 a(hence) p 1312 4622 a(w) m(e) p 1456 4622 a(ha) m(v) m(e) p Fl 320 4897 a(') p Fj 384 4912 a(in) p Fm 447 4897 a(\() p Fl(x=h) p Fm(\)) p 711 4897 a(=) p Fh 814 4751 a(\() p Fl 922 4836 a(e) p Ff 967 4800 a(\000) p Fg(i\014) s(\031) p Fm 1153 4836 a(exp) q(\() p Fl(ih) p Ff 1429 4800 a(\000) p Fj(1) p Fl 1524 4836 a(E) p Fj 1602 4800 a(1) p Fg(=) p Fj(2) p Fl 1712 4836 a(x) p Fi 1790 4836 a(\001) p Fl 1839 4836 a(!) p Ff 1900 4851 a(\000) p Fm 1959 4836 a(\)) p 2019 4836 a(+) p Fl 2117 4836 a(O) p Fm 2195 4836 a(\() p Fl(h) p Fj 2289 4800 a(1) p Ff(\000) p Fg(") p Fm 2416 4836 a(\)) p Fl(;) p 2661 4836 a(\027) p 2743 4836 a(>) p Fm 2847 4836 a(0) p Fl(;) 922 4958 y(e) p Fg 967 4922 a(i\014) s(\031) p Fm 1098 4958 a(exp) q(\() p Fl(ih) p Ff 1374 4922 a(\000) p Fj(1) p Fl 1469 4958 a(E) p Fj 1547 4922 a(1) p Fg(=) p Fj(2) p Fl 1657 4958 a(x) p Fi 1735 4958 a(\001) p Fl 1785 4958 a(!) p Ff 1846 4973 a(\000) p Fm 1904 4958 a(\)) p 1964 4958 a(+) p Fl 2062 4958 a(O) p Fm 2140 4958 a(\() p Fl(h) p Fj 2234 4922 a(1) p Ff(\000) p Fg(") p Fm 2361 4958 a(\)) p Fl(;) p 2661 4958 a(\027) p 2743 4958 a(<) p Fm 2847 4958 a(0) p Fl(:) p Fm 3294 4897 a(\(10.2\)) 146 5167 y(W) p 238 5167 a(e) p 314 5167 a(analyze) p 664 5167 a(the) p 832 5167 a(b) s(eha) m(vior) p 1230 5167 a(of) p Fl 436 5438 a(') p Fj 500 5453 a(sc) p Fm 563 5438 a(\() p Fl(x=h) p Fm(\)) p 827 5438 a(=) 941 5370 y(sin) p Fl 1077 5370 a(\014) p 1138 5370 a(\031) p 941 5414 256 4 v 1039 5506 a(\031) p Fh 1240 5320 a(Z) p Fm 1339 5438 a(exp) q(\() p Fl(ih) p Ff 1615 5396 a(\000) p Fj(1) p Fl 1710 5438 a(E) p Fj 1788 5396 a(1) p Fg(=) p Fj(2) p Fi 1898 5438 a(j) p Fl(x) p Fi(j) p Fm 2026 5438 a(cosh) p Fl 2227 5438 a(t) p Fm(\)) p Fh 2317 5291 a( ) p Fl 2488 5370 a(e) p Ff 2533 5334 a(\000) p Fg(\014) s(t) p 2392 5414 364 4 v Fl 2392 5506 a(e) p Ff 2437 5477 a(\000) p Fg(t) p Fi 2544 5506 a(\000) p Fl 2644 5506 a(e) p Fg 2689 5477 a(i\027) p Fh 2766 5291 a(!) p Fl 2865 5438 a(dt) p 2968 5438 a(e) p Fg 3013 5396 a(i\027) p Fl 3080 5438 a(:) p Fm 1723 5753 a(42) p 90 rotate dyy eop %%Page: 43 43 43 42 bop Fm 0 407 a(T) p 62 407 a(o) p 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337 4017 a(0) p Fm 376 4002 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p 591 4002 a(=) p 694 4002 a(1.) p 813 4002 a(W) p 905 4002 a(e) p 981 4002 a(further) p 1309 4002 a(rewrite) p 1640 4002 a(it) p 1737 4002 a(in) p 1851 4002 a(the) p 2019 4002 a(form) 645 4271 y(exp) q(\() p Fl(ih) p Ff 921 4230 a(\000) p Fj(1) p Fi 1016 4182 a(p) p 1099 4182 V Fl 1099 4271 a(E) p Fi 1177 4271 a(j) p Fl(x) p Fi(j) p Fl(t) p Fj 1323 4230 a(2) p Fl 1362 