Content-Type: multipart/mixed; boundary="-------------0304280210435" This is a multi-part message in MIME format. ---------------0304280210435 Content-Type: text/plain; name="03-199.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-199.keywords" Dirac operator, Aharonov-Bohm field, Norm resovent convergence ---------------0304280210435 Content-Type: application/postscript; name="Tamura.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Tamura.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: Tamura.dvi %%Pages: 35 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR12 CMMI12 CMMI8 CMR8 CMMIB10 CMEX10 CMSY10 %%+ CMSY8 CMR6 CMTI12 LASY10 CMMI6 CMSY6 %%EndComments %DVIPSCommandLine: dvipsk -D600 -t a4size -P dl Tamura.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.04.28:1530 %%BeginProcSet: texc.pro %! 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20830ecee7b1e8d255203f38cb9836953ec52060d4677fe6b37c1ec290e3d0f1 59f9e8aca844ca7bb895752de8c88cb1b3eba7d2621c58d8555f00766a88023d 31d7436bafbc60b5fb22db28734d20854500924391770875079943e5f68ea624 7694216e901d01abdd85c3040788b1cecf074b66dad6a6be955b0dad331247a8 3b48638693a57653f83b5ec26914920314e357ce55b115377a0d21f2dde4afdb 7443f6ab1baca13d37c870c7dfd4043ed3d915d780b0cd1ba49fa9350ec8e3f2 e34789b0a66bad0a9e2a16bfc7ae57ec87760d57466c980d5d6eb80544492cf9 a5cc1707012bc016ba20c845d8998d41ac9b9f7a11a059cbe00278a78c2c9d4b 7ccc987f22d269dfa0500d041e87dd0583d20bb53c5bb57b8fc74a29914198b8 98159fc322eb7c59e616a367cd22d5af79f96064bae49b640766294a28e3bae3 382ea3da0dcfe565e3f43789abe3cd61e5b3e1e775509cf643a9cd5684bba248 038069e6800f46780bfcc267df45c5b098343200ef22f442857a6b658899fce9 1ca8d25f9cc0e0bb2b58e479bfc832e1d991c6dadc34d3287f8b05053e79c2a7 aa27cbe475b79eb4b3652d9ffc54d8fb101ddb70ecd0ccfbd0bd17d7c5c60007 4844cd61b298c3a122997c0d35f89df62f047a01d38b4a0f1ed477869561d02d bb1fa8e8bcf3cc162dd1d5ce2ec9c71b4d261b693502d3fa3375a096f648b777 152659e887ee841c434daae6b3b33b5cfab76c207e844b75cc67acad46b1bdc8 579b9d2ed70eb5d36d2786e24defdbe0b34b00e055dc43c4993956555d029f97 1203f073740ce7dc6bfb2894a565a316d28b029de7dabb6fec146af428959e6b 892bda91b8dfaba70d42ebce93e90f0905e0626b4171b6981beaf74701e91325 e4919a753e27db0cdb7bf9c32d5a0cdceb716fbb2c1b59ffd9cc376bb20a984f 35af6ecb7b3ebc8c9b1b1545f21ea901fa45c03582f5d76a9d27cee24bd9b872 428327bf58fc2cd4a6514ca729b5d66641d4d8d2ab898d80809e0cfc6b179c56 44aa2f38ee8437d3dd842ce1c7665ca6fb38186c5ac9dbe413c47d49cda25583 48bec1d4e32a8dae30244c22b0824de0d13cd1c15a103e6da3dbca1080e6969e db5c5a82562a207e5df0da836a084da92a0e74e5b0f9a38ab24b611fcfa24fda 503309002672efea80170cd50ab4dff01fb849b07f623a8cd5e235aff04335d9 28e10d6e8ecee02875df7582ac95717e36f4352bb5fff040a6b779df4a767b98 544000dd72c468082db9d25f7b9fa2b4b565d9ae82a30991b8fd2a56ef733717 f21062fe121ff93aca8198b598bfff18ed7ae5fa4c5d019ed447be1f028ffe40 3287ad8b5de044750460845106f0e8fe85827223005dbac2deba80e43502d76a e69307e977d17bde11c9b4837acb9b49633dceb5df065c3e99b8dc4134464ebe 63589241fb 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 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523dfa618d367b001af bfc9543651fadf6389c92ef4a113933bfb4ce45b9ec1da149da8266d7ae816ac 591763c1ce0975ca2c6fad4dbf00da2d5ea9005dfe188787b84606f607dcb299 dbd62d54c0d9a3f63151b4605487b20b6612bacb429274d9c41584d6b0364b8e 3d9974f806134b12b859a7d761a1cf69b88c3b8fcd7df349ecea60c16041cf86 b3759ca18300e771a59922287a619d7d1e85a6c05fd807d62fb128a85222d66a 5ffdfc23a68bf4b49d6cb703a4b61c83a49b8e965c46262f03314b3b201179ba 4523b7f14bc486d8c369a8681b7a2837f5f82810d48ab9c8063598298c56340e 20e031c2603386b7564b3ff929be77050ce216cf7ccca14fd4916821b5e568bc 46c3ae7c6c63e4bb5f9cff87417005f6403af598ac4fbf73ff557e9124485569 1327cc0942e6061e12c0f107926d130a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 20 /lessequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 63 /perpendicular put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a4261be7bd48981fe5d74f36597276d570bdc1ca4d7a29ec280a13e7 cf740be69a5d79aff1ac325360e35ace9b7338a0d639d1a12ea484c43a1ae98c 3b6388532dbf33a3d9d0269db68b7a40451f68e14ea905164d8cfdf7e01d1a3d 7d97a280fd7b1664708aa91fdec822b75cbca7e846cc17cf2c03e485367838a8 44339ad3194ef665a11f1e1a246d1b7d6e005d5fbe263fc4b151e730ab3dc8f3 1b19da178175dbbfacb789821ab7c3fa6d28c9cd518bd5874253ec2a04729533 a3d4cacd2e697e38807d1245e753873a16e5254326c439e988498e60fe374897 d383c6ffa145fd7617fe093cf56c9552dd4dc003ced67336a1e10389b649144d 962a3cf7c16f4a43338bcf35cfc5b54f87cc0caa974179179c34ed5eee919f83 df67b2c7d175a6d085e8421d6ccacbb0f4cd6c8d559dab50997048f5b1a471da 1ff0f75d7d139afd61742807ce6a1fc6729936a057cd8173e74801be42825b65 9305fe04c79a211e887b0fb6ed5390bde19d453e565632ce56dda290a03ab241 aadbe56c880165eef59873eef2c9ffd220d65eff2e3322a8068e2643e1e1c008 0da0805be372a695a845a90ba4ccce269b9a6c176bae719433268b4106fc6d22 505ef5edd55b4660e669b7dde83e8ada23e55f11c70338ecd1fb411addeba51a c636d6e8dc091f83efacf6831de17f12a7b5fc87c89e09d843ae091b46ab5f6e 5e46d27043de4d01947e1002be4a56e78d9687a71ce3f15f88edbaffa35c5d92 9fa33c171265777ab8ed26b5fd87fcaf281192056053c8a93d39d28439b593d4 35b8903c913d30c85bacf32968090c4d079c5d3790eb6067af0f02f4126f6dbe 911938ba7171991bf5ab584620eadbfb9bb93063719f8ef102d80175254cc8be 1c92457620a6252f45535f208d1dd6c692caac9ff9929760a855cbb244011f34 7faed936f928acf0d807e3880a62eee00687ae29c3e81be8ccc80b36870fc283 93e3323025505041dbba63cd5fd8b57da7ed0c0f894f740ac3069ecb378716cd 0cffbc77f9ff2ee7db34eaeb17b4f52be2f7bd8ed64d34f96e75086fbe6e12ea 6c028932c35e235580928de87604074455aa1b3090888ef5601f00632d9d72f3 fa0f8ef5c8bc49a5567113f3b3b43d627ddc269f9c4aab0b74daa208a124c1ce 364a6c3380a5e477c98ddad4061b22ca1aa45546fccc023d2a87a88c22842f63 a8bc9ccf1659f311e2198a5e305b9b35e13f693dca496fb2bfa28fe5aac97ba0 5d76a473d9fc9cf13676a9b3a47d55cdcfa77a30ed4ff84e3c1fa0f7497f95a9 c45ff10fbda9b154f7e319c572f548008c232416de15df297947b68feb274c9b e9f56947c74765d5db0fcfddde4db3de17056c2055bd0619d00014af46f16e83 3fcaa107788207b07683462554beb7126625aaaf82dbb2ea7fe4507c05855277 610572cc054ffd84a767dfd58ce26466499071d5c8b7eaf3dd4b4b0c34b57560 052e7c67830ab9ba6c29174b98381c316b6fb2db1c0f69450c6fed9bf04e598d c307e6793a988028e0130489ce443f0b0a9ae73b0095730b0018e29e14b752ac 523ddbda39ee0b493c6c396aa7cf4ab55d5d9a6bef9b3f795025c61978bde60f e03ea6837a1c239ae8245c6bad870e38fcfe10c8ab813979cdbbae96beea25d4 43042efcce6a882caacd0edcd12d1449a2287b60484c05d3072839150057a697 9d0e2bdc4f5d321223a2643fa5b5c61c70e7608f42d0e9fc7d09f6aea8ef73f1 24ca34058302338b066755ba0e9a6c02e213e25a554a81104625c6bbd2219d5c 1e01d362ab285389ac20607f73a8d2b7b6a06ac3fa8fe16313d919ee9f23cc83 cdb5c4169028721b7682d4130d0c0b3ac711858861c73ecf646d3f25316ab7a7 a3760ff18b5106365eee24fe9290ad3504c6093aeae56f5769538717e4251465 73d7c56c2fd2ebdab593a6b19ed37d7cf30704080a0a06a42081098e352f95dc 42cd72cee708c27425fba58800e717507bf6ebcef0c3837db5abb4b388a9a90f 1854c6657607bc6cc289 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath 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 29 /greatermuch put dup 33 /arrowright put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 68 /D put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c43002591893a571bbe4dd05506a93c40f517d06cb123975ca3614a4e4dad 46370c34f8d1b9212235a51bf544f5601e8b068a3bc1c9d55b08d2115eae8b2f c460cfd0316bcb531869e2fa9a909134580c9c7a1cc20aea7cd103ce37b64831 7b452e029ba1099d3683220ad92791ab32ea08f4894258ed244f4505393a6dfb de8da7c6c514d5a13c2a3b627521f9f56e1e7e79d8decaf64d752f82b21990fd 3ec95910a8ee3537f5833968c018338eb7d6e9979576f1b4da14e21b913105aa 5323c55c4b3bfd8b327b93bc239f83af98c2ef99eef48c61a7799b69a22a8874 d048211f016536ab1e46a861519f59fc03fd4c62d85fd9fd13b00531614ee78e 485ee532e760b66af956dcccbc06469cb7d2d23c2d1814d0a548d1c646d80b26 0270e661571028df79a0a4a1654955147eba5bd760c55aa20e6ff116e6717a5f 03b4a8da867cd14e5ee69bb63b32ed877af39a9e14905d84f586ec8b89272c70 33a90cabf0defb337956da64e790c5ec2f25646e780747c648076566521ddec4 b4dc5c5c1650fb821e6baa37aa4e1c7e23141365fb50781c4fc8afe7423ca2dc 9ebbd329256f421d2c67c7a77ac72fe09fe1ed2f2cb89577749c33ffdbfa4eba 0aa8a6ba019d96153e6c42811786eff6ee05aac66f58c9bdf52cb325f83144b4 8e93e2b2ce2e52f1216bdedf0f091d9772709e6da34be3687b3fb8fdad6138b8 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /parenleftBig put dup 17 /parenrightBig put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 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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 67 /C put dup 82 /R put dup 90 /Z 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 f4561d817fa7ad9921e00b0ec4cb9ef1385d0cedcd674a913817a073b819d430 39764d974e2cd27d64ba38f5d7d9adfccec89ceb8e5113b44ce155c5e6bdcea8 e1ee10945210cdc4824c2a430b8634fb64700017c6f0add309e659b9834cce8b 2bde330fc6f40a2473a640d8c3c0d0901feeecf7620e866a05e3873660cceb3e c1dc9a5c657735c99bf8f04452b3873508b37cd6a4cbb57805985018f9ceb655 9c40826b95bb224ff4d7463fc76137b670fd3b31a565f0f29e3537ebb0e2110c aef2455802e8abb8d8d97d1ab1ca8fd9f61d04f8ca870c17b30bad03e94dd07c 1bb5f6a234fdf8c80a6bbe8104664f9fa441105a3c802d2c9bd150ce61828d9e cd1de0a47f79800e882061341e026b6c6bd40cf46d0e9046872e2abb34619c8c e8067a5370bea95748640f12837c23cc9ddbbe06aa2fe9db82abc47841a983b6 24fe9fa980bd93aac62a9501d9b0e0dbb849d0b5d99fc86682e5af6cb8a8d412 e0b857bcc3fe2cf35a74161d0aea9cabd008ea6e7df8640646d96e58676ba8bc e3469dfe9a6a3260a5696a85f18809e5a3d9934249b576457ef2187840eb16b6 98500157483778085c711f35ec56891775599d9db32f65bc3620850c29af4ed0 2c2c9aaa4bd82c4ca7f1e9aba4005a6134f47745a846d70626f77c03fe4b2268 1122b6f6c461c71c175ffcb42d4f481e38821f2f31ac42997e1f23f75f1f1a85 3d6e2402977c85c7998d68b588e62876fb09cdd4e45a48e5638c4bb9d4de670c 05dc53f7ca728f5164426b97223a8af8c433600536afc31d109310bea86a8239 02f31bbb1e858227ffebfc525f378553f253e804aa47a3c4dc012dbf93684916 4b813878cd84ff27a369a7bcfe938d3bbd4bfa51ed09d3f7712dc09acd46b041 8a76d9fa8117fbb5618799f78c77aa949ca45b8dd6b607234036018d5e68f5b5 95cb1d9979e3e5b6b0a1918309d214249764012f8a48d04f982c77e200c5eafe f9a69e88da4b7123edb13507dd50c20441fe6cbf228ac1dd66c0c96138c40a63 0e8e674f27aa7459e458b9bf382cb66ef35ec3240246e67ac26ac0350ad5de1d 78750689ec35282934d1b9216a7c98db3c0ae84989bf9b94e5ce8c9d05d420ca 32437bf7fdfbcd1dde1ba5 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 61 /equal put dup 99 /c put dup 108 /l put dup 111 /o put dup 116 /t put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 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6fd7acc9df3e3003942d88e33b310df8f98e6e75006ad46c25da551a00bde736 2262e8d9144a744c3730aff86d61a5075f2816997c20650ac96b4282f227bcd3 cea95efbe537f2ed4535e8f3300a85f426cb30c7ad94b7845ad415dd06ef8655 352044f6dca01f791c7c7b172dc4645109a0925b497479661ab816ebdc2e4025 deab39bac4a04170231054 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 16 /zeta put dup 18 /theta put dup 20 /kappa put dup 23 /nu put dup 25 /pi put dup 27 /sigma put dup 34 /epsilon put dup 39 /phi1 put dup 59 /comma put dup 61 /slash put dup 65 /A put dup 66 /B put dup 68 /D put dup 72 /H put dup 76 /L put dup 77 /M put dup 85 /U put dup 90 /Z put dup 99 /c 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 114 /r put dup 115 /s put dup 116 /t put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec 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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 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 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 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 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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aafe40cb00926886e7ea26951fadbe0ad912cd3d73bab9faa6a22dc8f9f50f7f c40af903fc93d0403d4e314e6e79bb31455f1243b1968bcc07525d13d268d063 b97f22e637defaefa5e670a12b66bbab87209b689b702f337c6b367cdced532f 888c6acd07032a41089483a2b9e7918771487ecd5da59e82cf6db83f639f727f 2896fac330ee685cb34ac2196ed85a3bc8e29ad75946d462e1b2cd1ef6135199 42c6d40aea62416751bd38007153b0f83566df35b287245ab4d584c65a9f6a40 8af110bfe30c457d0e141016b9017cd1c7c08d 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 11 /ff put dup 12 /fi put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 73 /I put dup 75 /K put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 123 /endash put dup 127 /dieresis 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 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b3a410e9898bb152342693517ae3e395f07edbe8ddc58f8ddc17dea05ff79886 38b0c11188df18f9d20f5fab5729f54ca554523f88e779993cef8f1556921128 30defbd97025fcfd00fae96d8328cae6bdfdf8a66a6ae7ec2d27203ee7606bc0 0cd5ccdfad6b5001 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 5 /Pi put dup 6 /Sigma put dup 8 /Phi put dup 9 /Psi put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 28 /oslash put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 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 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 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3[ 25 33 32 4[ 62 21 37 29 24 41 4[ 31 8[ 48 4[ 48 7[ 68 48 3[ 58 3[ 58 1[ 53 53 3[ 35 1[ 20 19[ 46 4[ 33 6[ 40 1[ 41 1[ 35 2[ 41 1[ 33 1[ 31 3[ 40 45 11[{ } 31 66.4176 /CMMI8 rf /Fl 133[ 45 48 55 70 47 56 1[ 46 44 43 49 47 58 85 29 51 40 33 56 47 48 45 51 42 41 51 6[ 67 57 81 1[ 57 66 57 60 74 77 63 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[{ } 77 99.6264 /CMMI12 rf /Fm 128[ 56 3[ 56 1[ 59 59 81 59 62 44 44 46 1[ 62 56 62 93 31 59 34 31 62 56 34 51 62 50 62 54 12[ 78 62 84 1[ 77 1[ 88 1[ 67 88 1[ 42 3[ 74 86 2[ 85 7[ 56 56 56 56 56 56 56 56 56 56 1[ 31 33[ 62 65 11[{ } 50 99.6264 /CMBX12 rf /Fn 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 3[ 27 1[ 27 1[ 73 73 100 73 73 70 54 72 1[ 66 76 73 89 61 76 50 35 73 77 64 66 75 70 69 73 3[ 76 1[ 27 27 49 49 49 49 49 49 49 49 49 49 49 27 33 27 76 1[ 38 38 11[ 49 8[ 49 4[ 81 54 54 57 1[ 76 70 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3319 2973 a(2) p Fn 3386 3010 a(and) 0 3130 y(it) p 97 3130 a(has) p 270 3130 a(the) p 437 3130 a(de\014ciency) p 884 3130 a(indices) p 1203 3130 a(\(1,1\).) p 1474 3130 a(If) p Fl 1571 3130 a(u) p Fg 1654 3130 a(2) p Fn 1748 3130 a([) p Fl(L) p Fj 1841 3094 a(2) p Fn 1881 3130 a(]) p Fj 1908 3094 a(2) p Fn 1980 3130 a(is) p 2077 3130 a(in) p 2190 3130 a(the) p 2357 3130 a(domain) p 2704 3130 a(of) p 2814 3130 a(some) p 3058 3130 a(self{adjoin) m(t) 0 3250 y(extension,) p 458 3250 a(then) p 681 3250 a(it) p 778 3250 a(b) s(eha) m(v) m(es) p 1142 3250 a(lik) m(e) p Fl 585 3527 a(u) p Fn 668 3527 a(=) p Fh 772 3381 a( ) p Fn 1006 3465 a(\() p Fl(u) p Ff 1100 3480 a(\000) p Fj(1) p Fn 1216 3465 a(+) p Fl 1314 3465 a(o) p Fn(\(1\)\)) p Fl(r) p Ff 1571 3429 a(\000) p Fk(\013) p Fn 879 3587 a(\() p Fl(u) p Ff 973 3602 a(\000) p Fj(2) p Fn 1089 3587 a(+) p Fl 1187 3587 a(o) p Fn(\(1\)\)) p Fl(e) p Fk 1442 3551 a(i\022) p Fl 1505 3587 a(r) p Ff 1552 3551 a(\000) p Fj(\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fh 1842 3381 a(!) p Fn 1930 3527 a(+) p Fl 2028 3527 a(o) p Fn(\(1\)) p Fl(;) p 2439 3527 a(r) p Fn 2513 3527 a(=) p Fg 2617 3527 a(j) p Fl(x) p Fg(j) p 2755 3527 a(!) p Fn 2882 3527 a(0) p Fl(;) p Fn 3343 3527 a(\(1.3\)) 0 3809 y(for) p 141 3809 a(some) p 377 3809 a(pair) p 569 3809 a(\() p Fl(u) p Ff 663 3824 a(\000) p Fj(1) p Fl 757 3809 a(;) p 801 3809 a(u) p Ff 857 3824 a(\000) p Fj(2) p Fn 950 3809 a(\)) p 1012 3809 a(in) p 1118 3809 a(the) p 1277 3809 a(p) s(olar) p 1521 3809 a(co) s(ordinate) p 1992 3809 a(system) p 2307 3809 a(\() p Fl(r) m(;) p 2430 3809 a(\022) p Fn 2478 3809 a(\)) p 2540 3809 a(under) p 2808 3809 a(assumption) p 3316 3809 a(\(1.2\).) 0 3930 y(The) p 205 3930 a(ratio) p Fl 443 3930 a(\024) p Fn 536 3930 a(=) p Fl 647 3930 a(iu) p Ff 736 3945 a(\000) p Fj(1) p Fl 831 3930 a(=u) p Ff 936 3945 a(\000) p Fj(2) p Fn 1067 3930 a(can) p 1250 3930 a(b) s(e) p 1388 3930 a(sho) m(wn) p 1689 3930 a(to) p 1813 3930 a(b) s(e) p 1951 3930 a(a) p 2037 3930 a(real) p 2231 3930 a(n) m(um) m(b) s(er) p 2591 3930 a(indep) s(enden) m(t) p 3149 3930 a(of) p Fl 3265 3930 a(u) p Fn(,) p 3386 3930 a(and) 0 4050 y(the) p 168 4050 a(self-adjoin) m(t) p 670 4050 a(extension) p Fl 1101 4050 a(H) p Fk 1182 4065 a(\024) p Fn 1259 4050 a(has) p 1433 4050 a(the) p 1601 4050 a(domain) p Fg 623 4270 a(D) p Fn 703 4270 a(\() p Fl(H) p Fk 822 4285 a(\024) p Fn 867 4270 a(\)) p 932 4270 a(=) p Fg 1036 4270 a(f) p Fl(u) p Fg 1169 4270 a(2) p Fn 1263 4270 a([) p Fl(L) p Fj 1356 4229 a(2) p Fn 1396 4270 a(]) p Fj 1423 4229 a(2) p Fn 1490 4270 a(:) p Fl 1545 4270 a(H) p Fk 1634 4229 a(D) p Fl 1697 4270 a(u) p Fg 1780 4270 a(2) p Fn 1875 4270 a([) p Fl(L) p Fj 1968 4229 a(2) p Fn 2007 4270 a(]) p Fj 2034 4229 a(2) p Fl 2074 4270 a(;) p 2164 4270 a(u) p Ff 2220 4285 a(\000) p Fj(1) p Fn 2336 4270 a(+) p Fl 2434 4270 a(i\024) p 2540 4270 a(u) p Ff 2596 4285 a(\000) p Fj(2) p Fn 2718 4270 a(=) p 2821 4270 a(0) p Fg(g) p Fn 3343 4270 a(\(1.4\)) 0 4490 y(parameterized) p 634 4490 a(b) m(y) p Fl 770 4490 a(\024;) p Fg 924 4490 a(\000) p 1024 4490 a(1) p Fl 1151 4490 a(<) p 1255 4490 a(\024) p Fg 1338 4490 a(\024) p 1444 4490 a(1) p Fn(,) p 1603 4490 a(where) p Fl 657 4710 a(u) p Ff 713 4725 a(\000) p Fj(1) p Fn 834 4710 a(=) p 962 4710 a(lim) p Ff 938 4774 a(j) p Fk(x) p Ff(j!) p Fj(0) p Fg 1139 4710 a(j) p Fl(x) p Fg(j) p Fk 1250 4669 a(\013) p Fl 1299 4710 a(u) p Fj 1355 4725 a(1) p Fn 1394 4710 a(\() p Fl(x) p Fn(\)) p Fl(;) p 1764 4710 a(u) p Ff 1820 4725 a(\000) p Fj(2) p Fn 1942 4710 a(=) p 2070 4710 a(lim) p Ff 2045 4774 a(j) p Fk(x) p Ff(j!) p Fj(0) p Fg 2247 4710 a(j) p Fl(x) p Fg(j) p Fj 2358 4669 a(1) p Ff(\000) p Fk(\013) p Fl 2497 4710 a(e) p Ff 2542 4669 a(\000) p Fk(i\022) p Fl 2660 4710 a(u) p Fj 2716 4725 a(2) p Fn 2755 4710 a(\() p Fl(x) p Fn(\)) 0 4988 y(for) p Fl 143 4988 a(u) p Fn 226 4988 a(=) p Fj 329 4952 a(t) p Fn 361 4988 a(\() p Fl(u) p Fj 455 5003 a(1) p Fl 494 4988 a(;) p 538 4988 a(u) p Fj 594 5003 a(2) p Fn 632 4988 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4413 a(a) p 1106 4413 a(resonance) p 1545 4413 a(state.) p 1820 4413 a(On) p 1976 4413 a(the) p 2138 4413 a(other) p 2387 4413 a(hand,) p Fl 2653 4413 a(L) p Fn(\() p Fl(A;) p 2874 4413 a(b) p Fn(\)) p 2980 4413 a(can) p 3153 4413 a(b) s(e) p 3280 4413 a(sho) m(wn) 0 4533 y(to) p 125 4533 a(ha) m(v) m(e) p 355 4533 a(no) p 496 4533 a(resonance) p 946 4533 a(state) p 1190 4533 a(at) p 1315 4533 a(zero) p 1526 4533 a(energy) p 1796 4533 a(.) p 1883 4533 a(Th) m(us) p 2136 4533 a(the) p 2309 4533 a(t) m(w) m(o) p 2498 4533 a(op) s(erators) p Fl 2935 4533 a(L) p Fn(\() p Fl(A;) p Fg 3156 4533 a(\006) p Fl(b) p Fn(\)) p 3351 4533 a(ha) m(v) m(e) 0 4654 y(the) p 163 4654 a(di\013eren) m(t) p 544 4654 a(sp) s(ectral) p 905 4654 a(prop) s(ert) m(y) p 1299 4654 a(at) p 1414 4654 a(zero) p 1615 4654 a(energy) p 1885 4654 a(.) p 1955 4654 a(It) p 2056 4654 a(seems) p 2329 4654 a(that) p 2536 4654 a(this) p 2721 4654 a(essen) m(tial) p 3105 4654 a(asp) s(ect) p 3402 4654 a(has) 0 4774 y(not) p 173 4774 a(b) s(een) p 404 4774 a(recognized) p 881 4774 a(in) p 994 4774 a(earlier) p 1293 4774 a(ph) m(ysical) p 1667 4774 a(literatures.) 