4271 a(=) p Fm(2\)) p 1525 4271 a(=) p Fg 1672 4163 a(n) p Fh 1633 4188 a(X) p Fg 1629 4372 a(k) p Fj 1668 4372 a(=0) p Fl 1774 4271 a(\014) p Fg 1829 4286 a(k) p Fm 1872 4271 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p Fl(h) p Ff 2115 4230 a(\000) p Fg(k) p Fl 2212 4271 a(\027) p Fj 2266 4230 a(2) p Fg(k) p Fm 938 4588 a(+) p Fg 1077 4480 a(n) p Ff(\000) p Fj(1) p Fh 1083 4505 a(X) p Fg 1087 4689 a(l) p Fj 1109 4689 a(=0) p Fh 1226 4417 a(0) 1226 4566 y(@) p Fg 1380 4480 a(n) p Fh 1342 4505 a(X) p Fg 1299 4689 a(k) p Fj 1338 4689 a(=) p Fg(l) p Fj 1415 4689 a(+1) p Fl 1521 4588 a(\015) p Fg 1572 4603 a(k) r(l) p Fm 1636 4588 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p Fl(h) p Ff 1879 4547 a(\000) p Fg(k) p Fl 1976 4588 a(s) p Fj 2022 4547 a(2\() p Fg(k) p Ff 2123 4547 a(\000) p Fg(l) p Fj 2200 4547 a(\)) p Fh 2232 4417 a(1) 2232 4566 y(A) p Fl 2321 4588 a(\027) p Fj 2375 4547 a(2) p Fg(l) p Fm 938 4920 a(+) p Fg 1077 4812 a(n) p Ff(\000) p Fj(1) p Fh 1083 4837 a(X) p Fg 1087 5022 a(l) p Fj 1109 5022 a(=0) p Fh 1226 4749 a(0) 1226 4899 y(@) p Fg 1380 4812 a(n) p Fh 1342 4837 a(X) p Fg 1299 5022 a(k) p Fj 1338 5022 a(=) p Fg(l) p Fj 1415 5022 a(+1) p Fm 1525 4920 a(~) p Fl 1521 4920 a(\015) p Fg 1572 4935 a(k) r(l) p Fm 1636 4920 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(\)) p Fl(h) p Ff 1879 4879 a(\000) p Fg(k) p Fl 1976 4920 a(s) p Fj 2022 4879 a(2\() p Fg(k) p Ff 2123 4879 a(\000) p Fg(l) p Fj 2200 4879 a(\)) p Ff(\000) p Fj(1) p Fh 2322 4749 a(1) 2322 4899 y(A) p Fl 2411 4920 a(\027) p Fj 2465 4879 a(2) p Fg(l) p Fj 2522 4879 a(+1) p Fm 2639 4920 a(+) p Fl 2737 4920 a(O) p Fm 2815 4920 a(\() p Fl(h) p Fm(\)) p Fi(j) p Fl(t) p Fi(j) p Fl(:) p Fm 0 5213 a(W) p 92 5213 a(e) p 168 5213 a(insert) p 439 5213 a(this) p 630 5213 a(expansion) p 1083 5213 a(in) m(to) p Fl 601 5449 a(') p Fj 665 5464 a(3) p Fm 705 5449 a(\() p Fl(x=h) p Fm(\)) p 969 5449 a(=) p Fh 1072 5332 a(Z) p Ff 1118 5521 a(j) p Fg(t) p Ff(j) p Fg() p Fm 2765 3173 a(0) p Fl 1710 3294 a(i\031) p Fm 1825 3294 a(+) p Fl 1923 3294 a(O) p Fm 2001 3294 a(\() p Fl(h) p Fj 2095 3257 a(1) p Ff(\000) p Fj(2) p Fg(") p Fm 2256 3294 a(\)) p Fl(;) p 2579 3294 a(\027) p 2662 3294 a(<) p Fm 2765 3294 a(0) 0 3488 y(and) p 190 3488 a(the) p 358 3488 a(second) p 673 3488 a(one) p 851 3488 a(is) p 949 3488 a(sho) m(wn) p 1245 3488 a(to) p 1365 3488 a(b) s(e) p 1497 3488 a(expanded) p 1934 3488 a(as) p Fh 689 3619 a(Z) p Fg 735 3808 a(h) p Fd 776 3788 a(1) p Fc(=) p Fd(2+) p Fc(") p Fg 948 3808 a(<) p Ff(j) p Fg(t) p Ff(j) p Fg() p Fm 2842 5377 a(0) p Fi 1205 5499 a(\000) p Fl(i) p Fm 1332 5499 