146 4939 y(W) p 238 4939 a(e) p 313 4939 a(discuss) p 639 4939 a(the) p 806 4939 a(e\013ect) p 1062 4939 a(of) p 1172 4939 a(p) s(erturbations) p 1781 4939 a(b) m(y) p 1915 4939 a(scalar) p 2191 4939 a(p) s(oten) m(tials) p 2641 4939 a(in) p 2753 4939 a(the) p 2920 4939 a(latter) p 3185 4939 a(sections.) 0 5060 y(The) p 204 5060 a(obtained) p 608 5060 a(result) p 883 5060 a(\(Theorem) p 1336 5060 a(5.1\)) p 1534 5060 a(strongly) p 1914 5060 a(dep) s(ends) p 2295 5060 a(on) p 2434 5060 a(\015ux) p Fl 2629 5060 a(\013) p Fn 2692 5060 a(,) p 2755 5060 a(and) p 2948 5060 a(the) p 3120 5060 a(limit) p 3356 5060 a(self{) 0 5180 y(adjoin) m(t) p 329 5180 a(extension) p Fl 759 5180 a(H) p Fk 840 5195 a(\024) p Fn 916 5180 a(c) m(hanges) p 1275 5180 a(at) p Fl 1393 5180 a(\013) p Fn 1484 5180 a(=) p 1587 5180 a(1) p Fl(=) p Fn(2.) p 1803 5180 a(What) p 2076 5180 a(is) p 2172 5180 a(in) m(teresting) p 2651 5180 a(is) p 2748 5180 a(that) p 2958 5180 a(it) p 3054 5180 a(o) s(ccurs) p 3354 5180 a(ev) m(en) 0 5301 y(for) p 149 5301 a(small) p 404 5301 a(p) s(erturbation) p 976 5301 a(of) p 1087 5301 a(scalar) p 1364 5301 a(p) s(oten) m(tials.) p 1852 5301 a(W) p 1944 5301 a(e) p 2020 5301 a(set) p Fl 1371 5504 a(V) p Fk 1428 5519 a(") p Fn 1465 5504 a(\() p Fl(x) p Fn(\)) p 1624 5504 a(=) p Fl 1728 5504 a(") p Ff 1774 5463 a(\000) p Fj(1) p Fl 1868 5504 a(V) p Fn 1946 5504 a(\() p Fl(x=") p Fn(\)) 1747 5753 y(4) p 90 rotate dyy eop %%Page: 5 5 5 4 bop Fn 0 407 a(for) p Fl 149 407 a(V) p Fg 255 407 a(2) p Fl 349 407 a(C) p Ff 426 371 a(1) p Fj 419 431 a(0) p Fn 501 407 a(\() p Fi(R) p Fj 626 365 a(2) p Fg 693 407 a(!) p Fi 821 407 a(R) p Fn(\),) p 1006 407 a(and) p 1195 407 a(w) m(e) p 1339 407 a(de\014ne) p Fl 1621 407 a(H) p Fk 1702 422 a(") p Fn 1738 407 a(\() p Fl(V) p Fk 1833 422 a(") p Fn 1870 407 a(\)) p 1940 407 a(b) m(y) p Fl 918 627 a(H) p Fk 999 642 a(") p Fn 1036 627 a(\() p Fl(V) p Fk 1131 642 a(") p Fn 1167 627 a(\)) p 1233 627 a(=) p Fl 1336 627 a(H) p Fk 1425 585 a(D) 1417 651 y(") p Fn 1511 627 a(+) p Fl 1609 627 a(V) p Fk 1666 642 a(") p Fn 1730 627 a(=) p Fl 1834 627 a(\033) p Fj 1889 642 a(1) p Fl 1929 627 a(\027) p Fj 1977 642 a(1) p Fk(") p Fn 2071 627 a(+) p Fl 2169 627 a(\033) p Fj 2224 642 a(2) p Fl 2264 627 a(\027) p Fj 2312 642 a(2) p Fk(") p Fn 2406 627 a(+) p Fl 2504 627 a(V) p Fk 2561 642 a(") p Fl 2598 627 a(:) p Fn 3294 627 a(\(1.12\)) 0 846 y(Roughly) p 384 846 a(sp) s(eaking,) p 809 846 a(the) p 972 846 a(op) s(erator) p Fl 1360 846 a(H) p Fn 1461 846 a(+) p Fl 1549 846 a(V) p Fn 1655 846 a(=) p Fl 1759 846 a(\033) p Fj 1814 861 a(1) p Fl 1854 846 a(\027) p Fj 1902 861 a(1) p Fn 1953 846 a(+) p Fl 2041 846 a(\033) p Fj 2096 861 a(2) p Fl 2136 846 a(\027) p Fj 2184 861 a(2) p Fn 2236 846 a(+) p Fl 2324 846 a(V) p Fn 2431 846 a(is) p 2524 846 a(said) p 2720 846 a(to) p 2834 846 a(ha) m(v) m(e) p 3054 846 a(a) p 3131 846 a(resonance) 0 967 y(state) p 235 967 a(at) p 351 967 a(zero) p 553 967 a(energy) p 823 967 a(,) p 880 967 a(if) p 966 967 a(the) p 1130 967 a(equation) p 1524 967 a(\() p Fl(H) p Fn 1665 967 a(+) p Fl 1755 967 a(V) p Fn 1834 967 a(\)) p Fl(u) p Fn 1955 967 a(=) p 2059 967 a(0) p 2136 967 a(admits) p 2453 967 a(a) p 2530 967 a(b) s(ounded) p 2924 967 a(but) p 3099 967 a(not) p 3269 967 a(square) 0 1087 y(in) m(tegrable) p 446 1087 a(solution.) p 851 1087 a(The) p 1046 1087 a(precise) p 1360 1087 a(de\014nition) p 1787 1087 a(is) p 1879 1087 a(form) m(ulated) p 2366 1087 a(in) p 2473 1087 a(section) p 2793 1087 a(5) p 2868 1087 a(\(De\014nition) p 3354 1087 a(5.1\).) 0 1208 y(If) p Fl 105 1208 a(H) p Fn 221 1208 a(+) p Fl 324 1208 a(V) p Fn 443 1208 a(do) p 586 1208 a(not) p 767 1208 a(ha) m(v) m(e) p 1000 1208 a(a) p 1089 1208 a(resonance) p 1542 1208 a(state) p 1788 1208 a(at) p 1915 1208 a(zero) p 2129 1208 a(energy) p 2399 1208 a(,) p 2469 1208 a(then) p Fl 2699 1208 a(H) p Fk 2780 1223 a(") p Fn 2816 1208 a(\() p Fl(V) p Fk 2911 1223 a(") p Fn 2948 1208 a(\)) p 3026 1208 a(is) p 3132 1208 a(pro) m(v) m(ed) p 3457 1208 a(to) 0 1328 y(con) m(v) m(erge) p 401 1328 a(to) p Fl 522 1328 a(H) p Ff 603 1343 a(1) p Fn 712 1328 a(for) p 863 1328 a(0) p Fl 944 1328 a(<) p 1051 1328 a(\013) p 1145 1328 a(<) p Fn 1252 1328 a(1) p Fl(=) p Fn(2) p 1433 1328 a(and) p 1625 1328 a(to) p Fl 1747 1328 a(H) p Fj 1828 1343 a(0) p Fn 1902 1328 a(for) p 2053 1328 a(1) p Fl(=) p Fn(2) p Fl 2231 1328 a(<) p 2338 1328 a(\013) p 2432 1328 a(<) p Fn 2539 1328 a(1) p 2623 1328 a(in) p 2739 1328 a(the) p 2909 1328 a(norm) p 3166 1328 a(resolv) m(en) m(t) 0 1448 y(sense.) p 288 1448 a(If) p Fl 385 1448 a(\013) p Fn 476 1448 a(=) p 579 1448 a(1) p Fl(=) p Fn(2,) p 785 1448 a(then) p Fl 1007 1448 a(H) p Fk 1088 1463 a(") p Fn 1124 1448 a(\() p Fl(V) p Fk 1219 1463 a(") p Fn 1256 1448 a(\)) p 1326 1448 a(is) p 1424 1448 a(con) m(v) m(ergen) m(t) p 1911 1448 a(to) p Fl 2030 1448 a(H) p Fk 2111 1463 a(\024) p Fn 2188 1448 a(for) p 2336 1448 a(some) p Fl 2580 1448 a(\024) p Fn 2669 1448 a(determined) p 3178 1448 a(from) p 3408 1448 a(the) 0 1569 y(ab) s(o) m(v) m(e) p 276 1569 a(resonance) p 721 1569 a(state) p 969 1569 a(~) p Fl 960 1569 a(\032) p Fn 1043 1569 a(of) p Fl 1154 1569 a(L) p Fn(\() p Fl(A;) p Fg 1375 1569 a(\000) p Fl(b) p Fn(\).) p 1603 1569 a(If,) p 1727 1569 a(on) p 1863 1569 a(the) p 2031 1569 a(other) p 2285 1569 a(hand,) p Fl 2556 1569 a(H) p Fn 2667 1569 a(+) p Fl 2765 1569 a(V) p Fn 2876 1569 a(has) p 3050 1569 a(a) p 3131 1569 a(resonance) 0 1689 y(state) p 253 1689 a(at) p 386 1689 a(zero) p 605 1689 a(energy) p 875 1689 a(,) p 953 1689 a(then) p 1189 1689 a(the) p 1370 1689 a(situation) p 1791 1689 a(is) p 1903 1689 a(completely) p 2407 1689 a(rev) m(ersed.) p 2866 1689 a(W) p 2958 1689 a(e) p 3047 1689 a(obtain) p 3364 1689 a(that) p Fl 0 1809 a(H) p Fk 81 1824 a(") p Fn 118 1809 a(\() p Fl(V) p Fk 213 1824 a(") p 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2100 a(\014elds) p 3052 2100 a(\([2,) p 3236 2100 a(7,) p 3354 2100 a(13]\).) 0 2220 y(F) p 56 2220 a(or) p 187 2220 a(example,) p 611 2220 a(the) p 791 2220 a(asymptotic) p 1305 2220 a(b) s(eha) m(vior) p 1716 2220 a(of) p 1839 2220 a(the) p 2019 2220 a(amplitude) p 2492 2220 a(in) p 2618 2220 a(the) p 2798 2220 a(scattering) p 3260 2220 a(b) m(y) p 3408 2220 a(the) 0 2341 y(small) p 255 2341 a(disk) p 459 2341 a(has) p 633 2341 a(b) s(een) p 863 2341 a(calculated) p 1324 2341 a(under) p 1600 2341 a(a) p 1682 2341 a(certain) p 2007 2341 a(imp) s(enetrable) p 2595 2341 a(b) s(oundary) p 3034 2341 a(condition) p 3462 2341 a(in) 0 2461 y(the) p 170 2461 a(b) s(o) s(ok) p 414 2461 a(\(Afanasiev) p 901 2461 a([2,) p 1039 2461 a(Sec.) p 1242 2461 a(7.10]\).) p 1558 2461 a(The) p 1760 2461 a(b) s(eha) m(vior) p 2161 2461 a(c) m(hanges) p 2524 2461 a(discon) m(tin) m(uously) p 3213 2461 a(at) p 3335 2461 a(half{) 0 2581 y(in) m(teger) p 327 2581 a(\015uxes.) p 653 2581 a(Another) p 1039 2581 a(motiv) p 1280 2581 a(ation) p 1534 2581 a(is) p 1637 2581 a(to) p 1760 2581 a(study) p 2034 2581 a(the) p 2206 2581 a(scattering) p 2661 2581 a(of) p 2776 2581 a(Dirac) p 3045 2581 a(particles) p 3440 2581 a(b) m(y) 0 2702 y(electromagnetic) p 707 2702 a(\014elds) p 966 2702 a(with) p 1196 2702 a(small) p 1460 2702 a(supp) s(ort) p 1829 2702 a(in) p 1951 2702 a(the) p 2127 2702 a(in) m(teraction) p 2626 2702 a(of) p 2745 2702 a(cosmic) p 3068 2702 a(string) p 3354 2702 a(with) 0 2822 y(matter) p 319 2822 a(\(Alford,) p 687 2822 a(Marc) m(h{Rusell) p 1301 2822 a(and) p 1490 2822 a(Wilczek) p 1857 2822 a([7]\).) p 2069 2822 a(The) p 2268 2822 a(amplitude) p 2729 2822 a(there) p 2977 2822 a(has) p 3150 2822 a(b) s(een) p 3380 2822 a(also) 0 2943 y(explicitly) p 423 2943 a(calculated) p 883 2943 a(for) p 1033 2943 a(the) p 1201 2943 a(electric) p 1537 2943 a(p) s(oten) m(tial) p 1949 2943 a(of) p 2060 2943 a(c) m(haracteristic) p 2659 2943 a(function) p 3041 2943 a(of) p 3153 2943 a(the) 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3424 a(suc) m(h) p 1151 3424 a(a) p 1240 3424 a(discon) m(tin) m (uit) m(y) p 1828 3424 a(at) p 1955 3424 a(half{in) m(teger) p 2494 3424 a(\015uxes) p 2776 3424 a(in) p 2898 3424 a(the) p 3074 3424 a(asymptotic) 0 3545 y(form) p 223 3545 a(is) p 315 3545 a(completely) p 798 3545 a(hidden) p 1111 3545 a(b) s(ehind) p 1427 3545 a(this) p 1610 3545 a(explicit) p 1947 3545 a(calculation) p 2433 3545 a(using) p 2682 3545 a(the) p 2843 3545 a(Bessel) p 3128 3545 a(functions.) 0 3665 y(The) p 207 3665 a(argumen) m(t) p 651 3665 a(dev) m(elop) s(ed) p 1110 3665 a(here) p 1328 3665 a(seems) p 1613 3665 a(to) p 1739 3665 a(accoun) m(t) p 2106 3665 a(for) p 2262 3665 a(this) p 2459 3665 a(phenomenon) p 3035 3665 a(partly) p 3284 3665 a(.) p 3375 3665 a(The) 0 3785 y(presen) m(t) p 345 3785 a(w) m(ork) p 589 3785 a(is) p 693 3785 a(the) p 867 3785 a(\014rst) p 1074 3785 a(step) p 1286 3785 a(to) m(w) m(ard) p 1617 3785 a(analyzing) p 2059 3785 a(this) p 2255 3785 a(problem) p 2640 3785 a(from) p 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2056 a(to) p 470 2056 a(Theorem) p 883 2056 a(X.2) p 1067 2056 a(and) p 1258 2056 a(its) p 1396 2056 a(Corollary) p 1829 2056 a(of) p 1942 2056 a([19],) p 2156 2056 a(there) p 2407 2056 a(is) p 2507 2056 a(a) p 2590 2056 a(one{to{one) p 3101 2056 a(corresp) s(on-) 0 2177 y(dence) p 277 2177 a(b) s(et) m(w) m(een) p 661 2177 a(the) p 835 2177 a(unitary) p 1186 2177 a(mapping) p Fl 1593 2177 a(U) p Fn 1708 2177 a(:) p 1774 2177 a(\006) p Fj 1844 2192 a(+) p Fg 1942 2177 a(!) p Fn 2081 2177 a(\006) p Ff 2151 2192 a(\000) p Fn 2249 2177 a(and) p 2445 2177 a(the) p 2620 2177 a(self{adjoin) m(t) p 3144 2177 a(extension) p Fl 0 2297 a(H) p Fk 81 2312 a(U) p Fn 140 2297 a(,) p 199 2297 a(whic) m(h) p 479 2297 a(acts) p 680 2297 a(as) p Fl 1208 2428 a(H) p Fk 1289 2443 a(U) p Fl 1348 2428 a(u) p Fn 1431 2428 a(=) p 1535 2350 89 4 v Fl 1535 2428 a(H) p Fk 1623 2370 a(D) p Fl 1687 2428 a(v) p Fn 1760 2428 a(+) p Fl 1858 2428 a(iv) p Fj 1938 2443 a(+) p Fg 2020 2428 a(\000) p Fl 2119 2428 a(iU) p 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m(v) m(es) p 3408 5216 a(the) 0 5336 y(lemma.) p Fc 352 5336 a(2) p Fn 1747 5753 a(7) p 90 rotate dyy eop %%Page: 8 8 8 7 bop Fn 146 407 a(W) p 238 407 a(e) p 313 407 a(examine) p 694 407 a(what) p 936 407 a(b) s(oundary) p 1374 407 a(condition) p Fl 1801 407 a(H) p Fk 1882 422 a(U) p Fn 1972 407 a(satis\014es) p 2330 407 a(at) p 2448 407 a(the) p 2615 407 a(origin.) p 2929 407 a(When) p Fl 3212 407 a(\027) p 3294 407 a(>) p Fn 3398 407 a(0) p 3478 407 a(is) 0 527 y(not) p 173 527 a(an) p 309 527 a(in) m(teger,) p Fl 658 527 a(H) p Fk 739 542 a(\027) p Fn 782 527 a(\() p Fl(z) p Fn 869 527 a(\)) p 941 527 a(is) p 1039 527 a(represen) m(ted) p 1557 527 a(as) p Fl 518 756 a(H) p Fk 599 771 a(\027) p Fn 642 756 a(\() p Fl(z) p Fn 729 756 a(\)) p 795 756 a(=) p Fl 899 756 a(J) p Fk 953 771 a(\027) p Fn 996 756 a(\() p Fl(z) p Fn 1083 756 a(\)) p 1144 756 a(+) p Fl 1242 756 a(iN) p Fk 1353 771 a(\027) p Fn 1396 756 a(\() p Fl(z) p Fn 1483 756 a(\)) p 1549 756 a(=) p 1653 756 a(\() p Fl(i=) 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726 3204 a(self{adjoin) m(t) p 1244 3204 a(extensions.) p Fm 146 3442 a(3.) p 271 3442 a(Norm) p 591 3442 a(resolv) m(en) m(t) p 1067 3442 a(con) m(v) m(ergence) p Fn 146 3662 a(W) p 238 3662 a(e) p 311 3662 a(consider) p 687 3662 a(the) p 852 3662 a(problem) p 1228 3662 a(as) p 1344 3662 a(to) p 1460 3662 a(whic) m(h) p 1735 3662 a(self{adjoin) m(t) p 2250 3662 a(extension) p 2678 3662 a(is) p 2773 3662 a(realized) p 3127 3662 a(as) p 3243 3662 a(a) p 3321 3662 a(norm) 0 3783 y(resolv) m(en) m(t) p 416 3783 a(limit) p 654 3783 a(of) p 771 3783 a(Hamiltonians) p 1376 3783 a(with) p 1604 3783 a(smo) s(oth) p 1955 3783 a(magnetic) p 2378 3783 a(\014elds) p 2634 3783 a(ha) m(ving) p 2954 3783 a(small) p 3215 3783 a(supp) s(ort) 0 3903 y(when) p 249 3903 a(the) p 411 3903 a(supp) s(ort) p 766 3903 a(is) p 858 3903 a(shrinking.) p 1320 3903 a(Let) p Fl 1489 3903 a(H) p Fk 1578 3867 a(D) 1570 3928 y(") p Fn 1668 3903 a(b) s(e) p 1795 3903 a(de\014ned) p 2125 3903 a(b) m(y) p 2255 3903 a(\(1.7\).) p 2524 3903 a(The) p 2718 3903 a(aim) p 2902 3903 a(here) p 3107 3903 a(is) p 3200 3903 a(to) p 3313 3903 a(pro) m(v) m(e) 0 4024 y(the) p 168 4024 a(follo) m(wing) p 580 4024 a(theorem.) p Fm 0 4302 a(Theorem) p 475 4302 a(3.1) p Fd 667 4302 a(Assume) p 1029 4302 a(\(1.2\).) p 1312 4302 a(Then) p Fl 1564 4302 a(H) p Fk 1653 4266 a(D) 1645 4326 y(") p Fd 1749 4302 a(is) p 1852 4302 a(c) p 1892 4302 a(onver) p 2123 4302 a(gent) p 2332 4302 a(to) p Fl 2447 4302 a(H) p Ff 2528 4317 a(1) p Fd 2635 4302 a(in) p 2753 4302 a(the) p 2913 4302 a(norm) p 3171 4302 a(r) p 3207 4302 a(esolvent) 0 4422 y(sense) p 259 4422 a(as) p Fl 384 4422 a(") p Fg 457 4422 a(!) p Fn 584 4422 a(0) p Fd(.) p Fm 0 4700 a(Remark) p 429 4700 a(3.1.) p Fn 700 4700 a(The) p 904 4700 a(p) s(oten) m(tial) p 1319 4700 a(asso) s(ciated) p 1787 4700 a(with) p 2012 4700 a(giv) m(en) p 2270 4700 a(\014eld) p Fl 2484 4700 a(b) p Fg 2559 4700 a(2) p Fl 2658 4700 a(C) p Ff 2735 4664 a(1) p Fj 2728 4725 a(0) p Fn 2810 4700 a(\() p Fi(R) p Fj 2935 4658 a(2) p Fg 3008 4700 a(!) p Fi 3140 4700 a(R) p Fn 3228 4700 a(\)) p 3301 4700 a(is) p 3402 4700 a(not) 0 4821 y(uniquely) p 401 4821 a(determined.) p 965 4821 a(Let) 1171 4795 y(~) p Fl 1145 4821 a(A) p Fg 1255 4821 a(2) p Fl 1359 4821 a(C) p Ff 1436 4785 a(1) p Fn 1510 4821 a(\() p Fi(R) p Fj 1636 4779 a(2) p Fg 1712 4821 a(!) p Fi 1849 4821 a(R) p Fj 1936 4779 a(2) p Fn 1975 4821 a(\)) p 2051 4821 a(b) s(e) p 2190 4821 a(another) p 2553 4821 a(p) s(oten) m(tial) p 2970 4821 a(ha) m(ving) p Fl 3290 4821 a(b) p Fn 3369 4821 a(as) p 3495 4821 a(a) 0 4941 y(\014eld.) p 248 4941 a(Then) p 498 4941 a(it) p 592 4941 a(tak) m(es) p 837 4941 a(the) p 1001 4941 a(form) 1253 4916 y(~) p Fl 1227 4941 a(A) p Fn 1328 4941 a(=) p Fl 1431 4941 a(A) p Fn 1517 4941 a(+) p Fg 1606 4941 a(r) p Fl(g) p Fn 1769 4941 a(with) p 1987 4941 a(some) p Fl 2227 4941 a(g) p Fg 2305 4941 a(2) p Fl 2399 4941 a(C) p Ff 2476 4905 a(1) p Fn 2551 4941 a(\() p Fi(R) p Fj 2676 4899 a(2) p Fg 2743 4941 a(!) p Fi 2870 4941 a(R) p Fn 2958 4941 a(\).) p 3065 4941 a(If) p Fl 3158 4941 a(g) p Fn 3209 4941 a(\() p Fl(x) p Fn(\)) p Fg 3367 4941 a(!) p Fn 3495 4941 a(0) 0 5061 y(at) p 123 5061 a(in\014nit) m(y) p 417 5061 a(,) p 483 5061 a(w) m(e) p 631 5061 a(can) p 814 5061 a(pro) m(v) m(e) p 1081 5061 a(the) p 1253 5061 a(norm) p 1512 5061 a(resolv) m(en) m(t) p 1926 5061 a(con) m(v) m(ergence) p 2469 5061 a(for) 2648 5036 y(~) p Fl 2622 5061 a(A) p Fk 2695 5076 a(") p Fn 2767 5061 a(=) p Fl 2878 5061 a(") p Ff 2924 5025 a(\000) p Fj(1) p Fn 3043 5036 a(~) p Fl 3018 5061 a(A) p Fn(\() p Fl(x=") p Fn(\)) p 3353 5061 a(also.) 0 5182 y(This) p 223 5182 a(can) p 402 5182 a(b) s(e) p 534 5182 a(sho) m(wn) p 830 5182 a(in) p 944 5182 a(the) p 1112 5182 a(course) p 1411 5182 a(of) p 1522 5182 a(the) p 1690 5182 a(pro) s(of) p 1944 5182 a(of) p 2056 5182 a(the) p 2224 5182 a(theorem.) 146 5352 y(Before) p 453 5352 a(going) p 716 5352 a(in) m(to) p 916 5352 a(the) p 1086 5352 a(pro) s(of,) p 1370 5352 a(w) m(e) p 1516 5352 a(\014x) p 1657 5352 a(the) p 1827 5352 a(notation) p 2219 5352 a(and) p 2411 5352 a(in) m(tro) s(duce) p 2847 5352 a(sev) m(eral) p 3169 5352 a(auxiliary) 0 5472 y(op) s(erators.) p 483 5472 a(W) p 575 5472 a(e) p 655 5472 a(assume) p 996 5472 a(for) p 1150 5472 a(brevit) m(y) p 1488 5472 a(that) p 1703 5472 a(the) p 1876 5472 a(\014eld) p Fl 2092 5472 a(b) p Fg 2168 5472 a(2) p Fl 2270 5472 a(C) p Ff 2347 5436 a(1) p Fj 2340 5497 a(0) p Fn 2421 5472 a(\() p Fi(R) p Fj 2547 5430 a(2) p Fg 2621 5472 a(!) p Fi 2756 5472 a(R) p Fn(\)) p 2918 5472 a(has) p 3097 5472 a(supp) s(ort) p 3462 5472 a(in) 1747 5753 y(9) p 90 rotate dyy eop %%Page: 10 10 10 9 bop Fn 0 407 a(the) p 173 407 a(unit) p 384 407 a(disk.) p 642 407 a(According) p 1111 407 a(to) p 1235 407 a([20,) p 1425 407 a(Lemma) p 1778 407 a(2.1]) p 1968 407 a(\(see) p 2168 407 a(\(2.2\)) p 2407 407 a(there\),) p 2728 407 a(w) m(e) p 2876 407 a(can) p 3061 407 a(construct) p 3495 407 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a(on) p Fl 150 5263 a(C) p Ff 227 5227 a(1) p Fj 220 5288 a(0) p Fn 302 5263 a(\() p Fi(R) p Fj 427 5221 a(2) p Fg 498 5263 a(n) p 580 5263 a(f) p Fn(0) p Fg(g) p Fn(\).) p 881 5263 a(As) p 1039 5263 a(stated) p 1347 5263 a(in) p 1475 5263 a(section) p 1816 5263 a(1,) p 1942 5263 a(the) p 2125 5263 a(limit) p 2372 5263 a(op) s(erator) p Fl 2780 5263 a(L) p Fn(\() p Fl(A) p Fj 2957 5278 a(0) p Fk(\013) p Fl 3042 5263 a(;) p Fn 3086 5263 a(0\)) p 3219 5263 a(has) p 3408 5263 a(the) 0 5384 y(de\014ciency) p 448 5384 a(indices) p 769 5384 a(\(2,2\).) p 1043 5384 a(The) p 1245 5384 a(Krein) p 1517 5384 a(theory) p 1824 5384 a(yields) p 2099 5384 a(a) p 2182 5384 a(family) p Fg 2481 5384 a(f) p Fl(L) p Fk 2597 5399 a(U) p Fg 2656 5384 a(g) p Fn 2739 5384 a(of) p 2851 5384 a(all) p 2988 5384 a(p) s(ossible) p 3356 5384 a(self{) 0 5504 y(adjoin) m(t) p 340 5504 a(extensions) p 819 5504 a(whic) m(h) p 1107 5504 a(is) p 1214 5504 a(parameterized) p 1858 5504 a(b) m(y) p 2002 5504 a(2) p Fg 2079 5504 a(\002) p Fn 2185 5504 a(2) p 2276 5504 a(unitary) p 2629 5504 a(mapping) p Fl 3039 5504 a(U) p Fn 3157 5504 a(from) p 3397 5504 a(one) 1723 5753 y(10) p 90 rotate dyy eop %%Page: 11 11 11 10 bop Fn 0 407 a(de\014ciency) p 452 407 a(subspace) p 864 407 a(to) p 987 407 a(the) p 1160 407 a(other) p 1419 407 a(one.) p 1649 407 a(The) p 1854 407 a(op) s(erator) p Fl 2251 407 a(L) p Fk 2317 422 a(U) p Fn 2413 407 a(is) p 2516 407 a(realized) p 2878 407 a(as) p 3002 407 a(a) p 3088 407 a(di\013eren) m(tial) 0 527 y(op) s(erator) p 391 527 a(with) p 611 527 a(some) p 853 527 a(b) s(oundary) p 1290 527 a(conditions) p 1755 527 a(at) p 1872 527 a(the) p 2038 527 a(origin.) p 2351 527 a(If) p Fl 2447 527 a(w) p Fn 2550 527 a(b) s(elongs) p 2898 527 a(to) p Fg 3015 527 a(D) p Fn 3095 527 a(\() p Fl(L) p Fk 3199 542 a(U) p Fn 3258 527 a(\),) p 3354 527 a(then) p Fl 0 648 a(w) p Fn 105 648 a(b) s(eha) m(v) m(es) p 469 648 a(lik) m(e) p Fl 106 862 a(w) p Fn 206 862 a(=) p Fh 310 766 a(\020) p 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a(these) p 631 1740 a(four) p 836 1740 a(co) s(e\016cien) m (ts.) p 1375 1740 a(F) p 1431 1740 a(or) p 1552 1740 a(later) p 1782 1740 a(references,) p 2259 1740 a(w) m(e) p 2405 1740 a(distinguish) p 2902 1740 a(the) p 3072 1740 a(t) m(w) m(o) p 3258 1740 a(sp) s(ecial) 0 1861 y(op) s(erators) p 432 1861 a(among) p 747 1861 a(the) p 915 1861 a(family) p 1214 1861 a(of) p 1325 1861 a(self{adjoin) m(t) p 1844 1861 a(extensions.) p 2353 1861 a(One) p 2560 1861 a(is) p 2658 1861 a(the) p 2827 1861 a(Aharono) m(v{Bohm) 0 1981 y(Hamiltonian) p Fl 561 1981 a(L) p Fk 627 1996 a(AB) p Fn 773 1981 a(with) p 995 1981 a(domain) p Fg 586 2196 a(D) p Fn 666 2196 a(\() p Fl(L) p Fk 770 2211 a(AB) p Fn 884 2196 a(\)) p 949 2196 a(=) p Fg 1053 2196 a(f) p Fl(w) p Fg 1203 2196 a(2) p Fl 1297 2196 a(L) p Fj 1363 2155 a(2) p Fn 1430 2196 a(:) p Fl 1485 2196 a(L) p Fn(\() p Fl(A) p Fj 1662 2211 a(0) p Fk(\013) p Fl 1747 2196 a(;) p Fn 1791 2196 a(0\)) p Fl(w) p Fg 1978 2196 a(2) p Fl 2072 2196 a(L) p Fj 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a(where) p Fl 282 407 a(g) p Fg 360 407 a(2) p Fl 454 407 a(L) p Fj 520 371 a(2) p Fg 582 407 a(\\) p Fl 670 407 a(C) p Ff 747 371 a(1) p Fn 855 407 a(ob) s(eys) p 1126 407 a(the) p 1294 407 a(b) s(ound) p 1595 407 a(as) p 1715 407 a(ab) s(o) m(v) m(e) p 1991 407 a(at) p 2110 407 a(in\014nit) m(y) p 2404 407 a(.) p 2476 407 a(If) p Fl 2574 407 a(u) p Fg 2657 407 a(2) p Fl 2751 407 a(E) p Ff 2823 422 a(\000) p Fn 2882 407 a(,) p 2942 407 a(then) p Fl 668 627 a(L) p Ff 734 642 a(\000) p Fl 793 627 a(u) p Fn 876 627 a(=) p Fl 980 627 a(p) p Ff 1029 586 a(\003) p Fj 1029 651 a(+) p Fl 1088 627 a(p) p Fj 1137 642 a(+) p Fl 1196 627 a(u) p Fn 1279 627 a(=) p Fl 1383 627 a(p) p Fj 1432 586 a(2) 1432 651 y(1) p Fl 1471 627 a(u) p Fn 1549 627 a(+) p Fl 1647 627 a(p) p Fj 1696 586 a(2) 1696 651 y(2) p Fl 1735 627 a(u) p Fg 1813 627 a(\000) p Fl 1913 627 a(bu) p Fn 2037 627 a(=) p 2141 627 a(0) p Fl(;) p 2331 627 a(b) p Fg 2400 627 a(2) p Fl 2494 627 a(C) p Ff 2571 586 a(1) p Fj 2564 651 a(0) p 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Fn 2017 5139 a(\() p Fl(u) p Fj 2111 5154 a(1) p Fl 2150 5139 a(;) p 2194 5139 a(u) p Fj 2250 5154 a(2) p Fn 2289 5139 a(\)) p 2359 5139 a(satis\014es) 634 5359 y(\() p Fl(L) p Fn(\() p Fl(A) p Fj 849 5374 a(0) p Fk(\013) p Fl 934 5359 a(;) p Fn 978 5359 a(0\)) p 1087 5359 a(+) p 1185 5359 a(1\)) p Fl 1288 5359 a(u) p Fj 1344 5374 a(2) p Fn 1411 5359 a(=) p Fl 1514 5359 a(\031) p Fj 1569 5374 a(+) p Fl 1629 5359 a(f) p Fj 1677 5374 a(1) p Fg 1738 5359 a(\000) p Fl 1838 5359 a(if) p Fj 1919 5374 a(2) p Fl 1959 5359 a(;) p 2198 5359 a(u) p Fj 2254 5374 a(1) p Fn 2320 5359 a(=) p Fl 2424 5359 a(i\031) p Ff 2512 5374 a(\000) p Fl 2572 5359 a(u) p Fj 2628 5374 a(2) p Fg 2689 5359 a(\000) p Fl 2788 5359 a(if) p Fj 2869 5374 a(1) p Fn 1723 5753 a(12) p 90 rotate dyy eop %%Page: 13 13 13 12 bop Fn 0 407 a(for) p 156 407 a(the) p 332 407 a(Aharono) m(v{Bohm) p 1089 407 a(p) s(oten) m(tial) p Fl 1508 407 a(A) p Fj 1581 422 a(0) p Fk(\013) p Fn 1666 407 a(\() p Fl(x) p Fn(\).) p 1890 407 a(W) p 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a(0) p Fd(.) p Fm 0 5007 a(Lemma) p 397 5007 a(3.5) p Fl 589 5007 a(\037) p Fn(\() p Fl(L) p Ff 754 5022 a(\000) p Fn 836 5007 a(+) p Fl 934 5007 a(") p Fj 980 4971 a(2) p Fn 1019 5007 a(\)) p Ff 1057 4971 a(\000) p Fj(1) p Fl 1151 5007 a(\037) p Fn 1240 5007 a(=) p Fl 1343 5007 a(O) s(p) p Fn(\() p Fl(") p Ff 1554 4971 a(\000) p Fj(2) p Fk(\013) p Fn 1693 5007 a(\)) p Fd 1766 5007 a(for) p Fl 1921 5007 a(\037) p Fg 2010 5007 a(2) p Fl 2104 5007 a(C) p Ff 2181 4971 a(1) p Fj 2174 5032 a(0) p Fn 2256 5007 a(\() p Fi(R) p Fj 2381 4965 a(2) p Fg 2448 5007 a(!) p Fi 2576 5007 a(R) p Fn(\)) p Fd(.) p Fn 1723 5753 a(13) p 90 rotate dyy eop %%Page: 14 14 14 13 bop Fd 0 407 a(Pr) p 102 407 a(o) p 147 407 a(of) p 271 407 a(of) p 394 407 a(The) p 554 407 a(or) p 640 407 a(em) p 808 407 a(3.1.) p Fn 1065 407 a(W) p 1157 407 a(e) p 1242 407 a(\014rst) p 1453 407 a(pro) m(v) m(e) p 1725 407 a(\(3.5\).) p 2025 407 a(The) p 2236 407 a(t) m(w) m(o) p 2430 407 a(resolv) m(en) m(ts) p 2887 407 a(\() p 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2645 1944 a(\013) p Fn 2708 1944 a(\)) p Fj 2745 1896 a(2) p Fn 0 2146 a(on) p Fg 140 2146 a(fj) p Fl(x) p Fg(j) p Fl 336 2146 a(>) p Fn 447 2146 a(2) p Fg(g) p Fn(,) p 611 2146 a(and) p 805 2146 a(hence) p Fl 1081 2146 a(u) p Fk 1137 2161 a(l) p Fn 1162 2146 a(\() p Fl(x) p Fn(\)) p 1329 2146 a(=) p Fl 1441 2146 a(r) p Fk 1488 2110 a(\027) p Fl 1530 2146 a(e) p Fk 1575 2110 a(il) q(\022) p Fl 1660 2146 a(;) p 1741 2146 a(\027) p Fn 1831 2146 a(=) p Fg 1942 2146 a(j) p Fl(l) p Fg 2027 2146 a(\000) p Fl 2129 2146 a(\013) p Fg 2192 2146 a(j) p Fn(,) p 2285 2146 a(satis\014es) p Fl 2649 2146 a(Lu) p Fk 2771 2161 a(l) p Fn 2832 2146 a(=) p 2943 2146 a(0) p 3029 2146 a(there.) p 3330 2146 a(If) p 3432 2146 a(w) m(e) 0 2266 y(de\014ne) p Fl 282 2266 a(!) p Fk 343 2281 a(l) p Fn 401 2266 a(b) m(y) p Fl 675 2468 a(!) p Fk 736 2483 a(l) p Fn 790 2468 a(=) p Fl 893 2468 a(c) p Fk 935 2483 a(l) p Fn 961 2468 a(\(1) p Fg 1070 2468 a(\000) p Fl 1170 2468 a(\037) p Fn(\)) p Fl(u) p Fk 1325 2483 a(l) 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a(=) p Fg 304 3072 a(j) p Fl(x) p Fg(j) p 445 3072 a(!) p 575 3072 a(1) p Fn(,) p 736 3072 a(and) p 928 3072 a(it) p 1027 3072 a(solv) m(es) p Fl 1306 3072 a(L!) p Fk 1433 3087 a(l) p Fn 1489 3072 a(=) p 1595 3072 a(0.) p 1719 3072 a(Suc) m(h) p 1956 3072 a(a) p 2039 3072 a(solution) p 2410 3072 a(is) p 2509 3072 a(sho) m(wn) p 2807 3072 a(to) p 2927 3072 a(b) s(e) p 3062 3072 a(unique) p 3380 3072 a(\(see) 0 3193 y([20,) p 184 3193 a(Lemma) p 531 3193 a(4.3]\).) p 791 3193 a(The) p 991 3193 a(argumen) m(t) p 1427 3193 a(here) p 1638 3193 a(is) p 1735 3193 a(based) p 2006 3193 a(on) p 2141 3193 a(the) p 2308 3193 a(prop) s(osition) p 2820 3193 a(b) s(elo) m(w,) p 3123 3193 a(whic) m(h) p 3402 3193 a(has) 0 3313 y(b) s(een) p 230 3313 a(pro) m(v) m(ed) p 547 3313 a(as) p 667 3313 a(Prop) s(osition) p 1192 3313 a(4.2) p 1349 3313 a(in) p 1463 3313 a([20].) p Fm 0 3565 a(Prop) s(osition) p 606 3565 a(4.1) p Fd 798 3565 a(L) p 854 3565 a(et) p 966 3565 a(the) p 1128 3565 a(notation) p 1516 3565 a(b) p 1556 3565 a(e) p 1636 3565 a(as) p 1760 3565 a(ab) p 1850 3565 a(ove) p 2024 3565 a(and) p 2214 3565 a(let) p Fl 2351 3565 a(\027) p Fn 2433 3565 a(=) p Fg 2536 3565 a(j) p Fl(l) p Fg 2617 3565 a(\000) p Fl 2717 3565 a(\013) p Fg 2780 3565 a(j) p Fd 2842 3565 a(again.) p 3146 3565 a(Then) p Fl 163 3767 a(\037) p Fn(\() p Fl(L) p Fg 350 3767 a(\000) p Fl 450 3767 a(k) p Fj 504 3725 a(2) p Fn 543 3767 a(\)) p Ff 581 3725 a(\000) p Fj(1) p Fl 676 3767 a(\037) p Fn 764 3767 a(=) p Fl 868 3767 a(\037G) p Fj 1006 3782 a(0) p Fl 1045 3767 a(\037) p Fn 1129 3767 a(+) p Fh 1250 3683 a(X) p Fk 1227 3868 a(l) p Fj 1249 3868 a(=0) p Fk(;) p Fj(1) p Fl 1410 3767 a(\015) p Fk 1461 3782 a(l) p Fn 1487 3767 a(\() p Fl(k) p Fn 1579 3767 a(\)) p Fl(i) p Ff 1650 3725 a(\000) p Fj(2) p Fk(\027) p Fl 1783 3767 a(k) p Fj 1837 3725 a(2) p Fk(\027) p Fn 1933 3767 a(\() p Fl(\037!) p Fk 2093 3782 a(l) p Fg 2141 3767 a(\012) p Fl 2240 3767 a(\037!) p Fk 2362 3782 a(l) p Fn 2388 3767 a(\)) p 2448 3767 a(+) p Fl 2546 3767 a(O) s(p) p Fn(\() p Fg(j) p Fl(k) p Fg 2793 3767 a(j) p Fj 2821 3725 a(2) p Fn 2859 3767 a(\)) p Fl(;) p Fg 3040 3767 a(j) p Fl(k) p Fg 3122 3767 a(j) p 3177 3767 a(!) p Fn 3305 3767 a(0) p Fl(;) p Fd 0 4053 a(for) p 156 4053 a(some) p 405 4053 a(c) p 445 4053 a(o) p 490 4053 a(e\016cients) p Fl 902 4053 a(\015) p Fk 953 4068 a(l) p Fn 978 4053 a(\() p Fl(k) p Fn 1070 4053 a(\)) p Fd(,) p 1173 4053 a(and) p Fl 1362 4053 a(\015) p Fk 1413 4068 a(l) p Fn 1439 4053 a(\() p Fl(k) p Fn 1531 4053 a(\)) p Fd 1604 4053 a(b) p 1644 4053 a(ehaves) p 1952 4053 a(like) p Fl 1419 4255 a(\015) p Fk 1470 4270 a(l) p Fn 1495 4255 a(\() p Fl(k) p Fn 1587 4255 a(\)) p 1653 4255 a(=) p Fl 1756 4255 a(\015) p Fk 1807 4270 a(l) p Fn 1855 4255 a(+) p Fl 1953 4255 a(o) p Fn(\(1\)) p 3343 4255 a(\(4.3\)) p Fd 0 4456 a(as) p Fg 125 4456 a(j) p Fl(k) p Fg 207 4456 a(j) p 262 4456 a(!) p Fn 389 4456 a(0) p Fd(,) p 502 4456 a(wher) p 698 4456 a(e) p Fl 944 4589 a(\015) p Fk 995 4604 a(l) p Fn 1048 4589 a(=) p Fg 1152 4589 a(\000) p Fh 1246 4493 a(\020) p Fn 1296 4589 a(2) p Fj 1345 4548 a(1) p Ff(\000) p Fj(2) p Fk(\027) p Fn 1513 4589 a(\000\(1) p Fg 1683 4589 a(\000) p Fl 1783 4589 a(\027) p Fn 1837 4589 a(\)) p Fh 1875 4493 a(\021) p Fl 1941 4589 a(=) p Fn 2007 4589 a(\() o(\() p Fl(l) p Fn 2136 4589 a(+) p Fl 2234 4589 a(\027) p Fn 2288 4589 a(\)\000\() p Fl(\027) p Fn 2479 4589 a(\)\)) p Fl 2572 4589 a(:) p Fn 3343 4589 a(\(4.4\)) 146 4841 y(The) p 348 4841 a(precise) p 669 4841 a(v) p 715 4841 a(alue) p 923 4841 a(of) p Fl 1035 4841 a(\015) p Fk 1086 4856 a(l) p Fn 1145 4841 a(is) p 1244 4841 a(not) p 1419 4841 a(required) p 1802 4841 a(to) p 1923 4841 a(pro) m(v) m(e) p 2187 4841 a(the) p 2356 4841 a(lemmas,) p 2737 4841 a(but) p 2917 4841 a(it) p 3016 4841 a(is) p 3115 4841 a(imp) s(ortan) m(t) 0 4961 y(in) p 114 4961 a(studying) p 513 4961 a(the) p 681 4961 a(e\013ect) p 938 4961 a(of) p 1049 4961 a(p) s(erturbation) p 1621 4961 a(b) m(y) p 1756 4961 a(scalar) p 2033 4961 a(p) s(oten) m(tials) p 2484 4961 a(in) p 2598 4961 a(the) p 2766 4961 a(latter) p 3031 4961 a(sections.) 146 5126 y(Next) p 400 5126 a(w) m(e) p 559 5126 a(consider) p 954 5126 a(the) p 1137 5126 a(op) s(erator) p Fl 1545 5126 a(L) p Fj 1611 5141 a(+) p Fn 1725 5126 a(=) p Fl 1854 5126 a(L) p Fn(\() p Fl(a;) p 2053 5126 a(b) p Fn(\)) p 2186 5126 a(=) p Fl 2316 5126 a(L) p Fn 2415 5126 a(+) p Fl 2523 5126 a(b) p Fn(.) p 2681 5126 a(W) p 2773 5126 a(e) p 2864 5126 a(shall) p 3107 5126 a(sho) m(w) p 3364 5126 a(that) 0 5247 y(\() p Fl(L) p Fj 104 5262 a(+) p Fg 189 5247 a(\000) p Fl 292 5247 a(k) p Fj 346 5211 a(2) p Fn 386 5247 a(\)) p Ff 424 5211 a(\000) p Fj(1) p Fn 555 5247 a(admits) p 881 5247 a(an) p 1021 5247 a(expansion) p 1479 5247 a(similar) p 1805 5247 a(to) p 1929 5247 a(that) p 2146 5247 a(in) p 2264 5247 a(Prop) s(osition) p 2794 5247 a(4.1.) p 3005 5247 a(W) p 3097 5247 a(e) p 3178 5247 a(ha) m(v) m(e) p 3408 5247 a(the) 0 5367 y(relation) 789 5487 y(\() p Fl(L) p Fj 893 5502 a(+) p Fg 974 5487 a(\000) p Fl 1074 5487 a(k) p Fj 1128 5446 a(2) p Fn 1167 5487 a(\)) p Ff 1205 5446 a(\000) p Fj(1) p Fn 1327 5487 a(=) p 1431 5487 a(\() p Fl(L) p Fg 1557 5487 a(\000) p Fl 1657 5487 a(k) p Fj 1711 5446 a(2) p Fn 1750 5487 a(\)) p Ff 1788 5446 a(\000) p Fj(1) p Fh 1899 5391 a(\020) p Fn 1949 5487 a(1) p 2020 5487 a(+) p Fl 2118 5487 a(b) p Fn(\() p Fl(L) p Fg 2285 5487 a(\000) p Fl 2385 5487 a(k) p Fj 2439 5446 a(2) p Fn 2479 5487 a(\)) p Ff 2517 5446 a(\000) p Fj(1) p Fh 2611 5391 a(\021) p Ff 2660 5414 a(\000) p Fj(1) p Fn 3343 5487 a(\(4.5\)) 1723 5753 y(15) p 90 rotate dyy eop %%Page: 16 16 16 15 bop Fn 0 407 a(b) m(y) p 132 407 a(the) p 297 407 a(resolv) m(en) m(t) p 704 407 a(iden) m(tit) m(y) p 1022 407 a(.) p 1093 407 a(Since) p Fl 1345 407 a(L) p Fj 1411 422 a(+) p Fn 1500 407 a(has) p 1670 407 a(neither) p 1998 407 a(b) s(ound) p 2296 407 a(states) p 2570 407 a(nor) p 2740 407 a(resonance) p 3182 407 a(states) p 3457 407 a(at) 0 527 y(zero) p 206 527 a(energy) p 476 527 a(,) p 537 527 a(1) p 607 527 a(+) p Fl 705 527 a(bG) p Fj 823 542 a(0) p Fn 891 527 a(:) p Fl 946 527 a(L) p Fj 1012 491 a(2) p Fk 1012 552 a(c) p Fg 1079 527 a(!) p Fl 1207 527 a(L) p Fj 1273 491 a(2) p Fk 1273 552 a(c) p Fn 1345 527 a(has) p 1519 527 a(the) p 1687 527 a(b) s(ounded) p 2085 527 a(in) m(v) m(erse) p Fl 1184 741 a(T) p Fn 1283 741 a(=) p 1386 741 a(\(1) p 1495 741 a(+) p Fl 1593 741 a(bG) p Fj 1711 756 a(0) p Fn 1751 741 a(\)) p Ff 1789 693 a(\000) p Fj(1) p Fn 1911 741 a(:) p Fl 1965 741 a(L) p Fj 2031 700 a(2) p Fk 2031 766 a(c) p Fg 2099 741 a(!) p Fl 2226 741 a(L) p Fj 2292 700 a(2) p Fk 2292 766 a(c) p Fl 2332 741 a(:) p Fn 0 956 a(W) p 92 956 a(e) p 168 956 a(see) p 326 956 a(that) p 537 956 a(there) p 786 956 a(exists) p 1056 956 a(a) p 1137 956 a(limit) p Fl 1283 1170 a(G) p Fj 1360 1185 a(+) p Fn 1447 1170 a(=) p 1555 1170 a(lim) p Fk 1550 1230 a(k) p Ff 1589 1230 a(!) p Fj(0) p Fn 1722 1170 a(\() p Fl(L) p Fj 1826 1185 a(+) p Fg 1908 1170 a(\000) p Fl 2007 1170 a(k) p Fj 2061 1129 a(2) p Fn 2101 1170 a(\)) p Ff 2139 1129 a(\000) p Fj(1) p Fl 2233 1170 a(:) p Fn 0 1419 a(and) p 205 1419 a(the) p 388 1419 a(limit) p 637 1419 a(op) s(erator) p Fl 1045 1419 a(G) p Fj 1122 1434 a(+) p Fn 1235 1419 a(=) p Fl 1365 1419 a(G) p Fj 1442 1434 a(0) p Fl 1481 1419 a(T) p Fn 1606 1419 a(:) p Fl 1687 1419 a(L) p Fj 1753 1383 a(2) p Fk 1753 1444 a(c) p Fg 1847 1419 a(!) p Fl 2000 1419 a(L) p Fj 2066 1383 a(2) p Ff 2066 1444 a(\000) p Fj(1) p Fn 2209 1419 a(is) p 2322 1419 a(b) s(ounded.) p 2805 1419 a(The) p 3021 1419 a(in) m(v) m(erse) p Fl 3359 1419 a(T) p Fn 3478 1419 a(is) 0 1539 y(represen) m(ted) p 518 1539 a(as) p Fl 1105 1660 a(T) p Fn 1204 1660 a(=) p Fl 1307 1660 a(LG) p Fj 1450 1675 a(+) p Fn 1537 1660 a(=) p 1641 1660 a(1) p Fg 1712 1660 a(\000) p Fl 1811 1660 a(bG) p Fj 1929 1675 a(+) p Fn 2017 1660 a(:) p Fl 2071 1660 a(L) p Fj 2137 1619 a(2) p Fk 2137 1684 a(c) p Fg 2205 1660 a(!) p Fl 2332 1660 a(L) p Fj 2398 1619 a(2) p Fk 2398 1684 a(c) p Fn 3343 1660 a(\(4.6\)) 0 1832 y(and) p 192 1832 a(it) p 292 1832 a(follo) m(ws) p 615 1832 a(that) p 829 1832 a(the) p 1000 1832 a(adjoin) m(t) p 1333 1832 a(op) s(erator) p Fl 1729 1832 a(T) p Ff 1800 1796 a(\003) p Fn 1871 1832 a(=) p 1979 1832 a(1) p Fg 2052 1832 a(\000) p Fl 2153 1832 a(G) p Fj 2230 1847 a(+) p Fl 2289 1832 a(b) p Fn 2363 1832 a(:) p Fl 2422 1832 a(L) p Fj 2488 1796 a(2) 2488 1856 y(lo) r(c) p Fg 2613 1832 a(!) p Fl 2745 1832 a(L) p Fj 2811 1796 a(2) 2811 1856 y(lo) r(c) p Fn 2939 1832 a(is) p 3039 1832 a(w) m(ell) p 3240 1832 a(de\014ned) 0 1952 y(as) p 121 1952 a(an) p 258 1952 a(op) s(erator) p 652 1952 a(from) p 884 1952 a(the) p 1053 1952 a(space) p Fl 1315 1952 a(L) p Fj 1381 1916 a(2) 1381 1977 y(lo) r(c) p Fn 1507 1952 a(of) p 1620 1952 a(lo) s(cally) p 1930 1952 a(square) p 2238 1952 a(in) m(tegrable) p 2692 1952 a(functions) p 3113 1952 a(in) m(to) p 3312 1952 a(itself.) 0 2072 y(If) p 98 2072 a(w) m(e) p 241 2072 a(de\014ne) p Fl 1235 2193 a(!) p Fj 1296 2208 a(+) p Fk(l) p Fn 1404 2193 a(=) p Fl 1508 2193 a(T) p Ff 1579 2152 a(\003) p Fl 1618 2193 a(!) p Fk 1679 2208 a(l) p Fn 1732 2193 a(=) p Fl 1836 2193 a(!) p Fk 1897 2208 a(l) p Fg 1945 2193 a(\000) p Fl 2044 2193 a(G) p Fj 2121 2208 a(+) p Fl 2180 2193 a(b!) p Fk 2282 2208 a(l) p Fn 3343 2193 a(\(4.7\)) 0 2365 y(for) p Fl 149 2365 a(l) p Fn 208 2365 a(=) p 312 2365 a(0) p Fl(;) p Fn 405 2365 a(1,) p 512 2365 a(then) p Fl 735 2365 a(!) p Fj 796 2380 a(+) p Fk(l) p Fn 909 2365 a(solv) m(es) p Fl 1186 2365 a(L) p Fj 1252 2380 a(+) p Fl 1312 2365 a(!) p Fj 1373 2380 a(+) p Fk(l) p Fn 1481 2365 a(=) p 1584 2365 a(0) p 1666 2365 a(and) p 1855 2365 a(ob) s(eys) p 2127 2365 a(\(4.2\)) p 2360 2365 a(at) p 2479 2365 a(in\014nit) m(y) p 2773 2365 a(.) p Fm 0 2634 a(Prop) s(osition) p 606 2634 a(4.2) p Fd 798 2634 a(L) p 854 2634 a(et) p 966 2634 a(the) p 1128 2634 a(notation) p 1516 2634 a(b) p 1556 2634 a(e) p 1636 2634 a(as) p 1760 2634 a(ab) p 1850 2634 a(ove.) p 2064 2634 a(Then) p Fl 283 2849 a(\037) p Fn(\() p Fl(L) p Fj 448 2864 a(+) p Fg 529 2849 a(\000) p Fl 629 2849 a(k) p Fj 683 2808 a(2) p Fn 723 2849 a(\)) p Ff 761 2808 a(\000) p Fj(1) p Fl 855 2849 a(\037) p Fn 944 2849 a(=) p Fl 1047 2849 a(\037G) p Fj 1185 2864 a(+) p Fl 1244 2849 a(\037) p Fn 1328 2849 a(+) p Fh 1449 2766 a(X) p Fk 1426 2950 a(l) p Fj 1448 2950 a(=0) p Fk(;) p Fj(1) p Fl 1609 2849 a(\015) p Fj 1660 2864 a(+) p Fk(l) p Fn 1741 2849 a(\() p Fl(k) p Fn 1833 2849 a(\)) p Fl(i) p Ff 1904 2808 a(\000) p Fj(2) p Fk(\027) p Fl 2037 2849 a(k) p Fj 2091 2808 a(2) p Fk(\027) p Fn 2186 2849 a(\() p Fl(\037!) p Fj 2346 2864 a(+) p Fk(l) p Fg 2449 2849 a(\012) p Fl 2549 2849 a(\037!) p Fj 2671 2864 a(+) p Fk(l) p Fn 2751 2849 a(\)) p 2812 2849 a(+) p Fl 2910 2849 a(O) s(p) p Fn(\() p Fg(j) p Fl(k) p Fg 3157 2849 a(j) p Fj 3185 2808 a(2) p Fn 3223 2849 a(\)) p Fd 0 3148 a(for) p 156 3148 a(some) p 405 3148 a(c) p 445 3148 a(o) p 490 3148 a(e\016cients) p Fl 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p Fh 1952 3559 a(\020) p Fn 2001 3656 a(1) p 2072 3656 a(+) p Fl 2170 3656 a(b) p Fn(\() p Fl(L) p Fg 2338 3656 a(\000) p Fl 2438 3656 a(k) p Fj 2492 3614 a(2) p Fn 2531 3656 a(\)) p Ff 2569 3614 a(\000) p Fj(1) p Fh 2664 3559 a(\021) p Ff 2713 3582 a(\000) p Fj(1) p Fl 2824 3656 a(\037) p Fn 0 3882 a(obtained) p 401 3882 a(from) p 631 3882 a(\(4.5\).) p 902 3882 a(Set) p Fl 799 4096 a(E) p Fn 877 4096 a(\() p Fl(k) p Fn 969 4096 a(\)) p 1035 4096 a(=) p Fh 1162 4013 a(X) p Fk 1138 4198 a(l) p Fj 1160 4198 a(=0) p Fk(;) p Fj(1) p Fl 1322 4096 a(\015) p Fk 1373 4111 a(l) p Fn 1398 4096 a(\() p Fl(k) p Fn 1490 4096 a(\)) p Fl(i) p Ff 1561 4055 a(\000) p Fj(2) p Fk(\027) p Fl 1695 4096 a(k) p Fj 1749 4055 a(2) p Fk(\027) p Fn 1844 4096 a(\() p Fl(!) p Fk 1943 4111 a(l) p Fg 1991 4096 a(\012) p Fl 2091 4096 a(!) p Fk 2152 4111 a(l) p Fn 2177 4096 a(\)) p 2243 4096 a(:) p Fl 2298 4096 a(L) p Fj 2364 4055 a(2) p Fk 2364 4121 a(c) p Fg 2431 4096 a(!) p Fl 2558 4096 a(L) p Fj 2624 4055 a(2) 2624 4121 y(lo) r(c) p Fl 2717 4096 a(:) p Fn 0 4390 a(Then) p 255 4390 a(w) m(e) p 398 4390 a(ha) m(v) m(e) p Fh 669 4508 a(\020) p Fn 719 4605 a(1) p 790 4605 a(+) p Fl 888 4605 a(b) p Fn(\() p Fl(L) p Fg 1056 4605 a(\000) p Fl 1155 4605 a(k) p Fj 1209 4563 a(2) p Fn 1249 4605 a(\)) p Ff 1287 4563 a(\000) p Fj(1) p Fh 1381 4508 a(\021) p Ff 1431 4531 a(\000) p Fj(1) p Fn 1553 4605 a(=) p 1656 4605 a(\(1) p 1765 4605 a(+) p Fl 1863 4605 a(T) p 1934 4605 a(bE) p Fn 2053 4605 a(\() p Fl(k) p Fn 2145 4605 a(\)\)) p Ff 2221 4556 a(\000) p Fj(1) p Fl 2332 4605 a(T) p Fn 2425 4605 a(+) p Fl 2523 4605 a(O) s(p) p Fn(\() p Fg(j) p Fl(k) p Fg 2770 4605 a(j) p Fj 2798 4563 a(2) p Fn 2836 4605 a(\)) 0 4835 y(b) m(y) p 135 4835 a(Prop) s(osition) p 660 4835 a(4.1,) p 845 4835 a(and) p 1034 4835 a(hence) p 1305 4835 a(\() p Fl(L) p Fj 1409 4850 a(+) p Fg 1491 4835 a(\000) p Fl 1590 4835 a(k) p Fj 1644 4799 a(2) p Fn 1684 4835 a(\)) p Ff 1722 4799 a(\000) p Fj(1) p Fn 1849 4835 a(is) p 1947 4835 a(expanded) p 2383 4835 a(as) p Fl 899 5050 a(\037) p Fn(\() p Fl(L) p Fj 1064 5065 a(+) p Fg 1146 5050 a(\000) p Fl 1245 5050 a(k) p Fj 1299 5009 a(2) p Fn 1339 5050 a(\)) p Ff 1377 5009 a(\000) p Fj(1) p Fl 1471 5050 a(\037) p Fn 1560 5050 a(=) p Fl 1663 5050 a(G) p Fj 1740 5065 a(1) p Fn 1802 5050 a(+) p Fl 1900 5050 a(G) p Fj 1977 5065 a(2) p Fn 2016 5050 a(\() p Fl(k) p Fn 2108 5050 a(\)) p 2168 5050 a(+) p Fl 2266 5050 a(O) s(p) p Fn(\() p Fg(j) p Fl(k) p Fg 2513 5050 a(j) p Fj 2541 5009 a(2) p Fn 2579 5050 a(\)) p Fl(;) p Fn 0 5264 a(where) p Fl 282 5264 a(G) p Fj 359 5279 a(1) p Fn 426 5264 a(=) p Fl 529 5264 a(\037G) p Fj 667 5279 a(0) p Fl 707 5264 a(T) p 778 5264 a(\037) p Fn 866 5264 a(=) p Fl 970 5264 a(\037G) p Fj 1108 5279 a(+) p Fl 1167 5264 a(\037) p Fn 1261 5264 a(and) p Fl 327 5487 a(G) p Fj 404 5502 a(2) p Fn 443 5487 a(\() p Fl(k) p Fn 535 5487 a(\)) p 601 5487 a(=) p Fl 704 5487 a(\037E) p Fn 843 5487 a(\() p Fl(k) p Fn 935 5487 