a(sin) p Fl 1469 5499 a(\014) p 1530 5499 a(\031) p Fm 1605 5499 a(exp) q(\() p Fl(ih) p Ff 1881 5463 a(\000) p Fj(1) p Fl 1976 5499 a(E) p Fj 2054 5463 a(1) p Fg(=) p Fj(2) p Fl 2164 5499 a(x) p Fi 2242 5499 a(\001) p Fl 2291 5499 a(!) p Ff 2352 5514 a(\000) p Fm 2411 5499 a(\)) p Fl(;) p 2657 5499 a(\027) p 2739 5499 a(<) p Fm 2842 5499 a(0) 1723 5753 y(45) p 90 rotate dyy eop %%Page: 46 46 46 45 bop Fm 0 407 a(with) p 222 407 a(remainder) p 683 407 a(term) p 916 407 a(ha) m(ving) p 1230 407 a(the) p 1398 407 a(form) p Fh 713 532 a(0) 713 682 y(@) p Fg 825 595 a(n) p Fh 787 620 a(X) p Fg 785 802 a(j) p Fj 818 802 a(=0) p Fl 924 703 a(b) p Fg 965 718 a(j) p Fm 1002 703 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(;) p Fl 1195 703 a(h) p Fm(\)) p Fl(\034) p Fg 1342 662 a(j) p Fh 1379 532 a(1) 1379 682 y(A) p Fm 1468 703 a(exp) q(\() p Fl(ih) p Ff 1744 662 a(\000) p Fj(1) p Fl 1839 703 a(E) p Fj 1917 662 a(1) p Fg(=) p Fj(2) p Fl 2027 703 a(x) p Fi 2104 703 a(\001) p Fl 2154 703 a(!) p Ff 2215 718 a(\000) p Fm 2274 703 a(\)) p 2334 703 a(+) p Fl 2432 703 a(O) p Fm 2510 703 a(\() p Fl(h) p Fj 2604 662 a(1) p Ff(\000) p Fj(4) p Fg(") p Fm 2766 703 a(\)) p Fl(;) p Fm 0 1005 a(where) p Fl 287 1005 a(b) p Fg 328 1020 a(j) p Fm 365 1005 a(\() p Fi(j) p Fl(x) p Fi(j) p Fm(;) p Fl 558 1005 a(h) p Fm(\)) p 690 1005 a(satis\014es) p 1054 1005 a(the) p 1228 1005 a(b) s(ound) p 1534 1005 a(in) p 1653 1005 a(the) p 1826 1005 a(prop) s(osition.) p 2393 1005 a(This,) p 2649 1005 a(together) p 3039 1005 a(with) p 3267 1005 a(\(10.2\),) 0 1126 y(completes) p 450 1126 a(the) p 618 1126 a(pro) s(of.) p Fa 1009 1126 a(2) p Fn 1509 1466 a(References) p Fm 92 1839 a([1]) p 244 1839 a(R.) p 381 1839 a(Adami) p 704 1839 a(and) p 900 1839 a(A.) p 1038 1839 a(T) p 1100 1839 a(eta,) p 1298 1839 a(On) p 1466 1839 a(the) p 1640 1839 a(Aharono) m(v{Bohm) p 2395 1839 a(Hamiltonian,) p Fb 3037 1839 a(L) p 3093 1839 a(ett.) p 3294 1839 a(Math.) 244 1959 y(Phys.) p Fn 520 1959 a(43) p Fm 665 1959 a(\(1998\),) p 995 1959 a(43{53.) 92 2161 y([2]) p 244 2161 a(G.) p 392 2161 a(N.) p 536 2161 a(Afanasiev,) p Fb 1025 2161 a(T) p 1088 2161 a(op) p 1183 2161 a(olo) p 1303 2161 a(gic) p 1418 2161 a(al) p 1536 2161 a(E\013e) p 1702 2161 a(cts) p 1865 2161 a(in) p 1995 2161 a(Quantum) p 2436 2161 a(Me) p 2563 2161 a(chanics) p Fm(,) p 2998 2161 a(Klu) m(w) m(er) p 3346 2161 a(Aca-) 244 2281 y(demic) p 526 2281 a(Publishers) p 1000 2281 a(\(1999\).) 