a(\)) p 990 5487 a(\(1) p 1099 5487 a(+) p Fl 1197 5487 a(T) p 1268 5487 a(bE) p Fn 1387 5487 a(\() p Fl(k) p Fn 1479 5487 a(\)\)) p Ff 1555 5439 a(\000) p Fj(1) p Fl 1666 5487 a(T) p 1737 5487 a(\037) p Fn 1820 5487 a(+) p Fl 1918 5487 a(\037G) p Fj 2056 5502 a(0) p Fh 2112 5391 a(\020) p Fn 2162 5487 a(\(1) p 2270 5487 a(+) p Fl 2368 5487 a(T) p 2439 5487 a(bE) p Fn 2558 5487 a(\() p Fl(k) p Fn 2650 5487 a(\)\)) p Ff 2727 5439 a(\000) p Fj(1) p Fg 2843 5487 a(\000) p Fn 2943 5487 a(1) p Fh 2992 5391 a(\021) p Fl 3058 5487 a(T) p 3129 5487 a(\037:) p Fn 1723 5753 a(16) p 90 rotate dyy eop %%Page: 17 17 17 16 bop Fn 0 407 a(W) p 92 407 a(e) p 168 407 a(can) p 347 407 a(calculate) p Fl 753 407 a(G) p Fj 830 422 a(2) p Fn 870 407 a(\() p Fl(k) p Fn 962 407 a(\)) p 1032 407 a(as) p Fl 727 620 a(G) p Fj 804 635 a(2) p Fn 843 620 a(\() p Fl(k) p Fn 935 620 a(\)) p 1056 620 a(=) p Fl 1215 620 a(\037) p Fn 1293 620 a(\(1) p Fg 1402 620 a(\000) p Fl 1501 620 a(G) p Fj 1578 635 a(0) p Fl 1618 620 a(T) p 1689 620 a(b) p Fn(\)) p 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1468 a(0) p Ff(\024) p Fk(l) q(;m) p Ff(\024) p Fj(1) p Fl 1646 1367 a(\015) p Fk 1697 1382 a(l) q(m) p Fn 1785 1367 a(\() p Fl(k) p Fn 1877 1367 a(\)) p 1932 1367 a(\() p Fl(\037!) p Fj 2092 1382 a(+) p Fk(l) p Fg 2195 1367 a(\012) p Fl 2294 1367 a(\037!) p Fj 2416 1382 a(+) p Fk(m) p Fn 2538 1367 a(\)) 0 1669 y(for) p 153 1669 a(some) p 400 1669 a(2) p Fg 474 1669 a(\002) p Fn 576 1669 a(2) p 661 1669 a(matrix) p 981 1669 a(\() p Fl(\015) p Fk 1070 1684 a(l) q(m) p Fn 1158 1669 a(\() p Fl(k) p Fn 1250 1669 a(\)\)) p Fj 1326 1699 a(0) p Ff(\024) p Fk(l) q(;m) p Ff(\024) p Fj(1) p Fn 1614 1669 a(.) p 1695 1669 a(The) p 1899 1669 a(comp) s(onen) m(ts) p 2440 1669 a(ob) s(ey) p Fl 2677 1669 a(\015) p Fk 2728 1684 a(l) q(m) p Fn 2816 1669 a(\() p Fl(k) p Fn 2908 1669 a(\)) p 2979 1669 a(=) p Fl 3089 1669 a(O) p Fn 3167 1669 a(\() p Fg(j) p Fl(k) p Fg 3287 1669 a(j) p Fj 3315 1633 a(2) p Fn 3353 1669 a(\)) p 3427 1669 a(for) p Fl 0 1799 a(l) p Fg 59 1799 a(6) p Fn(=) p Fl 162 1799 a(m) p Fn(,) p 307 1799 a(and) p Fl 497 1799 a(\015) p Fk 548 1814 a(l) q(l) p Fn 596 1799 a(\() p Fl(k) p Fn 688 1799 a(\)) p 753 1799 a(=) p Fl 857 1799 a(\015) p Fk 908 1814 a(l) p Fl 933 1799 a(i) p Ff 966 1763 a(\000) p Fj(2) p Fk(\027) p Fl 1100 1799 a(k) p Fj 1154 1763 a(2) p Fk(\027) p Fn 1232 1799 a(\(1) p 1341 1799 a(+) p Fl 1439 1799 a(o) p Fn(\(1\)\).) p 1719 1799 a(This) p 1942 1799 a(completes) p 2392 1799 a(the) p 2560 1799 a(pro) s(of.) p Fc 2951 1799 a(2) p Fd 0 1967 a(Pr) p 102 1967 a(o) p 147 1967 a(of) p 262 1967 a(of) p 376 1967 a(L) p 432 1967 a(emma) p 721 1967 a(3.3.) p Fn 978 1967 a(The) p 1179 1967 a(lemma) p 1493 1967 a(follo) m(ws) p 1813 1967 a(from) p 2044 1967 a(Prop) s(osition) p 2569 1967 a(4.2.) p Fc 2861 1967 a(2) p Fd 0 2135 a(Pr) p 102 2135 a(o) p 147 2135 a(of) p 262 2135 a(of) p 376 2135 a(L) p 432 2135 a(emma) p 721 2135 a(3.4.) p Fn 978 2135 a(W) p 1070 2135 a(e) p 1146 2135 a(ha) m(v) m(e) p Fl 518 2349 a(\037) p Fh 596 2252 a(\020) p Fn 645 2349 a(\() p Fl(L) p Fj 749 2364 a(+) p Fn 831 2349 a(+) p Fl 929 2349 a(i") p Fj 1008 2307 a(2) p Fn 1047 2349 a(\)) p Ff 1085 2307 a(\000) p Fj(1) p Fg 1201 2349 a(\000) p Fn 1301 2349 a(\() p Fl(L) p Fj 1405 2364 a(+) p Fg 1486 2349 a(\000) p Fl 1586 2349 a(i") p Fj 1665 2307 a(2) p Fn 1704 2349 a(\)) p Ff 1742 2307 a(\000) p Fj(1) p Fh 1837 2252 a(\021) p Fl 1903 2349 a(\037) p Fn 1992 2349 a(=) p Fl 2095 2349 a(O) s(p) p Fn(\() p Fl(") p Fj 2306 2307 a(2) p Fk(\013) p Fn 2390 2349 a(\)) p 2450 2349 a(+) p Fl 2548 2349 a(O) s(p) p Fn(\() p Fl(") p Fj 2759 2307 a(2\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fn 2988 2349 a(\)) 0 2579 y(b) m(y) p 135 2579 a(Prop) s(osition) p 660 2579 a(4.2.) p 855 2579 a(Since) p Fl 1110 2579 a(J) p Ff 1173 2543 a(\003) p Fk 1164 2603 a(") p Fn 1213 2579 a(\() p Fl(L) p Fj 1317 2594 a(+) p Fk(") p Fn 1431 2579 a(+) p Fl 1529 2579 a(i) p Fn(\)) p Ff 1600 2543 a(\000) p Fj(1) p Fl 1694 2579 a(J) p Fk 1748 2594 a(") p Fn 1813 2579 a(=) p Fl 1916 2579 a(") p Fj 1962 2543 a(2) p Fn 2001 2579 a(\() p Fl(L) p Fj 2105 2594 a(+) p Fn 2187 2579 a(+) p Fl 2285 2579 a(i") p Fj 2364 2543 a(2) p Fn 2403 2579 a(\)) p Ff 2441 2543 a(\000) p Fj(1) p Fn 2535 2579 a(,) p 2595 2579 a(it) p 2693 2579 a(follo) m(ws) p 3013 2579 a(that) p Fg 71 2792 a(k) p Fl(\037) p Fk 182 2807 a(") p Fn 219 2792 a(\() p Fl(L) p Fj 323 2807 a(+) p Fk(") p Fn 437 2792 a(+) p Fl 535 2792 a(i) p Fn(\)) p Ff 606 2751 a(\000) p Fj(1) p Fg 701 2792 a(k) p Fj 751 2751 a(2) p Fn 818 2792 a(=) p Fg 921 2792 a(k) p Fl(\037J) p Ff 1095 2751 a(\003) p Fk 1086 2817 a(") p Fn 1135 2792 a(\() p Fl(L) p Fj 1239 2807 a(+) p Fk(") p Fn 1353 2792 a(+) p Fl 1451 2792 a(i) p Fn(\)) p Ff 1522 2751 a(\000) p Fj(1) p Fn 1616 2792 a(\() p Fl(L) p Fj 1720 2807 a(+) p Fk(") p Fg 1834 2792 a(\000) p Fl 1934 2792 a(i) p Fn(\)) p Ff 2005 2751 a(\000) p Fj(1) p Fl 2099 2792 a(J) p Fk 2153 2807 a(") p Fl 2190 2792 a(\037) p Fg(k) p Fn 2329 2792 a(=) p Fl 2432 2792 a(O) p Fn 2510 2792 a(\() p Fl(") p Fj 2594 2751 a(2+2) p Fk(\013) p Fn 2768 2792 a(\)) p 2828 2792 a(+) p Fl 2926 2792 a(O) p Fn 3004 2792 a(\() p Fl(") p Fj 3088 2751 a(2+2\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fn 3407 2792 a(\)) p Fl(;) p Fn 0 3005 a(where) p Fl 282 3005 a(\037) p Fk 343 3020 a(") p Fn 380 3005 a(\() p Fl(x) p Fn(\)) p 539 3005 a(=) p Fl 642 3005 a(\037) p Fn(\() p Fl(x=") p Fn(\).) p 999 3005 a(Hence) p Fg 874 3219 a(k) p Fl(\037) p Fk 985 3234 a(") p Fn 1022 3219 a(\() p Fl(L) p Fj 1126 3234 a(+) p Fk(") p Fn 1240 3219 a(+) p 1338 3219 a(1\)) p Ff 1425 3178 a(\000) p Fj(1) p Fg 1519 3219 a(k) p Fn 1596 3219 a(=) p Fl 1700 3219 a(O) p Fn 1778 3219 a(\() p Fl(") p Fj 1862 3178 a(1+) p Fk(\013) p Fn 2000 3219 a(\)) p 2061 3219 a(+) p Fl 2159 3219 a(O) p Fn 2237 3219 a(\() p Fl(") p Fj 2321 3178 a(1+\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fn 2604 3219 a(\)) p Fl(:) p Fn 0 3432 a(If) p 98 3432 a(w) m(e) p 241 3432 a(set) p Fl 393 3432 a(u) p Fk 449 3447 a(") p Fn 513 3432 a(=) p 617 3432 a(\() p Fl(L) p Fj 721 3447 a(+) p Fk(") p Fn 835 3432 a(+) p 933 3432 a(1\)) p Ff 1020 3396 a(\000) p Fj(1) p Fl 1114 3432 a(f) p Fn 1205 3432 a(for) p Fl 1354 3432 a(f) p Fg 1441 3432 a(2) p Fl 1535 3432 a(L) p Fj 1601 3396 a(2) p Fn 1641 3432 a(,) p 1700 3432 a(then) p Fl 1922 3432 a(u) p Fk 1978 3447 a(") p Fn 2047 3432 a(satis\014es) p 2406 3432 a(the) p 2574 3432 a(equation) 847 3645 y(\() p Fl(L) p Fj 951 3660 a(+) p Fk(") p Fn 1065 3645 a(+) p 1163 3645 a(1\)) p Fl(u) p Fk 1306 3660 a(") p Fn 1370 3645 a(=) p 1473 3645 a(\() p Fl(p) p Fj 1560 3604 a(2) 1560 3670 y(1) p Fk(") p Fn 1654 3645 a(+) p Fl 1752 3645 a(p) p Fj 1801 3604 a(2) 1801 3670 y(2) p Fk(") p Fn 1873 3645 a(\)) p Fl(u) p Fk 1967 3660 a(") p Fn 2026 3645 a(+) p Fl 2124 3645 a(b) p Fk 2165 3660 a(") p Fl 2202 3645 a(u) p Fk 2258 3660 a(") p Fn 2316 3645 a(+) p Fl 2414 3645 a(u) p Fk 2470 3660 a(") p Fn 2534 3645 a(=) p Fl 2638 3645 a(f) p Fn 0 3859 a(and) p 190 3859 a(ob) s(eys) p 461 3859 a(the) p 629 3859 a(b) s(ound) p Fg 853 4072 a(k) p Fl(\037) p Fk 964 4087 a(") p Fl 1000 4072 a(u) p Fk 1056 4087 a(") p Fg 1093 4072 a(k) p Fk 1143 4089 a(L) p Fe 1191 4070 a(2) p Fn 1257 4072 a(=) p Fh 1360 3976 a(\020) p Fl 1410 4072 a(O) p Fn 1488 4072 a(\() p Fl(") p Fj 1572 4031 a(1+) p Fk(\013) p Fn 1711 4072 a(\)) p 1771 4072 a(+) p Fl 1869 4072 a(O) p Fn 1947 4072 a(\() p Fl(") p Fj 2031 4031 a(1+\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fn 2314 4072 a(\)) p Fh 2352 3976 a(\021) p Fg 2418 4072 a(k) p Fl(f) p Fg 2527 4072 a(k) p Fk 2577 4089 a(L) p Fe 2625 4070 a(2) p Fl 2663 4072 a(:) p Fn 3343 4072 a(\(4.8\)) 0 4286 y(Th) m(us) p 247 4286 a(w) m(e) p 391 4286 a(ha) m(v) m(e) p Fg 911 4406 a(k) p Fl(\037) p Fk 1022 4421 a(") p Fl 1059 4406 a(p) p Fk 1108 4421 a(j) t(") p Fl 1177 4406 a(u) p Fk 1233 4421 a(") p Fg 1269 4406 a(k) p Fk 1319 4423 a(L) p Fe 1367 4404 a(2) p Fn 1434 4406 a(=) p Fh 1537 4310 a(\020) p Fl 1587 4406 a(O) p Fn 1665 4406 a(\() p Fl(") p Fk 1749 4365 a(\013) p Fn 1797 4406 a(\)) p 1857 4406 a(+) p Fl 1955 4406 a(O) p Fn 2033 4406 a(\() p Fl(") p Fj 2117 4365 a(1) p Ff(\000) p Fk(\013) p Fn 2256 4406 a(\)) p Fh 2294 4310 a(\021) p Fg 2360 4406 a(k) p Fl(f) p Fg 2469 4406 a(k) p Fk 2519 4423 a(L) p Fe 2567 4404 a(2) p Fl 2605 4406 a(:) p Fn 3343 4406 a(\(4.9\)) 0 4594 y(b) m(y) p 135 4594 a(elliptic) p 455 4594 a(estimate.) p 884 4594 a(A) p 990 4594 a(similar) p 1310 4594 a(argumen) m(t) p 1746 4594 a(applies) p 2072 4594 a(to) p Fl 2191 4594 a(v) p Fn 2269 4594 a(=) p 2373 4594 a(\() p Fl(L) p Fk 2477 4609 a(AB) p Fn 2613 4594 a(+) p 2711 4594 a(1\)) p Ff 2798 4558 a(\000) p Fj(1) p Fl 2892 4594 a(f) p Fn 2951 4594 a(.) p 3021 4594 a(Note) p 3257 4594 a(that) p Fl 1016 4807 a(J) p Ff 1079 4766 a(\003) p Fk 1070 4832 a(") p Fn 1119 4807 a(\() p Fl(L) p Fk 1223 4822 a(AB) p Fn 1359 4807 a(+) p 1457 4807 a(1\)) p Ff 1544 4766 a(\000) p Fj(1) p Fl 1638 4807 a(J) p Fk 1692 4822 a(") p Fn 1756 4807 a(=) p Fl 1860 4807 a(") p Fj 1906 4766 a(2) p Fn 1945 4807 a(\() p Fl(L) p Fk 2049 4822 a(AB) p Fn 2185 4807 a(+) p Fl 2283 4807 a(") p Fj 2329 4766 a(2) p Fn 2368 4807 a(\)) p Ff 2406 4766 a(\000) p Fj(1) p Fl 2500 4807 a(:) p Fn 0 5021 a(The) p 208 5021 a(Green) p 503 5021 a(k) m(ernel) p 797 5021 a(of) p 915 5021 a(\() p Fl(L) p Fk 1019 5036 a(AB) p Fg 1160 5021 a(\000) p Fl 1265 5021 a(k) p Fj 1319 4985 a(2) p Fn 1358 5021 a(\)) p Ff 1396 4985 a(\000) p Fj(1) p Fn 1530 5021 a(is) p 1635 5021 a(explicitly) p 2065 5021 a(represen) m(ted) p 2590 5021 a(in) p 2711 5021 a(terms) p 2990 5021 a(of) p 3108 5021 a(the) p 3283 5021 a(Bessel) 0 5141 y(functions) p 429 5141 a(after) p 668 5141 a(separation) p 1148 5141 a(in) m(to) p 1354 5141 a(the) p 1530 5141 a(p) s(olar) p 1791 5141 a(co) s(ordinates,) p 2346 5141 a(and) p 2544 5141 a(it) p 2650 5141 a(admits) p 2979 5141 a(an) p 3123 5141 a(expansion) 0 5262 y(similar) p 320 5262 a(to) p 440 5262 a(\() p Fl(L) p Fj 544 5277 a(+) p Fg 625 5262 a(\000) p Fl 725 5262 a(k) p Fj 779 5225 a(2) p Fn 818 5262 a(\)) p Ff 856 5225 a(\000) p Fj(1) p Fn 950 5262 a(.) p 1021 5262 a(Th) m(us) p 1268 5262 a(w) m(e) p 1412 5262 a(obtain) p Fg 887 5487 a(k) p Fl(\037) p Fk 998 5502 a(") p Fl 1035 5487 a(v) p Fg 1086 5487 a(k) p Fk 1136 5504 a(L) p Fe 1184 5485 a(2) p Fn 1250 5487 a(=) p Fh 1353 5391 a(\020) p Fl 1403 5487 a(O) p Fn 1481 5487 a(\() p Fl(") p Fj 1565 5446 a(1+) p Fk(\013) p Fn 1703 5487 a(\)) p 1763 5487 a(+) p Fl 1861 5487 a(O) p Fn 1939 5487 a(\() p Fl(") p Fj 2023 5446 a(1+\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fn 2307 5487 a(\)) p Fh 2345 5391 a(\021) p Fg 2411 5487 a(k) p Fl(f) p Fg 2520 5487 a(k) p Fk 2570 5504 a(L) p Fe 2618 5485 a(2) p Fn 3294 5487 a(\(4.10\)) 1723 5753 y(17) p 90 rotate dyy eop %%Page: 18 18 18 17 bop Fn 0 407 a(and) p Fg 945 527 a(k) p Fl(\037) p Fk 1056 542 a(") p Fl 1093 527 a(\031) p Fk 1148 542 a(j) p Fl 1185 527 a(v) p Fg 1236 527 a(k) p Fk 1286 544 a(L) p Fe 1334 525 a(2) p Fn 1400 527 a(=) p Fh 1503 431 a(\020) p Fl 1553 527 a(O) p Fn 1631 527 a(\() p Fl(") p Fk 1715 486 a(\013) p 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355 834 a(w) p Fk 425 849 a(") p Fn 490 834 a(=) p Fl 593 834 a(u) p Fk 649 849 a(") p Fg 708 834 a(\000) p Fl 807 834 a(v) p Fn 890 834 a(satis\014es) 1125 1054 y(\(1) p Fg 1233 1054 a(\000) p Fl 1333 1054 a(\037) p Fk 1394 1069 a(") p Fn 1431 1054 a(\)) p Fh 1486 958 a(\020) p Fl 1535 1054 a(p) p Fj 1584 1013 a(2) 1584 1079 y(1) p Fk(") p Fn 1678 1054 a(+) p Fl 1776 1054 a(p) p Fj 1825 1013 a(2) 1825 1079 y(2) p Fk(") p Fn 1919 1054 a(+) p 2017 1054 a(1) p Fh 2066 958 a(\021) p Fl 2132 1054 a(w) p Fk 2202 1069 a(") p Fn 2266 1054 a(=) p 2370 1054 a(0) 0 1287 y(and) p 190 1287 a(it) p 287 1287 a(follo) m(ws) p 608 1287 a(from) p 838 1287 a(\(4.8\)) p 1071 1287 a(and) p 1261 1287 a(\(4.10\)) p 1542 1287 a(that) p Fg 781 1519 a(k) p Fn(\(1) p Fg 940 1519 a(\000) p Fl 1039 1519 a(\037) p Fk 1100 1534 a(") p Fn 1137 1519 a(\)) p Fl(p) p Fk 1224 1534 a(j) t(") p Fl 1293 1519 a(w) p Fk 1363 1534 a(") p Fg 1400 1519 a(k) p Fk 1450 1536 a(L) p Fe 1498 1517 a(2) p Fn 1564 1519 a(=) p Fh 1667 1423 a(\020) p Fl 1717 1519 a(O) p Fn 1795 1519 a(\() p Fl(") p Fk 1879 1478 a(\013) p Fn 1927 1519 a(\)) p 1987 1519 a(+) p Fl 2085 1519 a(O) p Fn 2163 1519 a(\() p Fl(") p Fj 2247 1478 a(1) p Ff(\000) p Fk(\013) p Fn 2386 1519 a(\)) p Fh 2424 1423 a(\021) p Fg 2490 1519 a(k) p Fl(f) p Fg 2599 1519 a(k) p Fk 2649 1536 a(L) p Fe 2697 1517 a(2) p Fl 2735 1519 a(:) p Fn 0 1752 a(This,) p 250 1752 a(together) p 635 1752 a(with) p 857 1752 a(\(4.9\)) p 1090 1752 a(and) p 1280 1752 a(\(4.11\),) p 1588 1752 a(yields) p Fg 629 1972 a(k) p Fl(p) p Fk 728 1987 a(j) t(") p Fn 797 1972 a(\() p Fl(L) p Fj 901 1987 a(+) p Fk(") p Fn 1015 1972 a(+) p 1113 1972 a(1\)) p Ff 1200 1931 a(\000) p Fj(1) p Fg 1316 1972 a(\000) p Fl 1416 1972 a(\031) p Fk 1471 1987 a(j) p Fn 1508 1972 a(\() p Fl(L) p Fk 1612 1987 a(AB) p Fn 1747 1972 a(+) p 1845 1972 a(1\)) p Ff 1932 1931 a(\000) p Fj(1) p Fg 2027 1972 a(k) p Fn 2104 1972 a(=) p Fl 2208 1972 a(O) p Fn 2286 1972 a(\() p Fl(") p Fk 2370 1931 a(\013) p Fn 2418 1972 a(\)) p 2478 1972 a(+) p Fl 2576 1972 a(O) p Fn 2654 1972 a(\() p Fl(") p Fj 2738 1931 a(1) p Ff(\000) p Fk(\013) p Fn 2876 1972 a(\)) 0 2192 y(and) p 190 2192 a(the) p 358 2192 a(pro) s(of) p 612 2192 a(is) p 710 2192 a(complete.) p Fc 1258 2192 a(2) p Fn 146 2362 a(W) p 238 2362 a(e) p 322 2362 a(mo) m(v) m(e) p 582 2362 a(to) p 709 2362 a(the) p 885 2362 a(pro) s(of) p 1148 2362 a(of) p 1267 2362 a(Lemma) p 1623 2362 a(3.5.) p 1841 2362 a(W) p 1933 2362 a(e) p 2017 2362 a(analyze) p 2375 2362 a(the) p 2551 2362 a(b) s(eha) m(vior) p 2957 2362 a(as) p Fg 3084 2362 a(j) p Fl(k) p Fg 3166 2362 a(j) p 3235 2362 a(!) p Fn 3376 2362 a(0) p 3465 2362 a(of) 0 2482 y(\() p Fl(L) p Ff 104 2497 a(\000) p Fg 189 2482 a(\000) p Fl 291 2482 a(k) p Fj 345 2446 a(2) p Fn 385 2482 a(\)) p Ff 423 2446 a(\000) p Fj(1) p Fn 517 2482 a(.) p 601 2482 a(Decomp) s(ose) p Fl 1117 2482 a(b) p Fn 1195 2482 a(in) m(to) p 1398 2482 a(the) p 1570 2482 a(pro) s(duct) p Fl 1941 2482 a(b) p Fn 2018 2482 a(=) p Fl 2129 2482 a(b) p Fj 2170 2446 a(1) p Fk(=) p Fj(2) p Fg 2280 2482 a(j) p Fl(b) p Fg(j) p Fj 2377 2446 a(1) p Fk(=) p Fj(2) p Fn 2487 2482 a(,) p 2552 2482 a(where) p Fl 2839 2482 a(b) p Fj 2880 2446 a(1) p Fk(=) p Fj(2) p Fn 3026 2482 a(=) p Fg 3137 2482 a(j) p Fl(b) p Fg(j) p Fj 3234 2446 a(1) p Fk(=) p Fj(2) p Fn 3344 2482 a(sgn) p Fl 3502 2482 a(b) p Fn 0 2603 a(with) p 222 2603 a(sgn) p Fl 380 2603 a(b) p Fn 449 2603 a(=) p Fl 553 2603 a(b=) p Fg(j) p Fl(b) p Fg(j) p Fn(.) p 810 2603 a(Then) p 1065 2603 a(w) m(e) p 1209 2603 a(ha) m(v) m(e) 260 2823 y(\() p Fl(L) p Ff 364 2838 a(\000) p Fg 445 2823 a(\000) p Fl 545 2823 a(k) p Fj 599 2782 a(2) p Fn 638 2823 a(\)) p Ff 676 2782 a(\000) p Fj(1) p Fn 798 2823 a(=) p 902 2823 a(\() p Fl(L) p Fg 1028 2823 a(\000) p Fl 1128 2823 a(k) p Fj 1182 2782 a(2) p Fn 1222 2823 a(\)) p Ff 1260 2782 a(\000) p Fj(1) p Fn 1376 2823 a(+) p 1474 2823 a(\() p Fl(L) p Fg 1600 2823 a(\000) p Fl 1700 2823 a(k) p Fj 1754 2782 a(2) p Fn 1794 2823 a(\)) p Ff 1832 2782 a(\000) p Fj(1) p Fg 1926 2823 a(j) p Fl(b) p Fg(j) p Fj 2023 2782 a(1) p Fk(=) p Fj(2) p Fl 2133 2823 a(Z) p Fn 2207 2823 a(\() p Fl(k) p Fn 2299 2823 a(\)) p Ff 2337 2782 a(\000) p Fj(1) p Fl 2431 2823 a(b) p Fj 2472 2782 a(1) p Fk(=) p Fj(2) p Fn 2582 2823 a(\() p Fl(L) p Fg 2709 2823 a(\000) p Fl 2808 2823 a(k) p Fj 2862 2782 a(2) p Fn 2902 2823 a(\)) p Ff 2940 2782 a(\000) p Fj(1) p Fn 3294 2823 a(\(4.12\)) 0 3043 y(b) m(y) p 135 3043 a(rep) s(eated) p 534 3043 a(use) p 702 3043 a(of) p 813 3043 a(the) p 981 3043 a(resolv) m(en) m(t) p 1391 3043 a(iden) m(tit) m(y) p 1709 3043 a(,) p 1771 3043 a(where) p Fl 1100 3263 a(Z) p Fn 1174 3263 a(\() p Fl(k) p Fn 1266 3263 a(\)) p 1332 3263 a(=) p 1435 3263 a(1) p Fg 1506 3263 a(\000) p Fl 1606 3263 a(b) p Fj 1647 3222 a(1) p Fk(=) p Fj(2) p Fn 1757 3263 a(\() p Fl(L) p Fg 1884 3263 a(\000) p Fl 1983 3263 a(k) p Fj 2037 3222 a(2) p Fn 2077 3263 a(\)) p Ff 2115 3222 a(\000) p Fj(1) p Fg 2209 3263 a(j) p Fl(b) p Fg(j) p Fj 2306 3222 a(1) p Fk(=) p Fj(2) p Fl 2416 3263 a(:) p Fn 0 3483 a(Since) p Fl 263 3483 a(L) p Ff 329 3498 a(\000) p Fn 430 3483 a(has) p 613 3483 a(a) p 703 3483 a(resonance) p 1157 3483 a(state) p 1404 3483 a(at) p 1532 3483 a(zero) p 1747 3483 a(energy) p 2017 3483 a(,) p 2089 3483 a(1) p Fg 2165 3483 a(\000) p Fl 2271 3483 a(b) p Fj 2312 3447 a(1) p Fk(=) p Fj(2) p Fl 2422 3483 a(G) p Fj 2499 3498 a(0) p Fg 2539 3483 a(j) p Fl(b) p Fg(j) p Fj 2636 3447 a(1) p Fk(=) p Fj(2) p Fn 2788 3483 a(:) p Fl 2858 3483 a(L) p Fj 2924 3447 a(2) p Fg 3006 3483 a(!) p Fl 3148 3483 a(L) p Fj 3214 3447 a(2) p Fn 3296 3483 a(is) p 3402 3483 a(not) 0 3603 y(in) m(v) m(ertible.) p 469 3603 a(Let) p Fl 1064 3724 a(X) p Fn 1181 3724 a(=) p Fg 1284 3724 a(f) p Fl(v) p Fg 1412 3724 a(2) p Fl 1507 3724 a(L) p Fj 1573 3682 a(2) p Fn 1640 3724 a(:) p Fl 1695 3724 a(v) p Fn 1773 3724 a(=) p Fl 1877 3724 a(b) p Fj 1918 3682 a(1) p Fk(=) p Fj(2) p Fl 2028 3724 a(G) p Fj 2105 3739 a(0) p Fg 2145 3724 a(j) p Fl(b) p Fg(j) p Fj 2242 3682 a(1) p Fk(=) p Fj(2) p Fl 2351 3724 a(v) p Fg 2402 3724 a(g) p Fl(:) p Fn 0 3898 a(According) p 469 3898 a(to) p 594 3898 a([20],) p 813 3898 a(dim) p Fl 992 3898 a(X) p Fn 1119 3898 a(=) p 1232 3898 a(1,) p 1348 3898 a(and) p Fl 1543 3898 a(v) p Fg 1632 3898 a(2) p Fl 1736 3898 a(X) r(;) p 1901 3898 a(v) p Fg 1989 3898 a(6) p Fn(=) p 2103 3898 a(0,) p 2219 3898 a(satis\014es) p 2584 3898 a(\() p Fl(v) t(;) p Fg 2717 3898 a(j) p Fl(b) p Fg(j) p Fj 2814 3862 a(1) p Fk(=) p Fj(2) p Fl 2923 3898 a(!) p Fj 2984 3913 a(0) p Fn 3023 3898 a(\)) p Fk 3061 3915 a(L) p Fe 3109 3896 a(2) p Fg 3186 3898 a(6) p Fn(=) p 3299 3898 a(0) p 3386 3898 a(and) 0 4018 y(\() p Fl(v) t(;) p Fg 133 4018 a(j) p Fl(b) p Fg(j) p Fj 230 3982 a(1) p Fk(=) p Fj(2) p Fl 339 4018 a(!) p Fj 400 4033 a(1) p Fn 439 4018 a(\)) p Fk 477 4035 a(L) p Fe 525 4016 a(2) p Fn 592 4018 a(=) p 695 4018 a(0) p 777 4018 a(for) p Fl 926 4018 a(!) p Fk 987 4033 a(l) p Fn 1045 4018 a(de\014ned) p 1381 4018 a(b) m(y) p 1516 4018 a(\(4.1\).) p 1787 4018 a(W) p 1879 4018 a(e) p 1955 4018 a(normalize) p Fl 2400 4018 a(\021) p Fj 2448 4033 a(0) p Fg 2515 4018 a(2) p Fl 2609 4018 a(X) p Fn 2730 4018 a(as) 871 4238 y(\() p Fl(\021) p Fj 957 4253 a(0) p Fl 997 4238 a(;) p Fg 1041 4238 a(j) p Fl(b) p Fg(j) p Fj 1138 4197 a(1) p Fk(=) p Fj(2) p Fl 1247 4238 a(!) p Fj 1308 4253 a(0) p Fn 1348 4238 a(\)) p Fk 1386 4255 a(L) p Fe 1434 4236 a(2) p Fn 1500 4238 a(=) p 1603 4238 a(1) p Fl(;) p Fn 1891 4238 a(\() p Fl(\021) p Fj 1977 4253 a(0) p Fl 2017 4238 a(;) p Fg 2061 4238 a(j) p Fl(b) p Fg(j) p Fj 2158 4197 a(1) p Fk(=) p Fj(2) p Fl 2267 4238 a(!) p Fj 2328 4253 a(1) p Fn 2367 4238 a(\)) p Fk 2405 4255 a(L) p Fe 2453 4236 a(2) p Fn 2520 4238 a(=) p 2623 4238 a(0) p 3294 4238 a(\(4.13\)) 0 4458 y(and) p 190 4458 a(de\014ne) p Fl 1442 4579 a(\032) p Fj 1492 4594 a(0) p Fn 1560 4579 a(=) p Fl 1663 4579 a(G) p Fj 1740 4594 a(0) p Fg 1780 4579 a(j) p Fl(b) p Fg(j) p Fj 1877 4538 a(1) p Fk(=) p Fj(2) p Fl 1986 4579 a(\021) p Fj 2034 4594 a(0) p Fl 2074 4579 a(:) p Fn 3294 4579 a(\(4.14\)) 0 4753 y(Then) p Fl 255 4753 a(\032) p Fj 305 4768 a(0) p Fn 377 4753 a(solv) m(es) p Fl 654 4753 a(L) p Ff 720 4768 a(\000) p Fl 780 4753 a(\032) p Fj 830 4768 a(0) p Fn 897 4753 a(=) p 1001 4753 a(0) p 1082 4753 a(and) p 1272 4753 a(b) s(eha) m(v) m(es) p 1635 4753 a(lik) m(e) p Fl 946 4973 a(\032) p Fj 996 4988 a(0) p Fn 1035 4973 a(\() p Fl(x) p Fn(\)) p 1194 4973 a(=) p 1298 4973 a(\(2) p Fl(\031) t(\013) p Fn 1507 4973 a(\)) p Ff 1545 4932 a(\000) p Fj(1) p Fk(=) p Fj(2) p Fl 1709 4973 a(r) p Ff 1756 4932 a(\000) p Fk(\013) p Fn 1882 4973 a(+) p Fl 1980 4973 a(g) t(;) p 2269 4973 a(r) p Fg 2344 4973 a(!) p 2471 4973 a(1) p Fl(;) p Fn 3294 4973 a(\(4.15\)) 0 5193 y(with) p 225 5193 a(some) p Fl 473 5193 a(g) p Fg 557 5193 a(2) p Fl 656 5193 a(L) p Fj 722 5157 a(2) p Fn 798 5193 a(\(see) p 997 5193 a(\(5.8\)) p 1233 5193 a(and) p 1426 5193 a(\(5.9\)) p 1663 5193 a(in) p 1780 5193 a([20]\).) p 2050 5193 a(Th) m(us) p Fl 2300 5193 a(\032) p Fj 2350 5208 a(0) p Fn 2426 5193 a(spans) p 2696 5193 a(the) p 2867 5193 a(resonance) p 3315 5193 a(space) p Fl 0 5313 a(E) p Ff 72 5328 a(\000) p Fn 164 5313 a(of) p Fl 275 5313 a(L) p Ff 341 5328 a(\000) p Fn 433 5313 a(at) p 552 5313 a(zero) p 758 5313 a(energy) p 1028 5313 a(,) p 1089 5313 a(b) s(ecause) p 1449 5313 a(dim) p Fl 1629 5313 a(E) p Ff 1701 5328 a(\000) p Fn 1788 5313 a(=) p Fl 1891 5313 a(l) p Fn 1955 5313 a(as) p 2075 5313 a(sho) m(wn) p 2371 5313 a(already) p 2715 5313 a(in) p 2829 5313 a(section) p 3154 5313 a(3.) 