92 2483 y([3]) p 244 2483 a(Y.) p 384 2483 a(Aharono) m(v) p 839 2483 a(and) p 1037 2483 a(D.) p 1179 2483 a(Bohm,) p 1502 2483 a(Signi\014cance) p 2041 2483 a(of) p 2159 2483 a(electromagnetic) p 2866 2483 a(p) s(oten) m(tial) p 3286 2483 a(in) p 3408 2483 a(the) 244 2603 y(quan) m(tum) p 656 2603 a(theory) p 921 2603 a(,) p Fb 1027 2603 a(Phys.) p 1305 2603 a(R) p 1371 2603 a(ev.) p Fn 1534 2603 a(115) p Fm 1735 2603 a(\(1959\),) p 2065 2603 a(485{491.) 92 2805 y([4]) p 244 2805 a(W.) p 406 2805 a(O.) p 544 2805 a(Amrein,) p 923 2805 a(J.) p 1035 2805 a(M.) p 1186 2805 a(Jauc) m(h) p 1469 2805 a(and) p 1660 2805 a(K.) p 1798 2805 a(B.) p 1929 2805 a(Sinha,) p Fb 2230 2805 a(Sc) p 2325 2805 a(attering) p 2691 2805 a(The) p 2851 2805 a(ory) p 3026 2805 a(in) p 3147 2805 a(Quantum) 244 2926 y(Me) p 371 2926 a(chanics) p Fm(,) p 791 2926 a(W.) p 951 2926 a(A.) p 1084 2926 a(Benjamin,) p 1551 2926 a(Inc.) p 1754 2926 a(\(1977\).) 92 3128 y([5]) p 244 3128 a(L.) p 358 3128 a(Dabro) m(wski) p 834 3128 a(and) p 1017 3128 a(P) p 1075 3128 a(.) p 1129 3128 a(Sto) m(vicek,) p 1539 3128 a(Aharono) m(v{Bohm) p 2282 3128 a(e\013ect) p 2533 3128 a(with) p Fl 2749 3128 a(\016) p Fm 2796 3128 a({t) m(yp) s(e) p 3058 3128 a(in) m(teraction,) p Fb 244 3248 a(J.) p 360 3248 a(Math.) p 654 3248 a(Phys.) p Fn 930 3248 a(39) p Fm 1075 3248 a(\(1998\),) p 1405 3248 a(47{62.) 92 3450 y([6]) p 244 3450 a(L.) p 395 3450 a(H\177) p 468 3450 a(ormander,) p Fb 973 3450 a(The) p 1201 3450 a(A) n(nalysis) p 1620 3450 a(of) p 1763 3450 a(Line) p 1949 3450 a(ar) p 2103 3450 a(Partial) p 2460 3450 a(Di\013er) p 2705 3450 a(ential) p 3004 3450 a(Op) p 3124 3450 a(er) p 3205 3450 a(ators) p Fm 3481 3450 a(I,) 244 3570 y(Springer) p 634 3570 a(V) p 699 3570 a(erlag) p 938 3570 a(\(1983\).) 92 3772 y([7]) p 244 3772 a(H.) p 381 3772 a(Isozaki) p 711 3772 a(and) p 905 3772 a(H.) p 1042 3772 a(Kitada,) p 1400 3772 a(Scattering) p 1870 3772 a(matrices) p 2265 3772 a(for) p 2418 3772 a(t) m(w) m(o{b) s(o) s(dy) p 2870 3772 a(Sc) m(hr\177) p 3056 3772 a(odinger) p 3408 3772 a(op-) 244 3893 y(erators,) p Fb 643 3893 a(Sci.) p 837 3893 a(Pap) p 998 3893 a(ers) p 1159 3893 a(Col) p 1309 3893 a(l.) p 1398 3893 a(of) p 1513 3893 a(A) n(rts) p 1731 3893 a(and) p 1920 3893 a(Sci.,) p 2144 3893 a(T) p 2207 3893 a(okyo) p 2433 3893 a(Univ.) p Fn 2708 3893 a(35) p Fm 2853 3893 a(\(1985\),) p 3183 3893 a(81{107.) 92 4095 y([8]) p 244 4095 a(H.) p 381 4095 a(T.) p 515 4095 a(Ito) p 673 4095 a(and) p 867 4095 a(H.) p 1004 4095 a(T) p 1066 4095 a(am) m(ura,) p 1399 4095 a(Aharono) m(v{Bohm) p 2153 4095 a(e\013ect) p 2414 4095 a(in) p 2532 4095 a(scattering) p 2986 4095 a(b) m(y) p 3126 4095 a(p) s(oin) m(t{lik) m(e) 244 4215 y(magnetic) p 661 4215 a(\014elds) p 911 4215 a(at) p 1030 4215 a(large) p 1269 4215 a(separation,) p Fb 1814 4215 a(A) n(nn.) p 2059 4215 a(H.) p 2196 4215 a(Poinc) p 2437 4215 a(ar) n(\023) p 2529 4215 a(e) p Fn 2604 4215 a(2) p Fm 2693 4215 a(\(2001\),) p 3024 4215 a(309{359.) 92 4417 y([9]) p 244 4417 a(H.) p 380 4417 a(T.) p 514 4417 a(Ito) p 672 4417 a(and) p 865 4417 a(H.) p 1001 4417 a(T) p 1063 4417 a(am) m(ura,) p 1395 4417 a(Aharono) m(v{Bohm) p 2148 4417 a(e\013ect) p 2409 4417 a(in) p 2526 4417 a(scattering) p 2980 4417 a(b) m(y) p 3119 4417 a(a) p 3204 4417 a(c) m(hain) p 3465 4417 a(of) 244 4537 y(p) s(oin) m(t{lik) m(e) p 694 4537 a(magnetic) p 1111 4537 a(\014elds,) p Fb 1434 4537 a(Asymptotic) p 1948 4537 a(A) n(nalysis) p Fn 2337 4537 a(34) p Fm 2481 4537 a(\(2003\),) p 2812 4537 a(199{240.) 43 4739 y([10]) p 244 4739 a(H.) p 386 4739 a(T.) p 525 4739 a(Ito) p 688 4739 a(and) p 887 4739 a(H.) p 1029 4739 a(T) p 1091 4739 a(am) m(ura,) p 1430 4739 a(Semiclassical) p 2020 4739 a(analysis) p 2396 4739 a(for) p 2555 4739 a(magnetic) p 2981 4739 a(scattering) p 3440 4739 a(b) m(y) 244 4859 y(t) m(w) m(o) p 428 4859 a(solenoidal) p 878 4859 a(\014elds,) p Fb 1202 4859 a(J.) p 1318 4859 a(L) p 1374 4859 a(ondon) p 1668 4859 a(Math.) p 1952 4859 a(So) p 2052 4859 a(c.) p Fn 2170 4859 a(74) p Fm 2314 4859 a(\(2006\),) p 2645 4859 a(695{716.) 43 5061 y([11]) p 244 5061 a(Y.) p 403 5061 a(Nam) m(bu,) p 804 5061 a(The) p 1031 5061 a(Aharono) m(v{Bohm) p 1806 5061 a(problem) p 2212 5061 a(revisited,) p Fb 2666 5061 a(Nucle) p 2900 5061 a(ar) p 3050 5061 a(Phys.) p Fm(,) p Fn 3375 5061 a(579) p Fm 244 5182 a(\(2000\),) p 574 5182 a(590{616.) 43 5384 y([12]) p 244 5384 a(Y.) p 386 5384 a(Ohn) m(uki,) p 772 5384 a(Aharono) m(v{Bohm) p 1530 5384 a(k) m(ouk) p 1727 5384 a(a) p 1819 5384 a(\(in) p 1980 5384 a(Japanese\),) p 2470 5384 a(Butsurigaku) p 3034 5384 a(saizensen) p 3467 5384 a(9,) 244 5504 y(Ky) m(ouritsu) p 700 5504 a(syuppan) p 1088 5504 a(\(1984\).) 1723 5753 y(46) p 90 rotate dyy eop %%Page: 47 47 47 46 bop Fm 43 407 a([13]) p 244 407 a(S.) p 372 407 a(W.) p 546 407 a(Qian,) p 830 407 a(Z.) p 963 407 a(Y.) p 1110 407 a(Gu) p 1288 407 a(and) p 1492 407 a(G.) p 1643 407 a(Q.) p 1792 407 a(Xie,) p 2013 407 a(Aharono) m(v{Bohm) p 2777 407 a(scattering) p 3242 407 a(on) p 3392 407 a(t) m(w) m(o) 244 527 y(parallel) p 594 527 a(\015ux) p 790 527 a(lines) p 1017 527 a(of) p 1132 527 a(the) p 1303 527 a(same) p 1551 527 a(magnitude) p 2037 527 a(b) m(y) p 2176 527 a(the) p 2348 527 a(metho) s(d) p 2707 527 a(of) p 2822 527 a(path) p 3053 527 a(in) m(tegration,) p Fb 244 648 a(J.) p 360 648 a(Phys.) p 628 648 a(A) p 735 648 a(:) p 800 648 a(Math.) p 1084 648 a(Gen.) p Fn 1332 648 a(30) p Fm 1477 648 a(\(1997\),) p 1807 648 a(1273{1285.) 