1723 5753 y(18) p 90 rotate dyy eop %%Page: 19 19 19 18 bop Fm 0 407 a(Prop) s(osition) p 606 407 a(4.3) p Fd 798 407 a(L) p 854 407 a(et) p Fl 966 407 a(\032) p Fj 1016 422 a(0) p Fg 1083 407 a(2) p Fl 1177 407 a(E) p Ff 1249 422 a(\000) p Fd 1343 407 a(b) p 1383 407 a(e) p 1463 407 a(the) p 1625 407 a(r) p 1661 407 a(esonanc) p 1996 407 a(e) p 2074 407 a(state) p 2309 407 a(de\014ne) p 2554 407 a(d) p 2637 407 a(ab) p 2727 407 a(ove.) p 2941 407 a(Then) p Fl 329 627 a(\037) p Fn(\() p Fl(L) p Ff 494 642 a(\000) p Fg 575 627 a(\000) p Fl 675 627 a(k) p Fj 729 586 a(2) p Fn 768 627 a(\)) p Ff 806 586 a(\000) p Fj(1) p Fl 901 627 a(\037) p Fn 989 627 a(=) p Fl 1093 627 a(\015) p Ff 1144 642 a(\000) p Fn 1203 627 a(\() p Fl(k) p Fn 1295 627 a(\)) p Fl(i) p Fj 1366 586 a(2) p Fk(\013) p Fl 1451 627 a(k) p Ff 1505 586 a(\000) p Fj(2) p Fk(\013) p Fn 1661 627 a(\() p Fl(\037\032) p Fj 1810 642 a(0) p Fg 1872 627 a(\012) p Fl 1972 627 a(\037\032) p Fj 2083 642 a(0) p Fn 2122 627 a(\)) p 2182 627 a(+) p Fl 2280 627 a(O) s(p) p Fn(\() p Fg(j) p Fl(k) p Fg 2527 627 a(j) p Fj 2555 586 a(0) p Fn 2593 627 a(\)) p Fl(;) p Fg 2874 627 a(j) p Fl(k) p Fg 2956 627 a(j) p 3011 627 a(!) p Fn 3139 627 a(0) p Fl(;) p Fd 0 847 a(for) p 156 847 a(some) p 405 847 a(c) p 445 847 a(o) p 490 847 a(e\016cient) p Fl 862 847 a(\015) p Ff 913 862 a(\000) p Fn 971 847 a(\() p Fl(k) p Fn 1063 847 a(\)) p Fd 1136 847 a(ob) p 1226 847 a(eying) p Fl 1482 847 a(\015) p Ff 1533 862 a(\000) p Fn 1592 847 a(\() p Fl(k) p Fn 1684 847 a(\)) p 1750 847 a(=) p Fg 1853 847 a(\000) p Fn(1) p Fl(=\015) p Fj 2079 862 a(0) p Fn 2140 847 a(+) p Fl 2238 847 a(o) p Fn(\(1\)) p Fd(,) p Fl 2475 847 a(\015) p Fj 2526 862 a(0) p Fd 2600 847 a(b) p 2640 847 a(eing) p 2849 847 a(as) p 2973 847 a(in) p 3093 847 a(\(4.4\).) 0 1125 y(Pr) p 102 1125 a(o) p 147 1125 a(of.) p Fn 354 1125 a(F) p 410 1125 a(or) p 523 1125 a(brevit) m(y) p 814 1125 a(,) p 871 1125 a(w) m(e) p 1008 1125 a(pro) m(v) m(e) p 1265 1125 a(the) p 1427 1125 a(lemma) p 1736 1125 a(when) p Fl 1984 1125 a(b) p Fn(\() p Fl(x) p Fn(\)) p Fg 2185 1125 a(\025) p Fn 2290 1125 a(0.) p 2407 1125 a(If) p Fl 2499 1125 a(b) p Fn(\() p Fl(x) p Fn(\)) p 2698 1125 a(is) p 2791 1125 a(not) p 2958 1125 a(non{negativ) m(e,) p Fl 0 1245 a(b) p Fj 41 1209 a(1) p Fk(=) p Fj(2) p Fl 151 1245 a(G) p Fj 228 1260 a(0) p Fg 268 1245 a(j) p Fl(b) p Fg(j) p Fj 365 1209 a(1) p Fk(=) p Fj(2) p 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2147 3369 a(\000) p Fj(1) p Fg 2264 3418 a(\003) p Fl 2336 3418 a(:) p Fn 0 3630 a(According) p 463 3630 a(to) p 583 3630 a(this) p 773 3630 a(notation,) p 1190 3630 a(w) m(e) p 1334 3630 a(de\014ne) p Fl 1130 3853 a(p) p Ff 1179 3812 a(\000) p Fj(1) 1179 3877 y(+) p Fn 1301 3853 a(=) p Fg 1404 3853 a(\000) p Fn(\(2) p Fl(i) p Fn(\)) p Ff 1639 3812 a(\000) p Fj(1) p Fl 1734 3853 a(e) p Fk 1779 3812 a(ih) p Fl 1848 3853 a(e) p Ff 1893 3812 a(\000) p Fk(') p 1998 3774 V Fl 1998 3853 a(@) p Ff 2055 3793 a(\000) p Fj(1) p Fl 2149 3853 a(e) p Fk 2194 3812 a(') p Fl 2245 3853 a(e) p Ff 2290 3812 a(\000) p Fk(ih) p Fn 0 4089 a(and) p Fl 190 4089 a(p) p Ff 239 4053 a(\000) p Fj(1) p Ff 239 4114 a(\000) p Fn 361 4089 a(=) p Fh 464 3993 a(\020) p Fl 514 4089 a(p) p Ff 563 4053 a(\000) p Fj(1) 563 4114 y(+) p Fh 657 3993 a(\021) p Ff 707 4016 a(\003) p Fn 746 4089 a(.) p 817 4089 a(By) p 970 4089 a(de\014nition,) p 1430 4089 a(w) m(e) p 1574 4089 a(ha) m(v) m(e) p Fl 1799 4089 a(p) p Ff 1848 4104 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a(d) p 974 3430 a(with) p 1186 3430 a(zer) p 1307 3430 a(o) p 1393 3430 a(eigenvalue.) p 1906 3430 a(If,) p 2039 3430 a(c) p 2079 3430 a(onversely,) p Fl 2537 3430 a(v) p Fd 2623 3430 a(is) p 2729 3430 a(a) p 2814 3430 a(b) p 2854 3430 a(ound) p 3096 3430 a(state,) p 3361 3430 a(then) p Fl 0 3551 a(u) p Fn 83 3551 a(=) p Fg 187 3551 a(\000) p Fl(V) p Fj 343 3514 a(1) p Fk(=) p Fj(2) p Fl 453 3551 a(v) p Fd 538 3551 a(b) p 578 3551 a(elongs) p 872 3551 a(to) p Fn 989 3551 a(\010) p Fj 1059 3566 a(0) p Fd 1099 3551 a(.) 0 3826 y(Pr) p 102 3826 a(o) p 147 3826 a(of.) p Fn 354 3826 a(Let) p Fl 530 3826 a(u) p Fn 614 3826 a(=) p Fj 719 3789 a(t) p Fn 750 3826 a(\() p Fl(u) p Fj 844 3841 a(1) p Fl 883 3826 a(;) p 927 3826 a(u) p Fj 983 3841 a(2) p Fn 1022 3826 a(\)) p Fg 1089 3826 a(2) p Fn 1184 3826 a(\010) p Fj 1254 3841 a(0) p Fn 1327 3826 a(and) p Fl 1518 3826 a(v) p Fn 1597 3826 a(=) p Fj 1702 3789 a(t) p Fn 1734 3826 a(\() p Fl(v) p Fj 1819 3841 a(1) p Fl 1858 3826 a(;) p 1902 3826 a(v) p Fj 1949 3841 a(2) p Fn 1989 3826 a(\)) p 2055 3826 a(=) p Fl 2160 3826 a(F) p Fj 2223 3841 a(0) p Fg 2263 3826 a(j) p Fl(V) p Fg 2369 3826 a(j) p Fj 2397 3789 a(1) p Fk(=) p Fj(2) p Fl 2507 3826 a(u) p Fn(.) p 2635 3826 a(Then) p 2890 3826 a(\() p Fl(u) p Fj 2984 3841 a(1) p Fl 3023 3826 a(;) p Fg 3067 3826 a(j) p Fl(V) p Fg 3173 3826 a(j) p Fj 3201 3789 a(1) p Fk(=) p Fj(2) p Fl 3311 3826 a(\032) p Fj 3361 3841 a(0) p Fn 3401 3826 a(\)) p 3467 3826 a(=) 0 3946 y(0) p 87 3946 a(b) m(y) p 229 3946 a(assumption,) p 779 3946 a(and) p 974 3946 a(it) p 1078 3946 a(is) p 1182 3946 a(easy) p 1402 3946 a(to) p 1527 3946 a(see) p 1691 3946 a(that) p Fl 1908 3946 a(v) p Fj 1955 3961 a(1) p Fg 2032 3946 a(2) p Fl 2136 3946 a(L) p Fj 2202 3910 a(2) p Fn 2242 3946 a(.) p 2330 3946 a(Since) p Fl 2591 3946 a(\032) p Fj 2641 3961 a(0) p Fn 2718 3946 a(=) p Fl 2832 3946 a(ce) p Ff 2919 3910 a(\000) p Fk(') p Fl 3024 3946 a(e) p Fk 3069 3910 a(ih) p Fn 3177 3946 a(for) p 3331 3946 a(some) p Fl 0 4066 a(c) p Fg 70 4066 a(6) p Fn(=) p 173 4066 a(0,) p Fl 282 4066 a(v) p Fj 329 4081 a(2) p Fn 396 4066 a(=) p Fl 499 4066 a(p) p Ff 548 4030 a(\000) p Fj(1) p Ff 548 4091 a(\000) p Fg 643 4066 a(j) p Fl(V) p Fg 749 4066 a(j) p Fj 777 4030 a(1) p Fk(=) p Fj(2) p Fl 887 4066 a(u) p Fj 943 4081 a(1) p Fn 1014 4066 a(b) s(eha) m(v) m(es) p 1378 4066 a(lik) m(e) p Fl 156 4295 a(v) p Fj 203 4310 a(2) p Fn 242 4295 a(\() p Fl(x) p Fn(\)) p 401 4295 a(=) p Fl 505 4295 a(c) p Fn 564 4295 a(\() p Fl(u) p Fj 658 4310 a(1) p Fl 696 4295 a(;) p Fg 740 4295 a(j) p Fl(V) p Fg 846 4295 a(j) p Fj 874 4253 a(1) p Fk(=) p Fj(2) p Fl 984 4295 a(\032) p Fj 1034 4310 a(0) p Fn 1073 4295 a(\)) p Fk 1111 4311 a(L) p Fe 1159 4292 a(2) p Fl 1198 4295 a(e) p Fk 1243 4253 a(') p Fl 1293 4295 a(e) p Ff 1338 4253 a(\000) p Fk(ih) p Fn 1462 4295 a(\() p Fl(x) p Fj 1555 4310 a(1) p Fg 1617 4295 a(\000) p Fl 1717 4295 a(ix) p Fj 1805 4310 a(2) p Fn 1845 4295 a(\)) p Ff 1883 4253 a(\000) p Fj(1) p Fn 2000 4295 a(+) p 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a(\014rst) p 906 4948 a(statemen) m(t.) p 1406 4948 a(The) p 1610 4948 a(second) p 1928 4948 a(one) p 2110 4948 a(is) p 2211 4948 a(also) p 2410 4948 a(easy) p 2627 4948 a(to) p 2750 4948 a(pro) m(v) m(e.) p 3060 4948 a(If) p Fl 3161 4948 a(v) p Fg 3244 4948 a(2) p Fn 3344 4948 a([) p Fl(L) p Fj 3437 4912 a(2) p Fn 3477 4948 a(]) p Fj 3504 4912 a(2) p Fn 0 5068 a(satis\014es) p 359 5068 a(\() p Fl(K) p Fn 510 5068 a(+) p Fl 608 5068 a(V) p Fn 686 5068 a(\)) p Fl(v) p Fn 802 5068 a(=) p 906 5068 a(0,) p 1014 5068 a(then) p Fl 1237 5068 a(v) p Fn 1315 5068 a(=) p Fg 1419 5068 a(\000) p Fl(F) p Fj 1559 5083 a(0) p Fl 1599 5068 a(V) p 1677 5068 a(v) p Fn 1728 5068 a(.) p 1798 5068 a(Hence) p 2088 5068 a(w) m(e) p 2232 5068 a(ha) m(v) m(e) p Fl 807 5286 a(u) p Fn 890 5286 a(=) p Fg 994 5286 a(\000) p Fl(V) p Fj 1150 5245 a(1) p Fk(=) p Fj(2) p Fl 1260 5286 a(v) p Fn 1338 5286 a(=) p Fl 1442 5286 a(V) p Fj 1520 5245 a(1) p Fk(=) p Fj(2) p Fl 1630 5286 a(F) p Fj 1693 5301 a(0) p Fl 1733 5286 a(V) p 1811 5286 a(v) p Fn 1890 5286 a(=) p Fl 1993 5286 a(Z) p Fj 2060 5301 a(0) p Fl 2100 5286 a(V) p Fj 2178 5245 a(1) p Fk(=) p Fj(2) p Fl 2288 5286 a(v) p Fn 2366 5286 a(=) p Fg 2470 5286 a(\000) p Fl(Z) p Fj 2614 5301 a(0) p Fl 2654 5286 a(u;) p Fn 0 5504 a(whic) m(h,) p 306 5504 a(together) p 691 5504 a(with) p 913 5504 a(\(5.4\),) p 1173 5504 a(implies) p 1504 5504 a(that) p Fl 1716 5504 a(u) p Fg 1799 5504 a(2) p Fn 1893 5504 a(\010) p Fj 1963 5519 a(0) p Fn 2003 5504 a(.) p Fc 2171 5504 a(2) p Fn 1723 5753 a(21) p 90 rotate dyy eop %%Page: 22 22 22 21 bop Fn 146 407 a(If) p 234 407 a(dim) p 413 407 a(\010) p Fl(=) p Fn(\010) p Fj 602 422 a(0) p Fn 670 407 a(=) p 773 407 a(1,) p 874 407 a(then) p 1086 407 a(the) p 1244 407 a(ab) s(o) m(v) m(e) p 1510 407 a(lemma) p 1815 407 a(implies) p 2136 407 a(that) p 2337 407 a(\() p Fl(K) p Fn 2487 407 a(+) p Fl 2585 407 a(V) p Fn 2664 407 a(\)) p Fl 2718 407 a(v) p Fn 2797 407 a(=) p 2900 407 a(0) p 2972 407 a(has) p 3135 407 a(a) p 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Fg 2217 5367 a(6) p Fn(=) p 2320 5367 a(0) p Fl(:) p Fn 1723 5753 a(22) p 90 rotate dyy eop %%Page: 23 23 23 22 bop Fn 0 407 a(Then) p 266 407 a(\() p Fl(V) p 383 407 a(v) t(;) p Fn 486 407 a(~) p Fl 478 407 a(\032) p Fj 528 422 a(0) p Fn 567 407 a(\)) p Fk 605 424 a(L) p Fe 653 405 a(2) p Fn 739 407 a(=) p 862 407 a(0,) p 985 407 a(and) p Fl 1186 407 a(v) p Fj 1233 422 a(1) p Fn 1273 407 a(\() p Fl(x) p Fn(\)) p 1451 407 a(=) p Fg 1574 407 a(\000) p Fl(d\032) p Fj 1752 422 a(0) p Fn 1792 407 a(\() p Fl(x) p Fn(\)) p 1940 407 a(\(1) p 2049 407 a(+) p Fl 2147 407 a(o) p Fn(\(1\)\)) p 2401 407 a(at) p 2531 407 a(in\014nit) m(y) p 2825 407 a(.) p 2932 407 a(W) p 3024 407 a(e) p 3111 407 a(sho) m(w) p 3364 407 a(that) 0 527 y(\() p Fl(K) p Fn 150 527 a(+) p Fl 248 527 a(V) p Fn 327 527 a(\)) p Fl(v) p Fn 443 527 a(=) p 547 527 a(0.) p 666 527 a(T) p 728 527 a(o) p 810 527 a(see) p 967 527 a(this,) p 1185 527 a(w) m(e) p 1328 527 a(calculate) p Fl 995 747 a(V) p Fj 1073 706 a(1) p Fk(=) p 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p Fl 2685 3030 a(c) p Fj 2727 3045 a(0) p Fg 2794 3030 a(6) p Fn(=) p 2898 3030 a(0) p Fl(:) p Fn 0 3250 a(This) p 223 3250 a(implies) p 554 3250 a(the) p 722 3250 a(second) p 1037 3250 a(statemen) m(t,) p 1517 3250 a(and) p 1707 3250 a(the) p 1875 3250 a(pro) s(of) p 2129 3250 a(is) p 2227 3250 a(complete.) p Fc 2775 3250 a(2) p Fn 146 3421 a(W) p 238 3421 a(e) p 313 3421 a(com) m(bine) p 693 3421 a(Lemmas) p 1078 3421 a(5.2,) p 1261 3421 a(5.3) p 1417 3421 a(and) p 1605 3421 a(5.4) p 1760 3421 a(to) p 1878 3421 a(form) m(ulate) p 2316 3421 a(the) p 2482 3421 a(precise) p 2801 3421 a(de\014nition) p 3233 3421 a(of) p 3342 3421 a(reso-) 0 3541 y(nance) p 276 3541 a(state) p 515 3541 a(at) p 635 3541 a(zero) p 841 3541 a(energy) p 1111 3541 a(.) p Fm 0 3711 a(De\014nition) p 532 3711 a(5.1) p Fn 773 3711 a(The) p 981 3711 a(op) s(erator) p Fl 1382 3711 a(K) p Fn 1500 3711 a(+) p Fl 1603 3711 a(V) p Fn 1722 3711 a(is) p 1828 3711 a(said) p 2037 3711 a(to) p 2164 3711 a(admit) p 2454 3711 a(a) p 2543 3711 a(resonance) p 2996 3711 a(state) p 3243 3711 a(at) p 3370 3711 a(zero) 0 3831 y(energy) p 270 3831 a(,) p 331 3831 a(if) p 420 3831 a(the) p 588 3831 a(follo) m(wing) p 1000 3831 a(condition) p 1428 3831 a(is) p 1526 3831 a(ful\014lled) p 1876 3831 a(:) 146 3952 y(\(1\)) p 369 3952 a(Assume) p 724 3952 a(that) p 930 3952 a(0) p Fl 1007 3952 a(<) p 1110 3952 a(\013) p Fg 1201 3952 a(\024) p Fn 1306 3952 a(1) p Fl(=) p Fn(2.) p 1521 3952 a(The) p 1716 3952 a(equation) p 2109 3952 a(\() p Fl(K) p Fn 2259 3952 a(+) p Fl 2357 3952 a(V) p Fn 2436 3952 a(\)) p Fl 2490 3952 a(v) p Fn 2569 3952 a(=) p 2672 3952 a(0) p 2748 3952 a(has) p 2916 3952 a(a) p 2992 3952 a(solution) p 3356 3952 a(suc) m(h) 0 4072 y(that) p Fl 211 4072 a(v) p Fn 290 4072 a(=) p Fj 393 4036 a(t) p Fn 425 4072 a(\() p Fl(v) p Fj 510 4087 a(1) p Fl 549 4072 a(;) p 593 4072 a(v) p Fj 640 4087 a(2) p Fn 680 4072 a(\)) p Fg 745 4072 a(2) p Fl 839 4072 a(L) p Fj 905 4036 a(2) p Fg 967 4072 a(\002) p Fl 1067 4072 a(L) p Ff 1133 4036 a(1) p Fn 1241 4072 a(and) p Fl 882 4292 a(v) p Fj 929 4307 a(2) p Fn 969 4292 a(\() p Fl(x) p Fn(\)) p 1128 4292 a(=) p Fl 1231 4292 a(r) p Ff 1278 4251 a(\000) p Fj(1+) p Fk(\013) p Fl 1472 4292 a(e) p Fk 1517 4251 a(i\022) p Fn 1597 4292 a(\(1) p 1706 4292 a(+) p Fl 1804 4292 a(o) p Fn(\(1\)\)) p Fl 2030 4292 a(;) p Fg 2269 4292 a(j) p Fl(x) p Fg(j) p 2407 4292 a(!) p 2535 4292 a(1) p Fl(:) p Fn 146 4512 a(\(2\)) p 369 4512 a(Assume) p 750 4512 a(that) p 982 4512 a(1) p Fl(=) p Fn(2) p Fl 1191 4512 a(<) p 1329 4512 a(\013) p 1454 4512 a(<) p Fn 1592 4512 a(1) p 1694 4512 a(and) p 1904 4512 a(that) p 2136 4512 a(\(5.1\)) p 2389 4512 a(is) p 2508 4512 a(ful\014lled.) p 2957 4512 a(The) p 3177 4512 a(equation) 0 4633 y(\() p Fl(K) p Fn 150 4633 a(+) p Fl 248 4633 a(V) p Fn 327 4633 a(\)) p Fl 381 4633 a(v) p Fn 460 4633 a(=) p 563 4633 a(0) p 645 4633 a(has) p 819 4633 a(a) p 900 4633 a(solution) p 1269 4633 a(suc) m(h) p 1489 4633 a(that) p Fl 1700 4633 a(v) p Fn 1779 4633 a(=) p Fj 1882 4596 a(t) p Fn 1914 4633 a(\() p Fl(v) p Fj 1999 4648 a(1) p Fl 2038 4633 a(;) p 2082 4633 a(v) p Fj 2129 4648 a(2) p Fn 2169 4633 a(\)) p Fg 2234 4633 a(2) p Fl 2328 4633 a(L) p Ff 2394 4596 a(1) p Fg 2492 4633 a(\002) p Fl 2591 4633 a(L) p Fj 2657 4596 a(2) p Fn 2730 4633 a(and) p Fl 981 4853 a(v) p Fj 1028 4868 a(1) p Fn 1068 4853 a(\() p Fl(x) p Fn(\)) p 1227 4853 a(=) p Fl 1330 4853 a(r) p Ff 1377 4812 a(\000) p Fk(\013) p Fn 1498 4853 a(\(1) p 1607 4853 a(+) p Fl 1705 4853 a(o) p Fn(\(1\)\)) p Fl 1931 4853 a(;) p Fg 2170 4853 a(j) p Fl(x) p Fg(j) p 2308 4853 a(!) p 2435 4853 a(1) p Fl(:) p Fn 146 5073 a(W) p 238 5073 a(e) p 322 5073 a(note) p 547 5073 a(that) p 766 5073 a(the) p 941 5073 a(de\014nition) p 1383 5073 a(is) p 1488 5073 a(in) m(v) p 1612 5073 a(arian) m(t) p 1905 5073 a(under) p 2189 5073 a(gauge) p 2474 5073 a(transformations.) p 3238 5073 a(W) p 3330 5073 a(e) p 3413 5073 a(are) 0 5193 y(no) m(w) p 203 5193 a(in) p 317 5193 a(a) p 398 5193 a(p) s(osition) p 770 5193 a(to) p 889 5193 a(state) p 1128 5193 a(the) p 1296 5193 a(second) p 1611 5193 a(main) p 1855 5193 a(theorem.) 1723 5753 y(23) p 90 rotate dyy eop %%Page: 24 24 24 23 bop Fm 0 407 a(Theorem) p 475 407 a(5.1) p Fd 667 407 a(Assume) p 1030 407 a(that) p 1228 407 a(the) p 1389 407 a(\015ux) p Fl 1577 407 a(\013) p Fd 1673 407 a(satis\014es) p 2038 407 a(\(1.2\)) p 2281 407 a(and) p 2469 407 a(that) p Fl 2668 407 a(K) p Fn 2777 407 a(+) p Fl 2873 407 a(V) p Fd 2985 407 a(has) p 3158 407 a(no) p 3297 407 a(b) p 3337 407 a(ound) 0 527 y(states) p 274 527 a(at) p 391 527 a(zer) p 512 527 a(o) p 597 527 a(ener) p 778 527 a(gy.) p 944 527 a(Then) p 1198 527 a(one) p 1382 527 a(has) p 1557 527 a(the) p 1719 527 a(fol) p 1829 527 a(lowing) p 2132 527 a(thr) p 2250 527 a(e) p 2290 527 a(e) p 2370 527 a(statements.) p Fn 146 697 a(\(1\)) p Fd 371 697 a(L) p 427 697 a(et) p Fn 538 697 a(0) p Fl 614 697 a(<) p 718 697 a(\013) p 808 697 a(<) p Fn 911 697 a(1) p Fl(=) p Fn(2) p Fd(.) p 1132 697 a(If) p Fl 1233 697 a(K) p Fn 1343 697 a(+) p Fl 1438 697 a(V) p Fd 1550 697 a(do) p 1645 697 a(es) p 1763 697 a(not) p 1933 697 a(have) p 2156 697 a(a) p 2240 697 a(r) p 2276 697 a(esonanc) p 2611 697 a(e) p 2688 697 a(state) p 2921 697 a(at) p 3036 697 a(zer) p 3157 697 a(o) p 3241 697 a(ener) p 3422 697 a(gy,) 0 818 y(then) p Fl 229 818 a(K) p Fk 312 833 a(") p Fn 349 818 a(\() p Fl(V) p Fk 444 833 a(") p Fn 480 818 a(\)) p Fd 565 818 a(c) p 605 818 a(onver) p 836 818 a(ges) p 1012 818 a(to) p Fl 1141 818 a(H) p Ff 1222 833 a(1) p Fd 1343 818 a(in) p 1475 818 a(the) p 1649 818 a(norm) p 1922 818 a(r) p 1958 818 a(esolvent) p 2341 818 a(sense,) p 2645 818 a(and) p 2846 818 a(if) p Fl 2953 818 a(K) p Fn 3074 818 a(+) p Fl 3181 818 a(V) p Fd 3307 818 a(has) p 3493 818 a(a) 0 938 y(r) p 36 938 a(esonanc) p 371 938 a(e) p 450 938 a(state,) p 714 938 a(then) p Fl 930 938 a(K) p Fk 1013 953 a(") p Fn 1050 938 a(\() p Fl(V) p Fk 1145 953 a(") p Fn 1182 938 a(\)) p Fd 1254 938 a(c) p 1294 938 a(onver) p 1525 938 a(ges) p 1689 938 a(to) p Fl 1806 938 a(H) p Fj 1887 953 a(0) p Fd 1926 938 a(.) p Fn 146 1108 a(\(2\)) p Fd 371 1108 a(L) p 427 1108 a(et) p Fl 541 1108 a(\013) p Fn 635 1108 a(=) p 742 1108 a(1) p Fl(=) p Fn(2) p Fd(.) p 968 1108 a(Assume) p 1334 1108 a(that) p Fl 1535 1108 a(K) p Fn 1649 1108 a(+) p Fl 1748 1108 a(V) p Fd 1864 1108 a(do) p 1959 1108 a(es) p 2080 1108 a(not) p 2254 1108 a(have) p 2480 1108 a(a) p 2566 1108 a(r) p 2602 1108 a(esonanc) p 2937 1108 a(e) p 3018 1108 a(state) p 3254 1108 a(at) p 3373 1108 a(zer) p 3494 1108 a(o) 0 1229 y(ener) p 181 1229 a(gy,) p 341 1229 a(so) p 468 1229 a(that) p Fn 671 1229 a(\(1) p 782 1229 a(+) p Fl 882 1229 a(Z) p Fj 949 1244 a(0) p Fn 988 1229 a(\)) p Ff 1026 1193 a(\000) p Fj(1) p Fn 1153 1229 a(:) p 1213 1229 a([) p Fl(L) p Fj 1306 1193 a(2) p Fn 1346 1229 a(]) p Fj 1373 1193 a(2) p Fg 1446 1229 a(!) p Fn 1578 1229 a([) p Fl(L) p Fj 1671 1193 a(2) p Fn 1711 1229 a(]) p Fj 1738 1193 a(2) p Fd 1815 1229 a(exists) p 2085 1229 a(as) p 2212 1229 a(a) p 2300 1229 a(b) p 2340 1229 a(ounde) p 2587 1229 a(d) p 2674 1229 a(op) p 2769 1229 a(er) p 2850 1229 a(ator.) p 3106 1229 a(De\014ne) p 3416 1229 a(the) 0 1349 y(r) p 36 1349 a(e) p 76 1349 a(al) p 186 1349 a(numb) p 413 1349 a(er) p Fl 533 1349 a(\025) p Fj 590 1364 a(2) p Fd 664 1349 a(by) p Fl 1026 1469 a(\025) p Fj 1083 1484 a(2) p Fn 1150 1469 a(=) p 1254 1469 a(\(\(1) p 1400 1469 a(+) p Fl 1498 1469 a(Z) p Fj 1565 1484 a(0) p Fn 1605 1469 a(\)) p Ff 1643 1428 a(\000) p Fj(1) p Fl 1737 1469 a(V) p Fj 1815 1428 a(1) p Fk(=) p Fj(2) p Fn 1934 1469 a(~) p Fl 1925 1469 a(\032) p Fj 1975 1484 a(0) p Fl 2015 1469 a(;) p Fg 2059 1469 a(j) p Fl(V) p Fg 2165 1469 a(j) p Fj 2193 1428 a(1) p Fk(=) p Fj(2) p Fn 2312 1469 a(~) p Fl 2303 1469 a(\032) p Fj 2353 1484 a(0) p Fn 2393 1469 a(\)) p Fk 2431 1486 a(L) p Fe 2479 1467 a(2) p Fd 0 1644 a(with) p Fn 225 1644 a(~) p Fl 216 1644 a(\032) p Fj 266 1659 a(0) p Fn 341 1644 a(=) p Fj 451 1608 a(t) p Fn 483 1644 a(\() p Fl(\032) p Fj 571 1659 a(0) p Fl 611 1644 a(;) p Fn 655 1644 a(0\)) p Fg 776 1644 a(2) p Fn 878 1644 a([) p Fl(L) p Fj 971 1608 a(2) p Fn 1011 1644 a(]) p Fj 1038 1608 a(2) p Fd 1077 1644 a(.) p 1164 1644 a(Then) p Fl 1422 1644 a(K) p Fk 1505 1659 a(") p Fn 1542 1644 a(\() p Fl(V) p Fk 1637 1659 a(") p Fn 1673 1644 a(\)) p Fd 1750 1644 a(c) p 1790 1644 a(onver) p 2021 1644 a(ges) p 2189 1644 a(to) p Fl 2310 1644 a(H) p Fk 2391 1659 a(\024) p Fd 2474 1644 a(with) p Fl 2690 1644 a(\024) p Fn 2781 1644 a(=) p 2892 1644 a(tan\() p Fl(\020) p 3122 1644 a(=) p Fn(2\)) p Fd 3295 1644 a(deter-) 0 1764 y(mine) p 205 1764 a(d) p 289 1764 a(thr) p 407 1764 a(ough) p 639 1764 a(\(2.6\)) p 883 1764 a(with) p Fl 1104 1984 a(\020) p Fn 1181 1984 a(=) p 1285 1984 a(arg) p 1438 1984 a(\(\() p Fl(i\025) p Fj 1604 1999 a(2) p Fg 1666 1984 a(\000) p Fl 1766 1984 a(\015) p Fj 1817 1999 a(0) p Fn 1856 1984 a(\)) p Fl(=) p Fn(\() p Fl(i\025) p Fj 2071 1999 a(2) p Fn 2132 1984 a(+) p Fl 2230 1984 a(\015) p Fj 2281 1999 a(0) p Fn 2320 1984 a(\)\)) p Fl 2413 1984 a(;) p Fd 0 2204 a(wher) p 196 2204 a(e) p Fl 270 2204 a(\015) p Fj 321 2219 a(0) p Fn 388 2204 a(=) p Fg 491 2204 a(\000) p Fn(2) p Fd 647 2204 a(is) p 747 2204 a(as) p 866 2204 a(in) p 981 2204 a(Pr) p 1083 2204 a(op) p 1178 2204 a(osition) p 1494 2204 a(4.1.) p 1696 2204 a(If) p Fl 1793 2204 a(K) p Fn 1894 2204 a(+) p Fl 1981 2204 a(V) p Fd 2089 2204 a(has) p 2259 2204 a(a) p 2338 2204 a(r) p 2374 2204 a(esonanc) p 2709 2204 a(e) p 2783 2204 a(state,) p 3043 2204 a(then) p Fl 3254 2204 a(K) p Fk 3337 2219 a(") p Fn 3374 2204 a(\() p Fl(V) p Fk 3469 2219 a(") p Fn 3505 2204 a(\)) p Fd 0 2325 a(c) p 40 2325 a(onver) p 271 2325 a(ges) p 435 2325 a(to) p Fl 552 2325 a(H) p Fj 633 2340 a(0) p Fd 672 2325 a(.) p Fn 146 2495 a(\(3\)) p Fd 371 2495 a(L) p 427 2495 a(et) p Fn 544 2495 a(1) p Fl(=) p Fn(2) p Fl 728 2495 a(<) p 841 2495 a(\013) p 941 2495 a(<) p Fn 1054 2495 a(1) p Fd(.) p 1193 2495 a(Assume) p 1562 2495 a(that) p Fn 1766 2495 a(\(5) p Fl(:) p Fn(1\)) p Fd 2007 2495 a(is) p 2117 2495 a(ful\014l) p 2309 2495 a(le) p 2374 2495 a(d.) p 2513 2495 a(If) p Fl 2621 2495 a(K) p Fn 2737 2495 a(+) p Fl 2839 2495 a(V) p Fd 2958 2495 a(do) p 3053 2495 a(es) p 3177 2495 a(not) p 3354 2495 a(have) 0 2615 y(a) p 85 2615 a(r) p 121 2615 a(esonanc) p 456 2615 a(e) p 535 2615 a(state) p 769 2615 a(at) p 887 2615 a(zer) p 1008 2615 a(o) p 1093 2615 a(ener) p 1274 2615 a(gy,) p 1430 2615 a(then) p Fl 1647 2615 a(K) p Fk 1730 2630 a(") p Fn 1767 2615 a(\() p Fl(V) p Fk 1862 2630 a(") p Fn 1899 2615 a(\)) p Fd 1972 2615 a(c) p 2012 2615 a(onver) p 2243 2615 a(ges) p 2407 2615 a(to) p Fl 2524 2615 a(H) p Fj 2605 2630 a(0) p Fd 2645 2615 a(,) p 2710 2615 a(and) p 2899 2615 a(if) p Fl 2994 2615 a(K) p Fn 3107 2615 a(+) p Fl 3205 2615 a(V) p Fd 3319 2615 a(has) p 3493 2615 a(a) 0 2736 y(r) p 36 2736 a(esonanc) p 371 2736 a(e) p 450 2736 a(state,) p 714 2736 a(then) p Fl 930 2736 a(K) p Fk 1013 2751 a(") p Fn 1050 2736 a(\() p Fl(V) p Fk 1145 2751 a(") p Fn 1182 2736 a(\)) p Fd 1254 2736 a(c) p 1294 2736 a(onver) p 1525 2736 a(ges) p 1689 2736 a(to) p Fl 1806 2736 a(H) p Ff 1887 2751 a(1) p Fd 1962 2736 a(.) p Fn 146 3014 a(The) p 359 3014 a(theorem) p 750 3014 a(is) p 860 3014 a(pro) m(v) m(ed) p 1189 3014 a(in) p 1315 3014 a(the) p 1495 3014 a(next) p 1726 3014 a(section.) p 2126 3014 a(W) p 2218 3014 a(e) p 2305 3014 a(follo) m(w) p 2599 3014 a(the) p 2779 3014 a(argumen) m(t) p 3227 3014 a(used) p 3462 3014 a(in) 0 3134 y(the) p 175 3134 a(pro) s(of) p 438 3134 a(of) p 556 3134 a(Theorem) p 976 3134 a(1.2.5) p 1216 3134 a(in) p 1337 3134 a([6]) p 1480 3134 a(and) p 1677 3134 a(of) p 1796 3134 a(Theorem) p 2215 3134 a(3.3) p 2380 3134 a(in) p 2501 3134 a([10].) p 2746 3134 a(The) p 2954 3134 a(ma) p 3089 3134 a(jor) p 3246 3134 a(part) p 3465 3134 a(of) 0 3254 y(the) p 168 3254 a(argumen) m(t) p 603 3254 a(is) p 701 3254 a(again) p 961 3254 a(o) s(ccupied) p 1364 3254 a(b) m(y) p 1499 3254 a(the) p 1667 3254 a(resolv) m(en) m(t) p 2076 3254 a(analysis) p 2442 3254 a(at) p 2561 3254 a(lo) m(w) p 2737 3254 a(energy) p 3048 3254 a(of) p 3159 3254 a(magnetic) 0 3375 y(Sc) m(hr\177) p 186 3375 a(odinger) p 541 3375 a(op) s(erator) p 940 3375 a(with) p 1169 3375 a(resonance) p 1621 3375 a(state) p 1867 3375 a(at) p 1993 3375 a(zero) p 2205 3375 a(energy) p 2475 3375 a(.) p 2567 3375 a(W) p 2659 3375 a(e) p 2742 3375 a(end) p 2933 3375 a(the) p 3108 3375 a(section) p 3440 3375 a(b) m(y) 0 3495 y(making) p 344 3495 a(some) p 589 3495 a(brief) p 813 3495 a(commen) m(ts) p 1272 3495 a(on) p 1407 3495 a(the) p 1575 3495 a(theorem.) p Fm 0 3665 a(Remark) p 432 3665 a(5.1) p Fn 672 3665 a(\(1\)) p 836 3665 a(If) p Fl 939 3665 a(V) p Fn 1017 3665 a(\() p Fl(x) p Fn(\)) p Fg 1186 3665 a(\025) p Fn 1302 3665 a(0) p 1389 3665 a(or) p Fl 1514 3665 a(V) p Fn 1593 3665 a(\() p Fl(x) p Fn(\)) p Fg 1762 3665 a(\024) p Fn 1877 3665 a(0) p 1964 3665 a(and) p 2160 3665 a(if) p 2255 3665 a(it) p 2358 3665 a(is) p 2462 3665 a(su\016cien) m(tly) p 2957 3665 a(small) p 3218 3665 a(but) p 3402 3665 a(not) 0 3786 y(iden) m(tically) p 479 3786 a(zero,) p 721 3786 a(then) p Fl 951 3786 a(K) p Fn 1068 3786 a(+) p Fl 1171 3786 a(V) p Fn 1290 3786 a(has) p 1471 3786 a(neither) p 1809 3786 a(b) s(ound) p 2117 3786 a(state) p 2364 3786 a(nor) p 2544 3786 a(resonance) p 2997 3786 a(state) p 3243 3786 a(at) p 3370 3786 a(zero) 0 3906 y(energy) p 270 3906 a(.) p 340 3906 a(The) p 535 3906 a(theorem) p 909 3906 a(asserts) p 1220 3906 a(that) p 1426 3906 a(the) p 1589 3906 a(limit) p 1817 3906 a(Hamiltonian) p 2372 3906 a(c) m(hanges) p 2728 3906 a(at) p Fl 2842 3906 a(\013) p Fn 2933 3906 a(=) p 3036 3906 a(1) p Fl(=) p Fn(2) p 3210 3906 a(ev) m(en) p 3427 3906 a(for) 0 4027 y(small) p 255 4027 a(p) s(erturbations) p 865 4027 a(of) p 976 4027 a(scalar) p 1253 4027 a(p) s(oten) m(tials,) p 1730 4027 a(and) p 1919 4027 a(also) p 2115 4027 a(it) p 2212 4027 a(is) p 2310 4027 a(in) m(teresting) p 2790 4027 a(that) p 3001 4027 a(the) p 3169 4027 a(situation) 0 4147 y(is) p 100 4147 a(completely) p 592 4147 a(rev) m(ersed) p 974 4147 a(when) p Fl 1230 4147 a(K) p Fn 1344 4147 a(+) p Fl 1443 4147 a(V) p Fn 1556 4147 a(has) p 1731 4147 a(a) p 1814 4147 a(resonance) p 2261 4147 a(state.) p 2543 4147 a(\(2\)) p 2702 4147 a(The) p 2904 4147 a(same) p 3150 4147 a(reason) p 3456 4147 a(as) 0 4267 y(in) p 116 4267 a(Remark) p 485 4267 a(3.2) p 645 4267 a(applies) p 973 4267 a(to) p Fl 1094 4267 a(K) p Fk 1177 4282 a(") p Fn 1214 4267 a(\() p Fl(V) p Fk 1309 4282 a(") p Fn 1346 4267 a(\)) p 1415 4267 a(=) p Fl 1523 4267 a(") p Ff 1569 4231 a(\000) p Fj(1) p Fl 1662 4267 a(J) p Fk 1716 4282 a(") p Fn 1753 4267 a(\() p Fl(K) p Fn 1905 4267 a(+) p Fl 2004 4267 a(V) p Fn 2083 4267 a(\)) p Fl(J) p Ff 2184 4231 a(\003) p Fk 2175 4292 a(") p Fn 2224 4267 a(.) p 2301 4267 a(The) p 2504 4267 a(norm) p 2761 4267 a(con) m(v) m(ergence) p 3302 4267 a(is) p 3402 4267 a(not) 0 4388 y(true) p 214 4388 a(without) p 586 4388 a(assuming) p 1018 4388 a(that) p Fl 1238 4388 a(K) p Fn 1356 4388 a(+) p Fl 1460 4388 a(V) p Fn 1579 4388 a(has) p 1762 4388 a(no) p 1906 4388 a(b) s(ound) p 2215 4388 a(states) p 2501 4388 a(at) p 2629 4388 a(zero) p 2843 4388 a(energy) p 3113 4388 a(.) p 3210 4388 a(\(3\)) p 3375 4388 a(The) 0 4508 y(restriction) p 474 4508 a(\(1.2\)) p 715 4508 a(is) p 820 4508 a(tec) m(hnical.) p 1290 4508 a(The) p 1497 4508 a(same) p 1749 4508 a(results) p 2067 4508 a(as) p 2194 4508 a(in) p 2315 4508 a(the) p 2491 4508 a(theorem) p 2878 4508 a(seem) p 3124 4508 a(to) p 3251 4508 a(remain) 0 4628 y(true) p 208 4628 a(ev) m(en) p 432 4628 a(for) p Fl 583 4628 a(\013) p 677 4628 a(>) p Fn 784 4628 a(1) p 867 4628 a(in) p 983 4628 a(the) p 1153 4628 a(strong) p 1454 4628 a(con) m(v) m(ergence) p 1995 4628 a(sense,) p 2275 4628 a(so) p 2397 4628 a(that) p 2610 4628 a(the) p 2780 4628 a(limit) p 3015 4628 a(Hamiltonian) 0 4749 y(c) m(hanges) p 360 4749 a(at) p 477 4749 a(half{in) m(teger) p 1007 4749 a(\015uxes.) p 1319 4749 a(\(4\)) p 1475 4749 a(The) p 1674 4749 a(assumption) p 2188 4749 a(\(5.1\)) p 2420 4749 a(also) p 2614 4749 a(seems) p 2890 4749 a(to) p 3008 4749 a(b) s(e) p 3140 4749 a(tec) m(hnical.) 0 4869 y(This) p 217 4869 a(is) p 309 4869 a(used) p 527 4869 a(for) p 670 4869 a(pro) m(ving) p 1016 4869 a(the) p 1179 4869 a(third) p 1417 4869 a(statemen) m(t) p 1864 4869 a(only) p 2037 4869 a(,) p 2093 4869 a(and) p 2277 4869 a(a) p 2352 4869 a(similar) p 2667 4869 a(assumption) p 3177 4869 a(has) p 3345 4869 a(b) s(een) 0 4990 y(used) p 222 4990 a(in) p 335 4990 a([10]) p 519 4990 a(for) p 667 4990 a(the) p 834 4990 a(analysis) p 1201 4990 a(on) p 1335 4990 a(resolv) m(en) m(ts) p 1783 4990 a(at) p 1901 4990 a(lo) m(w) p 2077 4990 a(energy) p 2388 4990 a(of) p 2498 4990 a(Sc) m(hr\177) p 2684 4990 a(odinger) p 3031 4990 a(op) s(erators) p 3462 4990 a(in) 0 5110 y(t) m(w) m(o) p 187 5110 a(dimensions.) p 733 5110 a(Ho) m(w) m(ev) m(er) p 1128 5110 a(the) p 1299 5110 a(idea) p 1507 5110 a(in) p 1624 5110 a(the) p 1795 5110 a(recen) m(t) p 2087 5110 a(w) m(ork) p 2328 5110 a([16]) p 2515 5110 a(ma) m(y) p 2729 5110 a(mak) m(e) p 2987 5110 a(it) p 3087 5110 a(p) s(ossible) p 3457 5110 a(to) 0 5230 y(remo) m(v) m(e) p 333 5230 a(the) p 501 5230 a(assumption.) p Fm 146 5469 a(6.) p 271 5469 a(Pro) s(of) p 580 5469 a(of) p 708 5469 a(Theorem) p 1183 5469 a(5.1) p Fn 1723 5753 a(24) p 90 rotate dyy eop %%Page: 25 25 25 24 bop Fn 146 407 a(W) p 238 407 a(e) p 309 407 a(pro) m(v) m(e) p 566 407 a(Theorem) p 972 407 a(5.1) p 1124 407 a(in) p 1232 407 a(this) p 1417 407 a(section.) p 1779 407 a(The) p 1974 407 a(pro) s(of) p 2223 407 a(requires) p 2583 407 a(sev) m(eral) p 2898 407 a(new) p 3093 407 a(lemmas) p 3440 407 a(on) 0 527 y(the) p 169 527 a(b) s(eha) m(vior) p 569 527 a(at) p 690 527 a(lo) m(w) p 867 527 a(energy) p 1180 527 a(of) p 1293 527 a(resolv) m(en) m(ts) p 1742 527 a(of) p 1855 527 a(magnetic) p 2273 527 a(Sc) m(hr\177) p 2459 527 a(odinger) p 2809 527 a(op) s(erators) p 3241 527 a(b) s(esides) 0 648 y(the) p 158 648 a(prop) s(ositions) p 699 648 a(in) p 802 648 a(section) p 1118 648 a(4.) p 1234 648 a(In) p 1345 648 a(form) m(ulating) p 1861 648 a(these) p 2100 648 a(lemmas,) p 2472 648 a(w) m(e) p 2605 648 a(use) p Fl 2764 648 a(\037) p Fg 2853 648 a(2) p Fl 2947 648 a(C) p Ff 3024 611 a(1) p Fj 3017 672 a(0) p Fn 3098 648 a(\() p Fi(R) p Fj 3224 606 a(2) p Fg 3291 648 a(!) p Fi 3418 648 a(R) p Fn(\)) 0 768 y(with) p 213 768 a(the) p 371 768 a(same) p 607 768 a(meaning) p 987 768 a(as) p 1098 768 a(ascrib) s(ed) p 1471 768 a(in) p 1575 768 a(section) p 1892 768 a(4) p 1964 768 a(and) p 2144 768 a(denote) p 2449 768 a(b) m(y) p Fl 2575 768 a(o) p Fj 2622 783 a(2) p Fn 2661 768 a(\() p Fl(") p Fk 2745 732 a(\033) p Fn 2792 768 a(\)) p 2853 768 a(remainder) p 3304 768 a(terms) 0 888 y(with) p Fl 222 888 a(L) p Fj 288 852 a(2) p Fn 361 888 a(norm) p 615 888 a(ob) s(eying) p 978 888 a(the) p 1146 888 a(b) s(ound) p Fl 1447 888 a(o) p Fn(\() p Fl(") p Fk 1578 852 a(\033) p Fn 1624 888 a(\).) p 1733 888 a(W) p 1825 888 a(e) p 1901 888 a(further) p 2229 888 a(de\014ne) p Fl 2511 888 a(\030) p Fk 2554 903 a(l) p Fn 2579 888 a(\() p Fl(x) p Fn(\)) p 2743 888 a(b) m(y) p Fl 1089 1108 a(\030) p Fk 1132 1123 a(l) p Fn 1157 1108 a(\() p Fl(x) p Fn(\)) p 1316 1108 a(=) p Fl 1420 1108 a(H) p Fk 1501 1123 a(\027) p Fn 1544 1108 a(\() p Fl(ir) p Fn 1662 1108 a(\)) p Fl(e) p Fk 1745 1067 a(il) q(\022) p Fl 1830 1108 a(;) p 1971 1108 a(\027) p Fn 2053 1108 a(=) p Fg 2157 1108 a(j) p Fl(l) p Fg 2238 1108 a(\000) p Fl 2337 1108 a(\013) p Fg 2400 1108 a(j) p Fl(;) p Fn 3343 1108 a(\(6.1\)) 0 1328 y(for) p Fl 149 1328 a(l) p Fn 208 1328 a(=) p 312 1328 a(0) p Fl(;) p Fn 405 1328 a(1.) p 523 1328 a(According) p 987 1328 a(to) p 1106 1328 a(this) p 1296 1328 a(notation,) p 1713 1328 a(w) m(e) p 1857 1328 a(ha) m(v) m(e) p Fl 703 1605 a( ) p Fj 766 1620 a(+) p Fn 853 1605 a(=) p Fl 956 1605 a(N) p Fk 1034 1620 a(\013) p Fh 1100 1459 a( ) p Fg 1208 1544 a(\000) p Fl(i) p Fj 1318 1508 a(1+2) p Fk(\013) p Fl 1493 1544 a(\030) p Fj 1536 1559 a(0) p Fl 1351 1664 a(\030) p Fj 1394 1679 a(1) p Fh 1617 1459 a(!) p Fl 1699 1605 a(;) p 1938 1605 a( ) p Ff 2001 1620 a(\000) p Fn 2088 1605 a(=) p Fl 2192 1605 a(N) p Fk 2270 1620 a(\013) p Fh 2336 1459 a( ) p Fl 2443 1544 a(i) p Fj 2476 1508 a(1+2) p Fk(\013) p Fl 2651 1544 a(\030) p Fj 2694 1559 a(0) p Fl 2547 1664 a(\030) p Fj 2590 1679 a(1) p Fh 2775 1459 a(!) p Fn 0 1887 a(b) m(y) p 135 1887 a(\(2.3\)) p 369 1887 a(and) p 558 1887 a(\(2.5\).) p Fm 0 2215 a(Lemma) p 397 2215 a(6.1) p Fd 589 2215 a(L) p 645 2215 a(et) p Fl 757 2215 a(!) p Fj 818 2230 a(+) p Fk(l) p Fd 934 2215 a(b) p 974 2215 a(e) p 1053 2215 a(de\014ne) p 1298 2215 a(d) p 1382 2215 a(by) p 1509 2215 a(\(4.7\).) p 1793 2215 a(Then) p Fn 587 2435 a(\() p Fl(L) p Fj 691 2450 a(+) p Fk(") p Fn 805 2435 a(+) p 903 2435 a(1\)) p Ff 990 2394 a(\000) p Fj(1) p Fl 1084 2435 a(J) p Fk 1138 2450 a(") p Fl 1175 2435 a(\037) p Fn 1263 2435 a(=) p Fh 1391 2352 a(X) p Fk 1367 2537 a(l) p Fj 1389 2537 a(=0) p Fk(;) p Fj(1) p Fl 1551 2435 a(\014) p Fj 1606 2450 a(+) p Fk(l) p Fn 1686 2435 a(\() p Fl(") p Fn(\)) p Fl(i) p Fk 1841 2394 a(\027) p Fl 1884 2435 a(") p Fj 1930 2394 a(1+) p Fk(\027) p Fn 2080 2435 a(\() p Fl(\030) p Fk 2161 2450 a(l) p Fg 2209 2435 a(\012) p Fl 2308 2435 a(\037!) p Fj 2430 2450 a(+) p Fk(l) p Fn 2511 2435 a(\)) p 2571 2435 a(+) p Fl 2669 2435 a(O) s(p) p Fn(\() p Fl(") p Fj 2880 2394 a(2) p Fn 2918 2435 a(\)) p Fd 0 2741 a(for) p 163 2741 a(some) p 420 2741 a(c) p 460 2741 a(o) p 505 2741 a(e\016cient) p Fl 885 2741 a(\014) p Fj 940 2756 a(+) p Fk(l) p Fn 1021 2741 a(\() p Fl(") p Fn(\)) p Fd(,) p 1217 2741 a(and) p Fl 1414 2741 a(\014) p Fj 1469 2756 a(+) p Fk(l) p Fn 1550 2741 a(\() p Fl(") p Fn(\)) p Fd 1714 2741 a(b) p 1754 2741 a(ehaves) p 2071 2741 a(like) p Fl 2258 2741 a(\014) p Fj 2313 2756 a(+) p Fk(l) p Fn 2394 2741 a(\() p Fl(") p Fn(\)) p 2558 2741 a(=) p Fl 2676 2741 a(\014) p Fk 2731 2756 a(l) p Fn 2785 2741 a(+) p Fl 2889 2741 a(o) p Fn(\(1\)) p Fd 3103 2741 a(as) p Fl 3235 2741 a(") p Fg 3323 2741 a(!) p Fn 3465 2741 a(0) p Fd(,) 0 2861 y(wher) p 196 2861 a(e) p Fl 787 2981 a(\014) p Fk 842 2996 a(l) p Fn 896 2981 a(=) p Fl 999 2981 a(i) p Fn(\(2) p Fl(\031) p Fn 1178 2981 a(\)) p Ff 1216 2940 a(\000) p Fj(1) p Fk(=) p Fj(2) p Fh 1398 2885 a(\020) p Fn 1447 2981 a(2) p Ff 1496 2940 a(\000) p Fk(\027) p Fn 1594 2981 a(\000\(1) p Fg 1764 2981 a(\000) p Fl 1864 2981 a(\027) p Fn 1918 2981 a(\)) p Fl(=) p Fn(\() p Fl(l) p Fn 2096 2981 a(+) p Fl 2194 2981 a(\027) p Fn 2248 2981 a(\)) p Fj 2286 2940 a(1) p Fk(=) p Fj(2) p Fh 2397 2885 a(\021) p Fn 2463 2981 a(sin) p Fl 2616 2981 a(\027) p 2670 2981 a(\031) t(:) p Fn 3343 2981 a(\(6.2\)) p Fm 0 3367 a(Lemma) p 397 3367 a(6.2) p Fd 589 3367 a(L) p 645 3367 a(et) p Fl 761 3367 a(\014) p Fj 816 3382 a(0) p Fd 895 3367 a(b) p 935 3367 a(e) p 1018 3367 a(as) p 1147 3367 a(ab) p 1237 3367 a(ove) p 1415 3367 a(and) p 1608 3367 a(let) p Fl 1749 3367 a(\015) p Fj 1800 3382 a(0) p Fd 1878 3367 a(b) p 1918 3367 a(e) p 2001 3367 a(as) p 2130 3367 a(in) p 2254 3367 a(Pr) p 2356 3367 a(op) p 2451 3367 a(osition) p 2776 3367 a(4.1.) p 2992 3367 a(L) p 3048 3367 a(et) p Fl 3164 3367 a(\032) p Fj 3214 3382 a(0) p Fd 3293 3367 a(b) p 3333 3367 a(e) p 3416 3367 a(the) 0 3488 y(r) p 36 3488 a(esonanc) p 371 3488 a(e) p 450 3488 a(state) p 684 3488 a(de\014ne) p 929 3488 a(d) p 1012 3488 a(by) p 1139 3488 a(\(4.14\).) p 1473 3488 a(Then) p Fn 413 3708 a(\() p Fl(L) p Ff 517 3723 a(\000) p Fk(") p Fn 631 3708 a(+) p 729 3708 a(1\)) p Ff 816 3667 a(\000) p Fj(1) p Fl 910 3708 a(J) p Fk 964 3723 a(") p Fl 1001 3708 a(\037) p Fn 1090 3708 a(=) p Fg 1193 3708 a(\000) p Fl(i) p Fk 1303 3667 a(\013) p Fn 1370 3708 a(\() p Fl(\014) p Fj 1463 3723 a(0) p Fl 1502 3708 a(=\015) p Fj 1602 3723 a(0) p Fn 1641 3708 a(\)) p Fl 1696 3708 a(") p Fj 1742 3667 a(1) p Ff(\000) p Fk(\013) p Fn 1898 3708 a(\(\() p Fl(\030) p Fj 2017 3723 a(0) p Fn 2078 3708 a(+) p Fl 2176 3708 a(o) p Fj 2223 3723 a(2) p Fn 2262 3708 a(\(1\)\)) p Fg 2447 3708 a(\012) p Fl 2546 3708 a(\037\032) p Fj 2657 3723 a(0) p Fn 2697 3708 a(\)) p 2757 3708 a(+) p Fl 2855 3708 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(:) p Fm 0 4094 a(Lemma) p 397 4094 a(6.3) p Fd 589 4094 a(One) p 798 4094 a(has) p Fl 1174 4214 a(p) p Ff 1223 4229 a(\000) p Fk(") p Fn 1314 4214 a(\() p Fl(L) p Fj 1418 4229 a(+) p Fk(") p Fn 1533 4214 a(+) p 1631 4214 a(1\)) p Ff 1718 4173 a(\000) p Fj(1) p Fl 1812 4214 a(J) p Fk 1866 4229 a(") p Fl 1902 4214 a(\037) p Fn 1991 4214 a(=) p Fl 2095 4214 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(:) p Fm 0 4600 a(Lemma) p 397 4600 a(6.4) p Fd 589 4600 a(One) p 798 4600 a(has) p Fl 354 4820 a(p) p Fj 403 4835 a(+) p Fk(") p Fn 495 4820 a(\() p Fl(L) p Ff 599 4835 a(\000) p Fk(") p Fn 713 4820 a(+) p 811 4820 a(1\)) p Ff 898 4779 a(\000) p Fj(1) p Fl 992 4820 a(J) p Fk 1046 4835 a(") p Fl 1082 4820 a(\037) p Fn 1171 4820 a(=) p Fl 1275 4820 a(i) p Ff 1308 4779 a(\000) p Fk(\013) p Fn 1429 4820 a(\() p Fl(\014) p Fj 1522 4835 a(0) p Fl 1561 4820 a(=\015) p Fj 1661 4835 a(0) p Fn 1700 4820 a(\)) p Fl 1755 4820 a(") p Fj 1801 4779 a(1) p Ff(\000) p Fk(\013) p Fn 1957 4820 a(\(\() p Fl(\030) p Fj 2076 4835 a(1) p Fn 2137 4820 a(+) p Fl 2235 4820 a(o) p Fj 2282 4835 a(2) p Fn 2321 4820 a(\(1\)\)) p Fg 2506 4820 a(\012) p Fl 2605 4820 a(\037\032) p Fj 2716 4835 a(0) p Fn 2756 4820 a(\)) p 2816 4820 a(+) p Fl 2914 4820 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(:) p Fn 146 5148 a(W) p 238 5148 a(e) p 308 5148 a(pro) s(ceed) p 662 5148 a(to) p 774 5148 a(pro) m(ving) p 1120 5148 a(Theorem) p 1525 5148 a(5.1,) p 1705 5148 a(accepting) p 2132 5148 a(the) p 2293 5148 a(ab) s(o) m(v) m(e) p 2563 5148 a(lemmas) p 2909 5148 a(as) p 3023 5148 a(pro) m(v) m(ed.) p 3375 5148 a(The) 0 5269 y(pro) s(of) p 255 5269 a(of) p 366 5269 a(these) p 616 5269 a(lemmas) p 968 5269 a(is) p 1067 5269 a(done) p 1300 5269 a(in) p 1413 5269 a(section) p 1739 5269 a(7.) 