43 851 y([14]) p 244 851 a(M.) p 403 851 a(Reed) p 658 851 a(and) p 858 851 a(B.) p 996 851 a(Simon,) p Fb 1334 851 a(Metho) p 1593 851 a(ds) p 1727 851 a(of) p 1850 851 a(Mo) p 1982 851 a(dern) p 2217 851 a(Mathematic) p 2713 851 a(al) p 2831 851 a(A) n(nalysis) p Fm(,) p 3260 851 a(V) p 3325 851 a(ol) p 3443 851 a(I) s(I,) 244 971 y(Academic) p 691 971 a(Press,) p 975 971 a(\(1976\).) 43 1175 y([15]) p 244 1175 a(S.) p 381 1175 a(N.) p 536 1175 a(M.) p 708 1175 a(Ruijsenaars,) p 1289 1175 a(The) p 1513 1175 a(Aharono) m(v{Bohm) p 2285 1175 a(e\013ect) p 2565 1175 a(and) p 2777 1175 a(scattering) p 3251 1175 a(theory) p 3516 1175 a(,) p Fb 244 1295 a(A) n(nn.) p 488 1295 a(of) p 603 1295 a(Phys.) p Fn 879 1295 a(146) p Fm 1080 1295 a(\(1983\),) p 1410 1295 a(1{34.) 43 1499 y([16]) p 244 1499 a(P) p 302 1499 a(.) p 373 1499 a(Sto) m(vicek,) p 801 1499 a(Scattering) p 1278 1499 a(matrix) p 1606 1499 a(for) p 1766 1499 a(the) p 1945 1499 a(t) m(w) m(o{solenoid) p 2531 1499 a(Aharono) m(v{Bohm) p 3291 1499 a(e\013ect,) p Fb 244 1619 a(Phys.) p 522 1619 a(L) p 578 1619 a(ett.) p 762 1619 a(A) p Fn 867 1619 a(161) p Fm 1068 1619 a(\(1991\),) p 1398 1619 a(13{20.) 43 1822 y([17]) p 244 1822 a(P) p 302 1822 a(.) p 355 1822 a(Sto) m(vicek,) p 764 1822 a(Scattering) p 1224 1822 a(on) p 1353 1822 a(t) m(w) m(o) p 1530 1822 a(solenoids,) p Fb 2012 1822 a(Phys.) p 2287 1822 a(R) p 2353 1822 a(ev.) p 2516 1822 a(A) p Fn 2614 1822 a(48) p Fm 2752 1822 a(\(1993\),) p 3077 1822 a(3987{3990.) 43 2026 y([18]) p 244 2026 a(G.) p 388 2026 a(N.) p 529 2026 a(W) p 621 2026 a(atson,) p Fb 919 2026 a(A) p 1034 2026 a(T) p 1097 2026 a(r) p 1133 2026 a(e) p 1173 2026 a(atise) p 1411 2026 a(on) p 1558 2026 a(the) p 1727 2026 a(The) p 1887 2026 a(ory) p 2067 2026 a(of) p 2189 2026 a(Bessel) p 2495 2026 a(F) p 2552 2026 a(unctions) p Fm(,) p 3026 2026 a(2nd) p 3224 2026 a(edition,) 244 2146 y(Cam) m(bridge) p 740 2146 a(Univ) m(ersit) m(y) p 1209 2146 a(Press) p 1466 2146 a(\(1995\).) 43 2350 y([19]) p 244 2350 a(D.) p 386 2350 a(Y) p 451 2350 a(afaev,) p Fb 742 2350 a(Sc) p 837 2350 a(attering) p 1209 2350 a(The) p 1369 2350 a(ory) p 1549 2350 a(:) p 1638 2350 a(Some) p 1909 2350 a(old) p 2076 2350 a(and) p 2273 2350 a(new) p 2479 2350 a(pr) p 2565 2350 a(oblems) p Fm(,) p 2965 2350 a(Lec.) p 3180 2350 a(Notes) p 3462 2350 a(in) 244 2470 y(Math.,) p 561 2470 a(1735,) p 816 2470 a(Springer) p 1206 2470 a(\(2000\).) 1723 5753 y(47) p 90 rotate dyy eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0701271854605--