1723 5753 y(25) p 90 rotate dyy eop %%Page: 26 26 26 25 bop Fn 0 407 a(Pro) s(of) p 261 407 a(of) p 366 407 a(Theorem) p 772 407 a(5.1.) p 1021 407 a(F) p 1077 407 a(or) p 1190 407 a(brevit) m(y) p 1481 407 a(,) p 1537 407 a(w) m(e) p 1675 407 a(assume) p 2006 407 a(throughout) p 2509 407 a(the) p 2671 407 a(pro) s(of) p 2919 407 a(that) p Fl 3125 407 a(V) p Fn 3203 407 a(\() p Fl(x) p Fn(\)) p Fg 3362 407 a(\025) p Fn 3467 407 a(0,) 0 527 y(so) p 135 527 a(that) p 361 527 a(the) p 543 527 a(op) s(erator) p Fl 951 527 a(Z) p Fj 1018 542 a(0) p Fn 1105 527 a(de\014ned) p 1455 527 a(b) m(y) p 1606 527 a(\(5.2\)) p 1854 527 a(b) s(ecomes) p 2256 527 a(self{adjoin) m(t.) p 2857 527 a(W) p 2949 527 a(e) p 3040 527 a(write) p Fl 3304 527 a(R) p Fk 3378 542 a(") p Fn 3467 527 a(=) 0 648 y(\() p Fl(K) p Fk 121 663 a(") p Fn 158 648 a(\() p Fl(V) p Fk 253 663 a(") p Fn 289 648 a(\)) p 349 648 a(+) p Fl 447 648 a(i) p Fn(\)) p Ff 518 611 a(\000) p Fj(1) p Fn 613 648 a(.) p 683 648 a(Then) p 938 648 a(w) m(e) p 1082 648 a(obtain) p Fl 645 859 a(R) p Fk 719 874 a(") p Fn 783 859 a(=) p 887 859 a(\() p Fl(K) p Fk 1008 874 a(") p Fn 1067 859 a(+) p Fl 1165 859 a(i) p Fn(\)) p Ff 1236 818 a(\000) p Fj(1) p Fg 1352 859 a(\000) p Fn 1452 859 a(\() p Fl(K) p Fk 1573 874 a(") p Fn 1632 859 a(+) p Fl 1730 859 a(i) p Fn(\)) p Ff 1801 818 a(\000) p Fj(1) p Fl 1895 859 a(V) p Fj 1974 818 a(1) p Fk(=) p Fj(2) p Fk 1952 884 a(") p Fl 2084 859 a(X) p Ff 2173 818 a(\000) p Fj(1) p Fk 2165 884 a(") p Fl 2267 859 a(V) p Fj 2345 818 a(1) p Fk(=) p Fj(2) p Fk 2324 884 a(") p Fn 2455 859 a(\() p Fl(K) p Fk 2576 874 a(") p Fn 2635 859 a(+) p Fl 2733 859 a(i) p Fn(\)) p Ff 2804 818 a(\000) p Fj(1) p Fn 0 1070 a(from) p 230 1070 a(the) p 398 1070 a(resolv) m(en) m(t) p 808 1070 a(iden) m(tit) m(y) p 1126 1070 a(,) p 1187 1070 a(where) p Fl 1469 1070 a(X) p Fk 1550 1085 a(") p Fn 1615 1070 a(=) p 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1508 a(") p Fn 398 1493 a(is) p 496 1493 a(rewritten) p 919 1493 a(as) p Fl 323 1704 a(R) p Fk 397 1719 a(") p Fn 461 1704 a(=) p 565 1704 a(\() p Fl(K) p Fk 686 1719 a(") p Fn 745 1704 a(+) p Fl 843 1704 a(i) p Fn(\)) p Ff 914 1663 a(\000) p Fj(1) p Fg 1030 1704 a(\000) p Fl 1130 1704 a(") p Ff 1176 1663 a(\000) p Fj(1) p Fh 1287 1608 a(\020) p Fn 1336 1704 a(\() p Fl(K) p Fk 1457 1719 a(") p Fn 1516 1704 a(+) p Fl 1614 1704 a(i) p Fn(\)) p Ff 1685 1663 a(\000) p Fj(1) p Fl 1780 1704 a(J) p Fk 1834 1719 a(") p Fl 1870 1704 a(V) p Fj 1949 1663 a(1) p Fk(=) p Fj(2) p Fh 2059 1608 a(\021) p Fl 2125 1704 a(Y) p Ff 2203 1663 a(\000) p Fj(1) p Fk 2182 1729 a(") p Fh 2314 1608 a(\020) p Fn 2364 1704 a(\() p Fl(K) p Fk 2485 1719 a(") p Fg 2544 1704 a(\000) p Fl 2643 1704 a(i) p Fn(\)) p Ff 2714 1663 a(\000) p Fj(1) p Fl 2809 1704 a(J) p Fk 2863 1719 a(") p Fl 2899 1704 a(V) p Fj 2978 1663 a(1) p Fk(=) p Fj(2) p Fh 3088 1608 a(\021) p Ff 3137 1631 a(\003) p Fl 3194 1704 a(:) p Fn 0 1916 a(W) p 92 1916 a(e) p 169 1916 a(analyze) p 520 1916 a(the) p 690 1916 a(b) s(eha) m(vior) p 1089 1916 a(as) p Fl 1210 1916 a(") p Fg 1286 1916 a(!) p Fn 1415 1916 a(0) p 1498 1916 a(of) p 1610 1916 a(op) s(erators) p 2043 1916 a(on) p 2180 1916 a(the) p 2349 1916 a(righ) m(t) p 2586 1916 a(side.) p 2824 1916 a(By) p 2978 1916 a(Theorem) p 3392 1916 a(3.1,) 0 2036 y(\() p Fl(K) p Fk 121 2051 a(") p Fn 180 2036 a(+) p Fl 278 2036 a(i) p Fn(\)) p Ff 349 2000 a(\000) p Fj(1) p Fg 471 2036 a(!) p Fn 598 2036 a(\() p Fl(H) p Ff 717 2051 a(1) p Fn 814 2036 a(+) p Fl 912 2036 a(i) p Fn(\)) p Ff 983 2000 a(\000) p Fj(1) p Fn 1077 2036 a(.) p 1148 2036 a(If) p 1245 2036 a(w) m(e) p 1389 2036 a(mak) m(e) p 1644 2036 a(use) p 1812 2036 a(of) p 1923 2036 a(relation) p 2281 2036 a(\(3.3\),) p 2541 2036 a(then) p 2763 2036 a(w) m(e) p 2907 2036 a(can) p 3086 2036 a(obtain) 697 2309 y(\() p Fl(K) p Fk 818 2324 a(") p Fg 877 2309 a(\006) p Fl 977 2309 a(i) p Fn(\)) p Ff 1048 2261 a(\000) p Fj(1) p Fn 1170 2309 a(=) p Fh 1273 2163 a( ) p Fg 1395 2248 a(\007) p Fl(i) p Fn(\() p Fl(L) p Ff 1609 2263 a(\000) p Fk(") p Fn 1724 2248 a(+) p 1822 2248 a(1\)) p Ff 1909 2212 a(\000) p Fj(1) p Fl 2101 2248 a(p) p Ff 2150 2263 a(\000) p Fk(") p Fn 2242 2248 a(\() p Fl(L) p Fj 2346 2263 a(+) p Fk(") p Fn 2460 2248 a(+) p 2558 2248 a(1\)) p Ff 2645 2212 a(\000) p Fj(1) p Fl 1381 2369 a(p) p Fj 1430 2384 a(+) p Fk(") p Fn 1521 2369 a(\() p Fl(L) p Ff 1625 2384 a(\000) p Fk(") p Fn 1739 2369 a(+) p 1837 2369 a(1\)) p Ff 1924 2333 a(\000) p Fj(1) p Fg 2116 2369 a(\007) p Fl(i) p Fn(\() p Fl(L) p Fj 2330 2384 a(+) p Fk(") p Fn 2445 2369 a(+) p 2543 2369 a(1\)) p Ff 2630 2333 a(\000) p Fj(1) p Fh 2780 2163 a(!) p Fn 0 2583 a(from) p 230 2583 a(\(3.4\).) p 501 2583 a(By) p 654 2583 a(Lemmas) p 1041 2583 a(6) p Fl(:) p Fn(1) p Fg 1193 2583 a(\030) p Fn 1299 2583 a(6) p Fl(:) p Fn(4,) p 1483 2583 a(w) m(e) p 1626 2583 a(ha) m(v) m(e) 218 2794 y(\() p Fl(K) p Fk 339 2809 a(") p Fn 398 2794 a(+) p Fl 496 2794 a(i) p Fn(\)) p Ff 567 2753 a(\000) p Fj(1) p Fl 661 2794 a(J) p Fk 715 2809 a(") p Fl 752 2794 a(V) p Fj 831 2753 a(1) p Fk(=) p Fj(2) p Fn 968 2794 a(=) p 1072 2794 a(\() p Fl(\014) p Fj 1165 2809 a(0) p Fl 1204 2794 a(=\015) p Fj 1304 2809 a(0) p Fn 1343 2794 a(\)) p Fl 1398 2794 a(N) p Ff 1486 2753 a(\000) p Fj(1) p Fk 1476 2819 a(\013) p Fl 1580 2794 a(i) p Ff 1613 2753 a(\000) p Fk(\013) p Fl 1718 2794 a(") p Fj 1764 2753 a(1) p Ff(\000) p Fk(\013) p Fn 1920 2794 a(\(\() p Fl( ) p Ff 2059 2809 a(\000) p Fn 2140 2794 a(+) p Fl 2238 2794 a(o) p Fj 2285 2809 a(2) p Fn 2325 2794 a(\(1\)\)) p Fg 2510 2794 a(\012) p Fl 2609 2794 a(q) p Fj 2652 2809 a(0) p Fn 2692 2794 a(\)) p 2752 2794 a(+) p Fl 2850 2794 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(;) p Fn 3343 2794 a(\(6.3\)) 0 3023 y(where) p Fl 282 3023 a(q) p Fj 325 3038 a(0) p Fn 392 3023 a(=) p Fj 496 2987 a(t) p Fn 527 3023 a(\() p Fl(V) p Fj 644 2987 a(1) p Fk(=) p Fj(2) p Fl 754 3023 a(\032) p Fj 804 3038 a(0) p Fl 844 3023 a(;) p Fn 888 3023 a(0\).) p 1044 3023 a(Similarly) p Fh 1459 2927 a(\020) p Fn 1509 3023 a(\() p Fl(K) p Fk 1630 3038 a(") p Fg 1688 3023 a(\000) p Fl 1788 3023 a(i) p Fn(\)) p Ff 1859 2987 a(\000) p Fj(1) p Fl 1954 3023 a(J) p Fk 2008 3038 a(") p Fl 2044 3023 a(V) p Fj 2123 2987 a(1) p Fk(=) p Fj(2) p Fh 2233 2927 a(\021) p Ff 2282 2949 a(\003) p Fn 2354 3023 a(tak) m(es) p 2604 3023 a(the) p 2772 3023 a(form) p Fh 164 3180 a(\020) p Fn 213 3276 a(\() p Fl(K) p Fk 334 3291 a(") p Fg 393 3276 a(\000) p Fl 493 3276 a(i) p Fn(\)) p Ff 564 3235 a(\000) p Fj(1) p Fl 658 3276 a(J) p Fk 712 3291 a(") p Fl 749 3276 a(V) p Fj 827 3235 a(1) p Fk(=) p Fj(2) p Fh 937 3180 a(\021) p Ff 987 3203 a(\003) p Fn 1054 3276 a(=) p Fh 1158 3180 a(\020) p 1207 3197 95 4 v Fl 1207 3276 a(\014) p Fj 1262 3291 a(0) p Fl 1302 3276 a(=\015) p Fj 1402 3291 a(0) p Fh 1441 3180 a(\021) p Fl 1507 3276 a(N) p Ff 1595 3235 a(\000) p Fj(1) p Fk 1585 3301 a(\013) p Fl 1690 3276 a(i) p Fk 1723 3235 a(\013) p Fl 1772 3276 a(") p Fj 1818 3235 a(1) p Ff(\000) p Fk(\013) p Fn 1974 3276 a(\() p Fl(q) p Fj 2055 3291 a(0) p Fg 2117 3276 a(\012) p Fn 2217 3276 a(\() p Fl( ) p Fj 2318 3291 a(+) p Fn 2399 3276 a(+) p Fl 2497 3276 a(o) p Fj 2544 3291 a(2) p Fn 2584 3276 a(\(1\)\)\)) p 2806 3276 a(+) p Fl 2904 3276 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(:) p Fn 3343 3276 a(\(6.4\)) 0 3504 y(The) p 201 3504 a(op) s(erator) p 593 3504 a(\() p Fl(K) p Fn 744 3504 a(+) p Fl 842 3504 a(i") p Fn(\)) p Ff 959 3468 a(\000) p Fj(1) p Fn 1085 3504 a(also) p 1281 3504 a(has) p 1455 3504 a(b) s(een) p 1685 3504 a(calculated) p 2146 3504 a(as) 670 3778 y(\() p Fl(K) p Fn 821 3778 a(+) p Fl 919 3778 a(i") p Fn(\)) p Ff 1035 3729 a(\000) p Fj(1) p Fn 1157 3778 a(=) p Fh 1261 3632 a( ) p Fg 1368 3717 a(\000) p Fl(i") p Fn(\() p Fl(L) p Ff 1628 3732 a(\000) p Fn 1710 3717 a(+) p Fl 1808 3717 a(") p Fj 1854 3681 a(2) p Fn 1893 3717 a(\)) p Ff 1931 3681 a(\000) p Fj(1) p Fl 2133 3717 a(p) p Ff 2182 3732 a(\000) p Fn 2241 3717 a(\() p Fl(L) p Fj 2345 3732 a(+) p Fn 2426 3717 a(+) p Fl 2524 3717 a(") p Fj 2570 3681 a(2) p Fn 2609 3717 a(\)) p Ff 2647 3681 a(\000) p Fj(1) p Fn 1392 3837 a(\() p Fl(L) p Fj 1496 3852 a(+) p Fn 1578 3837 a(+) p Fl 1676 3837 a(") p Fj 1722 3801 a(2) p Fn 1761 3837 a(\)) p Ff 1799 3801 a(\000) p Fj(1) p Fl 1893 3837 a(p) p Fj 1942 3852 a(+) p Fg 2108 3837 a(\000) p Fl(i") p Fn(\() p Fl(L) p Fj 2368 3852 a(+) p Fn 2450 3837 a(+) p Fl 2548 3837 a(") p Fj 2594 3801 a(2) p Fn 2633 3837 a(\)) p Ff 2671 3801 a(\000) p Fj(1) p Fh 2807 3632 a(!) p Fn 0 4063 a(in) p 115 4063 a(\(3.10\).) p 438 4063 a(By) p 593 4063 a(\(4.2\)) p 827 4063 a(and) p 1018 4063 a(\(4.7\),) p Fl 1280 4063 a(!) p Fj 1341 4078 a(+0) p Fn 1468 4063 a(ob) s(eys) p Fl 1741 4063 a(!) p Fj 1802 4078 a(+0) p Fn 1926 4063 a(=) p 2032 4063 a(\(1) p Fl(=) p Fn(2\)) p Fl(\013) p Ff 2318 4026 a(\000) p Fj(1) p Fk(=) p Fj(2) p Fl 2481 4063 a(r) p Fk 2528 4026 a(\013) p Fn 2601 4063 a(+) p Fl 2699 4063 a(g) p Fn 2783 4063 a(for) p 2934 4063 a(some) p Fl 3179 4063 a(g) p Fg 3259 4063 a(2) p Fl 3356 4063 a(L) p Fj 3422 4026 a(2) p Ff 3422 4087 a(\000) p Fj(1) p Fn 3516 4063 a(,) 0 4183 y(and) p 190 4183 a(it) p 287 4183 a(solv) m(es) p Fl 565 4183 a(L) p Fj 631 4198 a(+) p Fl 690 4183 a(!) p Fj 751 4198 a(+0) p Fn 873 4183 a(=) p 976 4183 a(0) p 1058 4183 a(uniquely) p 1453 4183 a(\(see) p 1649 4183 a(Lemma) p 1997 4183 a(4.3) p 2154 4183 a(of) p 2265 4183 a([20]\).) p 2526 4183 a(Since) p Fl 2780 4183 a(L) p Fj 2846 4198 a(+) p Fn 2933 4183 a(=) p Fl 3037 4183 a(p) p Fj 3086 4198 a(+) p Fl 3145 4183 a(p) p Ff 3194 4198 a(\000) p Fn 3285 4183 a(with) p Fl 950 4394 a(p) p Ff 999 4409 a(\000) p Fn 1085 4394 a(=) p Fl 1189 4394 a(p) p Ff 1238 4353 a(\003) p Fj 1238 4419 a(+) p Fn 1324 4394 a(=) p Fl 1428 4394 a(ie) p Fk 1506 4353 a(ih) p Fl 1575 4394 a(e) p Ff 1620 4353 a(\000) p Fk(') p Fn 1742 4394 a(\() p Fg(\000) p Fl(@) p Fj 1908 4409 a(1) p Fn 1971 4394 a(+) p Fl 2069 4394 a(i@) p Fj 2153 4409 a(2) p Fn 2193 4394 a(\)) p Fl 2247 4394 a(e) p Ff 2292 4353 a(\000) p Fk(') p Fl 2398 4394 a(e) p Ff 2443 4353 a(\000) p Fk(ih) p Fl 2567 4394 a(;) p Fn 0 4606 a(w) m(e) p 149 4606 a(see) p 312 4606 a(that) p Fl 529 4606 a(p) p Ff 578 4621 a(\000) p Fl 637 4606 a(!) p Fj 698 4621 a(+0) p Fn 829 4606 a(=) p 942 4606 a(0.) p 1078 4606 a(In) p 1205 4606 a(fact,) p Fl 1431 4606 a(!) p Fj 1492 4621 a(+0) p Fn 1624 4606 a(is) p 1728 4606 a(giv) m(en) p 1988 4606 a(b) m(y) p Fl 2129 4606 a(!) p Fj 2190 4621 a(+0) p Fn 2321 4606 a(=) p Fl 2434 4606 a(ce) p Fj 2521 4569 a(+) p Fk(ih) p Fl 2645 4606 a(e) p Fk 2690 4569 a(') p Fn 2778 4606 a(for) p 2932 4606 a(some) p 3182 4606 a(constan) m(t) p Fl 0 4726 a(c) p Fg 70 4726 a(6) p Fn(=) p 173 4726 a(0.) p 292 4726 a(Th) m(us) p 540 4726 a(w) m(e) p 683 4726 a(ha) m(v) m(e) p Fl 0 4937 a(V) p Fj 79 4896 a(1) p Fk(=) p Fj(2) p Fl 189 4937 a(p) p Ff 238 4952 a(\000) p Fn 297 4937 a(\() p Fl(L) p Fj 401 4952 a(+) p Fn 466 4937 a(+) p Fl 549 4937 a(") p Fj 595 4896 a(2) p Fn 634 4937 a(\)) p Ff 672 4896 a(\000) p Fj(1) p Fl 766 4937 a(V) p Fj 845 4896 a(1) p Fk(=) p Fj(2) p Fn 982 4937 a(=) p Fl 1086 4937 a(V) p Fj 1165 4896 a(1) p Fk(=) p Fj(2) p Fh 1291 4841 a(\020) p Fl 1341 4937 a(p) p Ff 1390 4952 a(\000) p Fl 1449 4937 a(G) p Fj 1526 4952 a(+) p Fn 1607 4937 a(+) p Fl 1705 4937 a(") p Fj 1751 4896 a(2\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fl 1980 4937 a(\015) p Fj 2031 4952 a(+1) p Fn 2125 4937 a(\() p Fl(i") p Fn(\)) p 2297 4937 a(\() p Fl(p) p Ff 2384 4952 a(\000) p Fl 2443 4937 a(!) p Fj 2504 4952 a(+1) p Fg 2620 4937 a(\012) p Fl 2719 4937 a(!) p Fj 2780 4952 a(+1) p Fn 2874 4937 a(\)) p Fh 2912 4841 a(\021) p Fl 2979 4937 a(V) p Fj 3057 4896 a(1) p Fk(=) p Fj(2) p Fn 3174 4937 a(+) p Fl 3257 4937 a(O) s(p) p Fn(\() p Fl(") p Fj 3468 4896 a(2) p Fn 3505 4937 a(\)) 0 5172 y(b) m(y) p 129 5172 a(Prop) s(osition) p 648 5172 a(4.2) p 799 5172 a(\(see) p 988 5172 a(Remark) p 1349 5172 a(4.1\)) p 1538 5172 a(and) p 1722 5172 a(similarly) p 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Fk(\013) p Fj(\)) p Fl 2418 5504 a(Z) p Fj 2485 5519 a(1) p Fn 2524 5504 a(\() p Fl(") p Fn(\)) p 2668 5504 a(+) p Fl 2766 5504 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(;) p Fn 1723 5753 a(26) p 90 rotate dyy eop %%Page: 27 27 27 26 bop Fn 0 407 a(where) p Fl 282 407 a(\015) p Ff 333 422 a(\000) p Fn 391 407 a(\() p Fl(i") p Fn(\)) p 574 407 a(=) p Fg 677 407 a(\000) p Fn(1) p Fl(=\015) p Fj 903 422 a(0) p Fn 965 407 a(+) p Fl 1063 407 a(o) p Fn(\(1\)) p 1267 407 a(as) p Fl 1387 407 a(") p Fg 1460 407 a(!) p Fn 1587 407 a(0) p 1668 407 a(and) p Fl 459 674 a(Z) p Fj 526 689 a(1) p Fn 565 674 a(\() p Fl(") p Fn(\)) p 714 674 a(=) p Fl 818 674 a(\015) p Fj 869 689 a(+1) p Fn 963 674 a(\() p Fl(i") p Fn(\)) p Fl(V) p Fj 1196 633 a(1) p Fk(=) p Fj(2) p Fh 1323 528 a( ) p Fn 1714 613 a(0) p 2129 613 a(\() p Fl(p) p Ff 2216 628 a(\000) p Fl 2275 613 a(!) p Fj 2336 628 a(+1) p Fg 2452 613 a(\012) p Fl 2552 613 a(!) p Fj 2613 628 a(+1) p Fn 2707 613 a(\)) 1430 733 y(\() p Fl(!) p Fj 1529 748 a(+1) p Fg 1645 733 a(\012) p Fl 1745 733 a(p) p Ff 1794 748 a(\000) p Fl 1853 733 a(!) p Fj 1914 748 a(+1) p Fn 2008 733 a(\)) p 2412 733 a(0) p Fh 2786 528 a(!) p Fl 2869 674 a(V) p Fj 2947 633 a(1) p Fk(=) p Fj(2) p Fl 3057 674 a(:) p Fn 3343 674 a(\(6.5\)) 0 941 y(Note) p 235 941 a(that) p Fl 446 941 a(p) p Ff 495 956 a(\000) p Fn 581 941 a(=) p Fl 685 941 a(\031) p Ff 740 956 a(\000) p Fn 831 941 a(on) p Fg 966 941 a(fj) p Fl(x) p Fg(j) p Fl 1154 941 a(>) p Fn 1258 941 a(2) p Fg(g) p Fn(,) p 1415 941 a(and) p 1604 941 a(recall) p 1864 941 a(the) p 2031 941 a(form) p 2261 941 a(of) p 2371 941 a(op) s(erator) p Fl 2763 941 a(\031) p Ff 2818 956 a(\000) p Fn 2910 941 a(\(see) p 3104 941 a(section) p 3429 941 a(2\).) 0 1061 y(Then) p 251 1061 a(it) p 345 1061 a(follo) m(ws) p 662 1061 a(from) p 889 1061 a(\(4.7\)) p 1119 1061 a(that) p Fl 1326 1061 a(p) p Ff 1375 1076 a(\000) p Fl 1434 1061 a(!) p Fj 1495 1076 a(+1) p Fn 1617 1061 a(=) p Fl 1721 1061 a(cr) p Ff 1810 1025 a(\000) p 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p 1567 1302 a(0,) p 1675 1302 a(w) m(e) p 1818 1302 a(ha) m(v) m(e) p Fl 2042 1302 a(p) p Ff 2091 1317 a(\000) p Fl 2150 1302 a(!) p Fj 2211 1317 a(+1) p Fn 2333 1302 a(=) p Fl 2436 1302 a(c\032) p Fj 2528 1317 a(0) p Fn 2600 1302 a(for) p 2748 1302 a(another) p Fl 3105 1302 a(c) p Fg 3175 1302 a(6) p Fn(=) p 3278 1302 a(0,) p 3386 1302 a(and) 0 1422 y(hence) p Fl 1064 1543 a(Z) p Fj 1131 1558 a(1) p Fn 1170 1543 a(\() p Fl(") p Fn(\)) p 1319 1543 a(=) p Fl 1423 1543 a(c\015) p Fj 1516 1558 a(+1) p Fn 1610 1543 a(\() p Fl(i") p Fn(\)) p 1782 1543 a(\() p Fl 1819 1543 a(q) p Fj 1862 1558 a(0) p Fg 1924 1543 a(\012) p Fl 2023 1543 a(q) p Fn 2092 1543 a(+) p Fl 2190 1543 a(q) p Fg 2259 1543 a(\012) p Fl 2359 1543 a(q) p Fj 2402 1558 a(0) p Fn 2442 1543 a(\)) p 3343 1543 a(\(6.6\)) 0 1711 y(with) p Fl 229 1711 a(q) p Fn 316 1711 a(=) p Fj 432 1674 a(t) p Fn 463 1711 a(\(0) p Fl(;) p 594 1711 a(V) p Fj 672 1674 a(1) p Fk(=) p Fj(2) p Fl 782 1711 a(!) p Fj 843 1726 a(+1) p Fn 937 1711 a(\).) p 1067 1711 a(The) p 1275 1711 a(argumen) m(t) p 1718 1711 a(is) p 1823 1711 a(di\013eren) m(t) p 2215 1711 a(from) p 2453 1711 a(no) m(w) p 2663 1711 a(on) p 2806 1711 a(according) p 3252 1711 a(as) p 3379 1711 a(0) p Fl 3467 1711 a(<) 0 1831 y(\013) p 90 1831 a(<) p Fn 194 1831 a(1) p Fl(=) p Fn(2) p Fl(;) p 416 1831 a(\013) p Fn 507 1831 a(=) p 610 1831 a(1) p Fl(=) p Fn(2) p 789 1831 a(or) p 908 1831 a(1) p Fl(=) p Fn(2) p Fl 1082 1831 a(<) p 1186 1831 a(\013) p 1276 1831 a(<) p Fn 1380 1831 a(1.) 146 1997 y(\(1\)) p 369 1997 a(Assume) p 727 1997 a(that) p 936 1997 a(0) p Fl 1012 1997 a(<) p 1116 1997 a(\013) p 1206 1997 a(<) p Fn 1310 1997 a(1) p Fl(=) p Fn(2.) p 1525 1997 a(If) p Fl 1620 1997 a(K) p Fn 1727 1997 a(+) p Fl 1819 1997 a(V) p Fn 1927 1997 a(has) p 2098 1997 a(neither) p 2426 1997 a(b) s(ound) p 2724 1997 a(nor) p 2895 1997 a(resonance) p 3337 1997 a(state) 0 2117 y(at) p 115 2117 a(zero) p 316 2117 a(energy) p 586 2117 a(,) p 643 2117 a(then) p 861 2117 a(the) p 1024 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4679 a(1) p 1255 4679 a(+) p Fl 1353 4679 a(Z) p Fj 1420 4694 a(0) p Fn 1481 4679 a(+) p 1579 4679 a(\() p Fl(i=\015) p Fj 1750 4694 a(0) p Fn 1789 4679 a(\)) p 1844 4679 a(\() p Fl(q) p Fj 1925 4694 a(0) p Fg 1987 4679 a(\012) p Fl 2086 4679 a(q) p Fj 2129 4694 a(0) p Fn 2169 4679 a(\)) p 2229 4679 a(+) p Fl 2327 4679 a(op) p Fn(\() p Fl(") p Fj 2507 4638 a(0) p Fn 2546 4679 a(\)) 0 4884 y(and) p Fl 180 4884 a(\015) p Fj 231 4899 a(0) p Fn 298 4884 a(=) p Fg 402 4884 a(\000) p Fn(2.) p 595 4884 a(Assume) p 948 4884 a(that) p 1150 4884 a(zero) p 1347 4884 a(is) p 1435 4884 a(not) p 1600 4884 a(a) p 1672 4884 a(resonance) p 2108 4884 a(energy) p 2378 4884 a(.) p 2446 4884 a(If) p 2534 4884 a(w) m(e) p 2669 4884 a(set) p Fl 2812 4884 a(q) p Fj 2855 4899 a(2) p Fn 2922 4884 a(=) p 3026 4884 a(\(1) s(+) p Fl 3195 4884 a(Z) p Fj 3262 4899 a(0) p Fn 3301 4884 a(\)) p Ff 3339 4848 a(\000) p Fj(1) p Fl 3434 4884 a(q) p Fj 3477 4899 a(0) p Fn 3516 4884 a(,) 0 5005 y(then) p 220 5005 a(the) p 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a(\(1) p 2035 5330 a(+) p Fl 2133 5330 a(Z) p Fj 2200 5345 a(0) p Fn 2239 5330 a(\)) p Ff 2277 5289 a(\000) p Fj(1) p Fn 2394 5330 a(+) p Fl 2492 5330 a(op) p Fn(\() p Fl(") p Fj 2672 5289 a(0) p Fn 2710 5330 a(\)) 784 5487 y(=) p Fh 943 5391 a(\020) p Fn 992 5487 a(1) p Fg 1063 5487 a(\000) p Fn 1163 5487 a(\() p Fl(i=) p Fn(\() p Fl(\015) p Fj 1372 5502 a(0) p Fn 1433 5487 a(+) p Fl 1531 5487 a(i\025) p Fj 1621 5502 a(2) p Fn 1661 5487 a(\)\)) p 1753 5487 a(\() p Fl(q) p Fj 1834 5502 a(2) p Fg 1896 5487 a(\012) p Fl 1995 5487 a(q) p Fj 2038 5502 a(0) p Fn 2078 5487 a(\)) p Fh 2116 5391 a(\021) p Fn 2166 5487 a(\(1) p 2275 5487 a(+) p Fl 2373 5487 a(Z) p Fj 2440 5502 a(0) p Fn 2479 5487 a(\)) p Ff 2517 5446 a(\000) p Fj(1) p Fn 2633 5487 a(+) p Fl 2731 5487 a(op) p Fn(\() p Fl(") p Fj 2911 5446 a(0) p Fn 2950 5487 a(\)) p Fl(:) p Fn 1723 5753 a(27) p 90 rotate dyy eop %%Page: 28 28 28 27 bop Fn 0 407 a(Th) m(us) p 247 407 a(w) m(e) p 391 407 a(obtain) p Fl 892 527 a(R) p Fk 966 542 a(") p Fn 1031 527 a(=) p 1134 527 a(\() p Fl(H) p Ff 1253 542 a(1) p Fn 1350 527 a(+) p Fl 1448 527 a(i) p Fn(\)) p Ff 1519 486 a(\000) p Fj(1) p Fn 1636 527 a(+) p Fl 1734 527 a(c) p Fj 1776 542 a(2) p Fn 1832 527 a(\() p Fl( ) p Ff 1933 542 a(\000) p Fg 2014 527 a(\012) p Fl 2114 527 a( ) p Fj 2177 542 a(+) p Fn 2236 527 a(\)) p 2296 527 a(+) p Fl 2394 527 a(op) p Fn(\() p Fl(") p Fj 2574 486 a(0) p Fn 2613 527 a(\)) 0 701 y(with) p Fl 222 701 a(c) p Fj 264 716 a(2) p Fn 331 701 a(=) p Fl 435 701 a(\025) p Fj 492 716 a(2) p Fl 531 701 a(=) p Fn(\() p Fl(\015) p Fj 669 716 a(0) p Fn 730 701 a(+) p Fl 828 701 a(i\025) p Fj 918 716 a(2) p Fn 958 701 a(\),) p 1055 701 a(and) p Fl 965 919 a(e) p Fk 1010 878 a(i\020) p Fn 1101 919 a(=) p 1205 919 a(2) p Fl(ic) p Fj 1329 934 a(2) p Fg 1390 919 a(\000) p Fn 1490 919 a(1) p 1566 919 a(=) p 1670 919 a(\() p Fl(i\025) p Fj 1798 934 a(2) p Fg 1860 919 a(\000) p Fl 1959 919 a(\015) p Fj 2010 934 a(0) p Fn 2049 919 a(\)) p Fl(=) p Fn(\() p 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a(of.) p Fn 354 2219 a(If) p 460 2219 a(w) m(e) p 613 2219 a(again) p 882 2219 a(denote) p 1205 2219 a(b) m(y) p 1349 2219 a(\005) p Fj 1422 2234 a(1) p Fn 1503 2219 a(and) p 1701 2219 a(\005) p 1817 2219 a(=) p 1936 2219 a(1) p Fg 2013 2219 a(\000) p Fn 2118 2219 a(\005) p Fj 2191 2234 a(1) p Fn 2272 2219 a(the) p 2449 2219 a(pro) p 2595 2219 a(jections) p 2959 2219 a(on) p 3104 2219 a(\010) p 3215 2219 a(and) p 3414 2219 a(\010) p Ff 3484 2183 a(?) p Fn 0 2340 a(resp) s(ectiv) m(ely) p 488 2340 a(,) p 551 2340 a(then) p Fl 142 2558 a(Y) p Fj 199 2573 a(11) p Fn 301 2558 a(=) p 404 2558 a(\005) p Fj 477 2573 a(1) p Fn 517 2558 a(\(1) p 626 2558 a(+) p Fl 724 2558 a(Z) p Fj 791 2573 a(0) p Fn 830 2558 a(\)\005) p Fj 941 2573 a(1) p Fn 1008 2558 a(=) p 1112 2558 a(0) p Fl(;) p 1302 2558 a(Y) p Fj 1359 2573 a(01) p Fn 1461 2558 a(=) p 1564 2558 a(\005\(1) p 1746 2558 a(+) p Fl 1844 2558 a(Z) p Fj 1911 2573 a(0) p Fn 1950 2558 a(\)\005) p Fj 2061 2573 a(1) p Fn 2129 2558 a(=) p 2232 2558 a(0) p Fl(;) p 2422 2558 a(Y) p Fj 2479 2573 a(10) p Fn 2581 2558 a(=) p 2685 2558 a(\005) p Fj 2758 2573 a(1) p Fn 2797 2558 a(\(1) p 2906 2558 a(+) p Fl 3004 2558 a(Z) p Fj 3071 2573 a(0) p Fn 3110 2558 a(\)\005) p 3249 2558 a(=) p 3353 2558 a(0) 0 2776 y(and) p Fl 190 2776 a(Y) p Fj 247 2791 a(00) p Fn 349 2776 a(=) p 452 2776 a(\005\(1) p 634 2776 a(+) p Fl 732 2776 a(Z) p Fj 799 2791 a(0) p Fn 838 2776 a(\)\005) p 977 2776 a(:) p 1032 2776 a(\010) p Ff 1102 2740 a(?) p Fg 1189 2776 a(!) p Fn 1316 2776 a(\010) p Ff 1386 2740 a(?) p Fn 1478 2776 a(is) p 1576 2776 a(in) m(v) m(ertible.) p 2045 2776 a(W) p 2137 2776 a(e) p 2213 2776 a(write) p Fl 1206 2994 a(q) p Fj 1249 3009 a(0) p Fn 1317 2994 a(=) p 1420 2994 a(\005) p Fl(q) p Fj 1536 3009 a(0) p Fn 1598 2994 a(+) p 1696 2994 a(\005) p Fj 1769 3009 a(1) p Fl 1809 2994 a(q) p Fj 1852 3009 a(0) p Fn 1919 2994 a(=) p Fl 2023 2994 a(r) p Fj 2067 3009 a(0) p Fn 2128 2994 a(+) p Fl 2226 2994 a(r) p Fj 2270 3009 a(1) p Fl 2310 2994 a(:) p Fn 0 3212 a(W) p 92 3212 a(e) p 168 3212 a(set) p Fl 320 3212 a(D) p Fn 432 3212 a(=) p 535 3212 a(\() p Fl(i=\015) p Fj 706 3227 a(0) p Fn 745 3212 a(\)) p 800 3212 a(\() p Fl(q) p Fj 881 3227 a(0) p Fg 943 3212 a(\012) p Fl 1042 3212 a(q) p Fj 1085 3227 a(0) p Fn 1125 3212 a(\)) p 1195 3212 a(and) p 1385 3212 a(decomp) s(ose) p 1876 3212 a(it) p 1974 3212 a(in) m(to) p 2171 3212 a(the) p 2339 3212 a(sum) p Fl 845 3430 a(D) p Fn 956 3430 a(=) p Fh 1133 3347 a(X) p Fj 1060 3532 a(0) p Ff(\024) p Fk(j;k) p Ff 1238 3532 a(\024) p Fj(1) p Fl 1343 3430 a(D) p Fk 1424 3445 a(j) t(k) p Fl 1499 3430 a(;) p 1738 3430 a(D) p Fk 1819 3445 a(j) t(k) p Fn 1922 3430 a(=) p 2025 3430 a(\() p Fl(i=\015) p Fj 2196 3445 a(0) p Fn 2235 3430 a(\)) p 2290 3430 a(\() p Fl(r) p Fk 2372 3445 a(j) p Fg 2431 3430 a(\012) p Fl 2530 3430 a(r) p Fk 2574 3445 a(k) p Fn 2617 3430 a(\)) p Fl 2671 3430 a(:) p Fn 0 3738 a(W) p 92 3738 a(e) p 168 3738 a(represen) m(t) p Fl 589 3738 a(Y) p Fk 646 3753 a(") p Fn 710 3738 a(=) p 813 3738 a(1) p 884 3738 a(+) p Fl 982 3738 a(Z) p Fj 1049 3753 a(0) p Fn 1110 3738 a(+) p Fl 1208 3738 a(D) p Fn 1314 3738 a(+) p Fl 1412 3738 a(op) p Fn(\() p Fl(") p Fj 1592 3702 a(0) p Fn 1631 3738 a(\)) p 1702 3738 a(in) p 1815 3738 a(the) p 1983 3738 a(matrix) p 2300 3738 a(form) p Fl 556 4018 a(Y) p Fk 613 4033 a(") p Fn 677 4018 a(=) p Fh 781 3872 a( ) p Fl 888 3957 a(Y) p Fj 945 3972 a(00) p Fn 1041 3957 a(+) p Fl 1139 3957 a(D) p Fj 1220 3972 a(00) p Fl 1378 3957 a(D) p Fj 1459 3972 a(01) p Fl 1014 4078 a(D) p Fj 1095 4093 a(10) p Fl 1378 4078 a(D) p Fj 1459 4093 a(11) p Fh 1575 3872 a(!) p Fn 1663 4018 a(+) p Fl 1761 4018 a(op) p Fn(\() p Fl(") p Fj 1941 3977 a(0) p Fn 1980 4018 a(\)) p 2046 4018 a(:) p Fh 2101 3872 a( ) p Fn 2208 3957 a(\010) p Ff 2278 3921 a(?) p Fn 2237 4078 a(\010) p Fh 2379 3872 a(!) p Fg 2472 4018 a(!) p Fh 2599 3872 a( ) p Fn 2707 3957 a(\010) p Ff 2777 3921 a(?) p Fn 2736 4078 a(\010) p Fh 2878 3872 a(!) p Fl 2960 4018 a(:) p Fn 0 4299 a(By) p 153 4299 a(\(5.4\),) p Fl 413 4299 a(r) p Fj 457 4314 a(1) p Fg 524 4299 a(6) p Fn(=) p 628 4299 a(0,) p 736 4299 a(and) p 926 4299 a(hence) p Fl 1197 4299 a(D) p Fj 1278 4314 a(11) p Fn 1380 4299 a(:) p 1435 4299 a(\010) p Fg 1533 4299 a(!) p Fn 1660 4299 a(\010) p 1763 4299 a(is) p 1862 4299 a(in) m(v) m(ertible.) p 2330 4299 a(W) p 2422 4299 a(e) p 2498 4299 a(ha) m(v) m(e) p Fl 1187 4517 a(D) p Ff 1271 4476 a(\000) p Fj(1) 1268 4541 y(11) p Fn 1393 4517 a(=) p Fg 1497 4517 a(\000) p Fl(i\015) p Fj 1658 4532 a(0) p Fg 1697 4517 a(k) p Fl(r) p Fj 1791 4532 a(1) p Fg 1831 4517 a(k) p Ff 1881 4476 a(\000) p Fj(4) p Fk 1881 4547 a(L) p Fe 1929 4528 a(2) p Fn 1991 4517 a(\() p Fl(r) p Fj 2073 4532 a(1) p Fg 2135 4517 a(\012) p Fl 2235 4517 a(r) p Fj 2279 4532 a(1) p Fn 2318 4517 a(\)) 0 4735 y(and) p Fl 190 4735 a(D) p Fj 271 4750 a(00) p Fg 368 4735 a(\000) p Fl 467 4735 a(D) p Fj 548 4750 a(01) p Fl 623 4735 a(D) p Ff 707 4694 a(\000) p Fj(1) 704 4757 y(11) p Fl 801 4735 a(D) p Fj 882 4750 a(10) p Fn 984 4735 a(=) p 1088 4735 a(0.) p 1207 4735 a(If) p 1305 4735 a(w) m(e) p 1448 4735 a(mak) m(e) p 1703 4735 a(use) p 1871 4735 a(of) p 1983 4735 a(this) p 2173 4735 a(relation,) p 2558 4735 a(then) p Fl 435 5012 a(Y) p Ff 513 4971 a(\000) p Fj(1) p Fk 492 5037 a(") p Fn 635 5012 a(=) p Fh 738 4866 a( ) p Fl 1051 4951 a(Y) p Ff 1130 4910 a(\000) p Fj(1) 1108 4973 y(00) p Fg 1763 4951 a(\000) p Fl(Y) p Ff 1919 4910 a(\000) p Fj(1) 1897 4973 y(00) p Fl 2013 4951 a(D) p Fj 2094 4966 a(01) p Fl 2169 4951 a(D) p Ff 2253 4910 a(\000) p Fj(1) 2250 4973 y(11) p Fg 846 5072 a(\000) p Fl(D) p Ff 1007 5030 a(\000) p Fj(1) 1004 5093 y(11) p Fl 1101 5072 a(D) p Fj 1182 5087 a(10) p Fl 1257 5072 a(Y) p Ff 1335 5030 a(\000) p Fj(1) 1314 5093 y(00) p Fl 1513 5072 a(D) p Ff 1597 5030 a(\000) p Fj(1) 1594 5093 y(11) p Fn 1691 5072 a(\(1) p 1799 5072 a(+) p Fl 1897 5072 a(D) p Fj 1978 5087 a(10) p Fl 2053 5072 a(Y) p Ff 2131 5030 a(\000) p Fj(1) 2110 5093 y(00) p Fl 2226 5072 a(D) p Fj 2307 5087 a(01) p Fl 2381 5072 a(D) p Ff 2465 5030 a(\000) p Fj(1) 2462 5093 y(11) p Fn 2559 5072 a(\)) p Fh 2639 4866 a(!) p Fn 2727 5012 a(+) p Fl 2825 5012 a(op) p Fn(\() p Fl(") p Fj 3005 4971 a(0) p Fn 3044 5012 a(\)) p Fl(:) p Fn 0 5286 a(W) p 92 5286 a(e) p 168 5286 a(compute) 145 5504 y(\() p Fl(r) p Fj 227 5519 a(0) p Fl 266 5504 a(;) p 310 5504 a(Y) p Ff 388 5463 a(\000) p Fj(1) 367 5529 y(00) p Fl 482 5504 a(D) p Fj 563 5519 a(01) p Fl 638 5504 a(D) p Ff 722 5463 a(\000) p Fj(1) 719 5529 y(11) p Fl 816 5504 a(r) p Fj 860 5519 a(1) p Fn 899 5504 a(\)) p Fk 937 5521 a(L) p Fe 985 5502 a(2) p Fn 1052 5504 a(=) p 1155 5504 a(\() p Fl(r) p Fj 1237 5519 a(0) p Fl 1277 5504 a(;) p 1321 5504 a(Y) p Ff 1399 5463 a(\000) p Fj(1) 1378 5529 y(00) p Fl 1493 5504 a(r) p Fj 1537 5519 a(0) p Fn 1576 5504 a(\)) p Fk 1614 5521 a(L) p Fe 1662 5502 a(2) p Fl 1701 5504 a(;) p Fn 1842 5504 a(\() p Fl(r) p Fj 1924 5519 a(1) p Fl 1964 5504 a(;) p 2008 5504 a(D) p Ff 2092 5463 a(\000) p Fj(1) 2089 5529 y(11) p Fl 2185 5504 a(D) p Fj 2266 5519 a(10) p Fl 2341 5504 a(Y) p Ff 2419 5463 a(\000) p Fj(1) 2398 5529 y(00) p Fl 2514 5504 a(r) p Fj 2558 5519 a(0) p Fn 2597 5504 a(\)) p Fk 2635 5521 a(L) p Fe 2683 5502 a(2) p Fn 2749 5504 a(=) p 2853 5504 a(\() p Fl(Y) p Ff 2969 5463 a(\000) p Fj(1) 2948 5529 y(00) p Fl 3063 5504 a(r) p Fj 3107 5519 a(0) p Fl 3147 5504 a(;) p 3191 5504 a(r) p Fj 3235 5519 a(0) p Fn 3274 5504 a(\)) p Fk 3312 5521 a(L) p Fe 3360 5502 a(2) p Fn 1723 5753 a(28) p 90 rotate dyy eop %%Page: 29 29 29 28 bop Fn 0 407 a(and) 569 527 y(\() p Fl(r) p Fj 651 542 a(1) p Fl 690 527 a(;) p 734 527 a(D) p Ff 818 486 a(\000) p Fj(1) 815 552 y(11) p Fn 912 527 a(\(1) p 1021 527 a(+) p Fl 1119 527 a(D) p Fj 1200 542 a(10) p Fl 1275 527 a(Y) p Ff 1353 486 a(\000) p Fj(1) 1332 552 y(00) p Fl 1447 527 a(D) p Fj 1528 542 a(01) p Fl 1603 527 a(D) p Ff 1687 486 a(\000) p Fj(1) 1684 552 y(11) p Fn 1781 527 a(\)) p Fl(r) p Fj 1863 542 a(1) p Fn 1902 527 a(\)) p Fk 1940 544 a(L) p Fe 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a(1) p Fg 1079 1516 a(\000) p Fl 1179 1516 a(i\025) p Fj 1269 1531 a(0) p Fl 1308 1516 a(\015) p Ff 1359 1531 a(\000) p Fn 1418 1516 a(\() p Fl(i") p Fn(\)) p Fl(") p Fj 1619 1475 a(1) p Ff(\000) p Fj(2) p Fk(\013) p Fn 1821 1516 a(=) p Fl 1925 1516 a(") p Fj 1971 1475 a(1) p Ff(\000) p Fj(2) p Fk(\013) p Fn 2162 1516 a(\() p Fl(i\025) p Fj 2290 1531 a(0) p Fl 2329 1516 a(=\015) p Fj 2429 1531 a(0) p Fn 2490 1516 a(+) p Fl 2588 1516 a(o) p Fn(\(1\)\)) p Fl 2814 1516 a(:) p Fn 0 1685 a(W) p 92 1685 a(e) p 168 1685 a(can) p 347 1685 a(easily) p 616 1685 a(pro) m(v) m(e) p 878 1685 a(that) 468 1892 y(\() p Fl(\034) p Fn 559 1892 a(\() p Fl(") p Fn(\)) p Fl(P) p Fn 779 1892 a(+) p Fl 877 1892 a(Q) p Fn(\)) p Ff 992 1851 a(\000) p Fj(1) p Fn 1114 1892 a(=) p Fl 1218 1892 a(\016) p Fn 1265 1892 a(\() p Fl(") p Fn(\)) p Fl(P) p Fn 1485 1892 a(+) p Fl 1583 1892 a(Q;) p Fn 1899 1892 a(\(1) p 2008 1892 a(+) p Fl 2106 1892 a(QZ) p Fj 2250 1907 a(0) p Fl 2289 1892 a(P) p Fn 2366 1892 a(\)) p Ff 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s(p) p Fn(\() p Fl(") p Fj 1032 3400 a(0) p Fn 1070 3436 a(\)) p 1130 3436 a(+) p Fl 1228 3436 a(O) s(p) p Fn(\() p Fl(") p Fj 1439 3400 a(3) p Ff(\000) p Fj(4) p Fk(\013) p Fn 1613 3436 a(\)\)) p Fl(P) p 2181 3436 a(QO) s(p) p Fn(\() p Fl(") p Fj 2469 3400 a(1) p Ff(\000) p Fj(2) p Fk(\013) p Fn 2643 3436 a(\)) p Fl(Q) p Fh 3132 3230 a(!) p Fl 3214 3377 a(:) p Fn 0 3659 a(This,) p 250 3659 a(together) p 635 3659 a(with) p 857 3659 a(\(6.9\)) p 1090 3659 a(and) p 1280 3659 a(\(6.10\),) p 1588 3659 a(implies) p 1920 3659 a(that) p Fl 318 3941 a(Y) p Ff 396 3900 a(\000) p Fj(1) p Fk 375 3966 a(") p Fn 518 3941 a(=) p Fh 621 3795 a( ) p Fl 729 3880 a(\016) p Fn 776 3880 a(\() p Fl(") p Fn(\)) p Fl(P) p Fn 975 3880 a(\(1) p Fg 1082 3880 a(\000) p Fn 1182 3880 a(\() p Fl(\025) p Fj 1277 3895 a(0) p Fl 1316 3880 a(=) p Fg(j) p Fl(\025) p Fj 1450 3895 a(3) p Fg 1489 3880 a(j) p Fj 1517 3844 a(2) p Fn 1556 3880 a(\)) p Fl(Z) p Fj 1661 3895 a(0) p Fl 1700 3880 a(Q) p Fj 1777 3895 a(3) p Fl 1817 3880 a(Z) p Fj 1884 3895 a(0) p Fn 1945 3880 a(+) p Fl 2043 3880 a(op) p Fn(\() p Fl(") p Fj 2223 3844 a(0) p Fn 2262 3880 a(\)\)) p Fl(P) p 2566 3880 a(P) p 2643 3880 a(O) s(p) p Fn(\() p Fl(") p Fj 2854 3844 a(0) p Fn 2891 3880 a(\)) p Fl(Q) 1351 4001 y(QO) s(p) p Fn(\() p Fl(") p Fj 1639 3964 a(0) p Fn 1678 4001 a(\)) p Fl(P) p 2498 4001 a(QO) s(p) p Fn(\() p Fl(") p Fj 2786 3964 a(1) p Ff(\000) p Fj(2) p Fk(\013) p Fn 2960 4001 a(\)) p Fl(Q) p Fh 3116 3795 a(!) p Fl 3199 3941 a(:) p Fn 0 4228 a(Since) p Fl 258 4228 a(P) p 335 4228 a(Z) p Fj 402 4243 a(0) p Fl 441 4228 a(Q) p Fj 518 4243 a(3) p Fl 557 4228 a(Z) p Fj 624 4243 a(0) p Fl 664 4228 a(P) p Fn 773 4228 a(=) p 883 4228 a(\() p Fg(j) p Fl(\025) p Fj 1006 4243 a(3) p Fg 1044 4228 a(j) p Fj 1072 4192 a(2) p Fl 1112 4228 a(=\025) p Fj 1218 4243 a(0) p Fn 1257 4228 a(\)) p Fl(P) p Fn 1372 4228 a(,) p 1435 4228 a(\(6.11\)) p 1720 4228 a(follo) m(ws) p 2044 4228 a(at) p 2166 4228 a(once.) p 2436 4228 a(If) p Fl 2537 4228 a(K) p Fn 2652 4228 a(+) p Fl 2752 4228 a(V) p Fn 2866 4228 a(do) s(es) p 3090 4228 a(not) p 3266 4228 a(ha) m(v) m(e) p 3495 4228 a(a) 0 4348 y(resonance) p 451 4348 a(state,) p 724 4348 a(then) p 952 4348 a(dim) p 1132 4348 a(\011) p 1245 4348 a(=) p 1359 4348 a(0,) p 1475 4348 a(and) p Fl 1670 4348 a(T) p Fj 1727 4363 a(11) p Fn 1802 4348 a(\() p Fl(") p Fn(\)) p 1962 4348 a(:) p 2026 4348 a(\006) p Fg 2135 4348 a(!) p Fn 2272 4348 a(\006) p 2381 4348 a(admits) p 2707 4348 a(an) p 2849 4348 a(in) m(v) m(erse) p 3177 4348 a(b) s(ounded) 0 4468 y(uniformly) p 444 4468 a(in) p Fl 558 4468 a(") p Fn(.) p 674 4468 a(W) p 766 4468 a(e) p 842 4468 a(rep) s(eat) p 1143 4468 a(the) p 1311 4468 a(same) p 1555 4468 a(argumen) m(t) p 1992 4468 a(as) p 2112 4468 a(ab) s(o) m(v) m(e) p 2388 4468 a(to) p 2507 4468 a(obtain) p 2811 4468 a(that) p Fl 749 4745 a(Y) p Ff 827 4704 a(\000) p Fj(1) p Fk 806 4770 a(") p Fn 949 4745 a(=) p Fh 1053 4599 a( ) p Fl 1160 4684 a(\016) p Fn 1207 4684 a(\() p Fl(") p Fn(\)) p Fl(P) p Fn 1406 4684 a(\(1) p 1514 4684 a(+) p Fl 1612 4684 a(op) p Fn(\() p Fl(") p Fj 1792 4648 a(0) p Fn 1831 4684 a(\)\)) p Fl(P) p 2134 4684 a(P) p 2211 4684 a(O) s(p) p Fn(\() p Fl(") p Fj 2422 4648 a(0) p Fn 2460 4684 a(\)) p Fl(Q) 1351 4805 y(QO) s(p) p Fn(\() p Fl(") p Fj 1639 4768 a(0) p Fn 1678 4805 a(\)) p Fl(P) p 2066 4805 a(QO) s(p) p Fn(\() p Fl(") p Fj 2354 4768 a(1) p Ff(\000) p Fj(2) p Fk(\013) p Fn 2528 4805 a(\)) p Fl(Q) p Fh 2685 4599 a(!) p Fl 2767 4745 a(;) p Fn 0 5032 a(so) p 120 5032 a(that) p Fl 331 5032 a(Y) p Ff 409 4996 a(\000) p Fj(1) p Fk 388 5056 a(") p Fg 531 5032 a(\030) p 637 5032 a(\000) p Fl(i) p Fn(\() p Fl(\015) p Fj 836 5047 a(0) p Fl 875 5032 a(=\025) p Fj 981 4996 a(2) 981 5056 y(0) p Fn 1020 5032 a(\)) p Fl(") p Fj 1104 4996 a(2) p Fk(\013) p Ff(\000) p Fj(1) p Fn 1296 5032 a(\() p Fl 1333 5032 a(q) p Fj 1376 5047 a(0) p Fg 1438 5032 a(\012) p Fl 1538 5032 a(q) p Fj 1581 5047 a(0) p Fn 1621 5032 a(\).) p 1729 5032 a(Hence) p 2019 5032 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5472 a(theorem) p 2630 5472 a(is) p 2724 5472 a(no) m(w) p 2923 5472 a(complete.) p Fc 3469 5472 a(2) p Fn 1723 5753 a(30) p 90 rotate dyy eop %%Page: 31 31 31 30 bop Fm 146 407 a(7.) p 271 407 a(Resolv) m(en) m(t) p 784 407 a(analysis) p 1203 407 a(at) p 1338 407 a(lo) m(w) p 1540 407 a(energy) p 1903 407 a(on) p 2059 407 a(Sc) m(hr\177) p 2276 407 a(odinger) p 2678 407 a(op) s(erators) p 3178 407 a(I) s(I) p Fn 146 624 a(The) p 340 624 a(last) p 518 624 a(section) p 838 624 a(is) p 929 624 a(dev) m(oted) p 1286 624 a(to) p 1398 624 a(pro) m(ving) p 1744 624 a(Lemmas) p 2124 624 a(6) p Fl(:) p Fn(1) p Fg 2276 624 a(\030) p Fn 2382 624 a(6) p Fl(:) p Fn(4) p 2532 624 a(whic) m(h) p 2805 624 a(remain) p 3123 624 a(unpro) m(v) m(ed.) 0 745 y(The) p 208 745 a(argumen) m(t) p 652 745 a(here) p 871 745 a(is) p 977 745 a(based) p 1256 745 a(on) p 1399 745 a(the) p 1575 745 a(follo) m(wing) p 1994 745 a(prop) s(osition) p 2515 745 a(obtained) p 2924 745 a(as) p 3051 745 a(Prop) s(osition) 0 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523 2844 a(4.2) p 679 2844 a(with) p Fl 899 2844 a(k) p Fn 981 2844 a(=) p Fl 1085 2844 a(i") p Fn 1194 2844 a(to) p Fl 1312 2844 a(\037) p Fn(\() p Fl(L) p Fj 1477 2859 a(+) p Fn 1555 2844 a(+) p Fl 1650 2844 a(") p Fj 1696 2808 a(2) p Fn 1735 2844 a(\)) p Ff 1773 2808 a(\000) p Fj(1) p Fl 1867 2844 a(\037) p Fn(.) p 1998 2844 a(Since) p Fl 2251 2844 a(!) p Fj 2312 2859 a(+) p Fk(l) p Fn 2421 2844 a(=) p Fl 2524 2844 a(!) p Fk 2585 2859 a(l) p Fg 2630 2844 a(\000) p Fl 2726 2844 a(G) p Fj 2803 2859 a(+) p Fl 2862 2844 a(b!) p Fk 2964 2859 a(l) p Fn 3021 2844 a(b) m(y) p 3155 2844 a(\(4.7\)) p 3386 2844 a(and) 0 2964 y(since) p Fl 239 2964 a(\026) p Fk 298 2979 a(l) p Fn 351 2964 a(=) p Fl 455 2964 a(\030) p Fk 498 2979 a(l) p Fn 556 2964 a(for) p Fl 705 2964 a(\033) p Fn 792 2964 a(=) p Fl 895 2964 a(i) p Fn(,) p 988 2964 a(the) p 1156 2964 a(desired) p 1487 2964 a(relation) p 1845 2964 a(is) p 1943 2964 a(obtained.) p Fc 2480 2964 a(2) p Fd 0 3133 a(Pr) p 102 3133 a(o) p 147 3133 a(of) p 262 3133 a(of) p 376 3133 a(L) p 432 3133 a(emma) p 721 3133 a(6.2.) p Fn 978 3133 a(W) p 1070 3133 a(e) p 1146 3133 a(ha) m(v) m(e) 456 3349 y(\() p Fl(L) p Ff 560 3364 a(\000) p Fk(") p Fn 674 3349 a(+) p 772 3349 a(1\)) p Ff 859 3307 a(\000) p Fj(1) p Fl 953 3349 a(J) p Fk 1007 3364 a(") p Fl 1044 3349 a(\037) p Fn 1133 3349 a(=) p 1236 3349 a(\() p Fl(L) p Fk 1340 3364 a(") p Fn 1400 3349 a(+) p 1498 3349 a(1\)) p Ff 1585 3307 a(\000) p Fj(1) p Fl 1679 3349 a(J) p Fk 1733 3364 a(") p Fl 1769 3349 a(\037) p Fn 1853 3349 a(+) p 1951 3349 a(\() p Fl(L) p Fk 2055 3364 a(") p Fn 2114 3349 a(+) p 2212 3349 a(1\)) p Ff 2299 3307 a(\000) p Fj(1) p Fl 2393 3349 a(J) p Fk 2447 3364 a(") p Fl 2484 3349 a(b) p Fn(\() p Fl(L) p Ff 2629 3364 a(\000) p Fn 2710 3349 a(+) p Fl 2808 3349 a(") p Fj 2854 3307 a(2) p Fn 2894 3349 a(\)) p Ff 2932 3307 a(\000) p Fj(1) p Fl 3026 3349 a(\037) p Fn 0 3564 a(b) m(y) p 141 3564 a(the) p 314 3564 a(resolv) m(en) m(t) p 729 3564 a(iden) m(tit) m(y) p 1047 3564 a(.) p 1135 3564 a(The) p 1341 3564 a(\014rst) p 1547 3564 a(op) s(erator) p 1945 3564 a(on) p 2086 3564 a(the) p 2259 3564 a(righ) m(t) p 2500 3564 a(side) p 2701 3564 a(is) p 2804 3564 a(of) p 2921 3564 a(class) p Fl 3155 3564 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p 3440 3564 a(b) m(y) 0 3684 y(Prop) s(osition) p 521 3684 a(7.1.) p 715 3684 a(W) p 807 3684 a(e) p 879 3684 a(apply) p 1144 3684 a(Prop) s(osition) p 1665 3684 a(4.3) p 1818 3684 a(to) p Fl 1934 3684 a(\037) p Fn(\() p Fl(L) p Ff 2099 3699 a(\000) p Fn 2173 3684 a(+) p Fl 2264 3684 a(") p Fj 2310 3648 a(2) p Fn 2348 3684 a(\)) p Ff 2386 3648 a(\000) p Fj(1) p Fl 2480 3684 a(\037) p Fn 2570 3684 a(in) p 2680 3684 a(the) p 2845 3684 a(second) p 3156 3684 a(op) s(erator.) 0 3805 y(Since) 493 3925 y(\() p Fl(b\032) p Fj 622 3940 a(0) p Fl 663 3925 a(;) p 707 3925 a(!) p Fj 768 3940 a(0) p Fn 806 3925 a(\)) p Fk 844 3942 a(L) p Fe 892 3923 a(2) p Fn 959 3925 a(=) p 1062 3925 a(\() p Fl(b) p Fj 1141 3884 a(1) p Fk(=) p Fj(2) p Fl 1252 3925 a(G) p Fj 1329 3940 a(0) p Fg 1368 3925 a(j) p Fl(b) p Fg(j) p Fj 1465 3884 a(1) p Fk(=) p Fj(2) p Fl 1575 3925 a(\021) p Fj 1623 3940 a(0) p Fl 1662 3925 a(;) p Fg 1706 3925 a(j) p Fl(b) p Fg(j) p Fj 1803 3884 a(1) p Fk(=) p Fj(2) p Fl 1913 3925 a(!) p Fj 1974 3940 a(0) p Fn 2013 3925 a(\)) p Fk 2051 3942 a(L) p Fe 2099 3923 a(2) p Fn 2166 3925 a(=) p 2269 3925 a(\() p Fl(\021) p Fj 2355 3940 a(0) p Fl 2395 3925 a(;) p Fg 2439 3925 a(j) p Fl(b) p Fg(j) p Fj 2536 3884 a(1) p Fk(=) p Fj(2) p Fl 2645 3925 a(!) p Fj 2706 3940 a(0) p Fn 2745 3925 a(\)) p Fk 2783 3942 a(L) p Fe 2831 3923 a(2) p Fn 2898 3925 a(=) p 3001 3925 a(1) 0 4097 y(and) p 203 4097 a(since) p 456 4097 a(\() p Fl(b\032) p Fj 585 4112 a(0) p Fl 625 4097 a(;) p 669 4097 a(!) p Fj 730 4112 a(1) p Fn 769 4097 a(\)) p Fk 807 4114 a(L) p Fe 855 4095 a(2) p Fn 944 4097 a(=) p 1071 4097 a(\() p Fl(\021) p Fj 1157 4112 a(0) p Fl 1196 4097 a(;) p Fg 1240 4097 a(j) p Fl(b) p Fg(j) p Fj 1337 4061 a(1) p Fk(=) p Fj(2) p Fl 1447 4097 a(!) p Fj 1508 4112 a(1) p Fn 1547 4097 a(\)) p Fk 1585 4114 a(L) p Fe 1633 4095 a(2) p Fn 1722 4097 a(=) p 1849 4097 a(0) p 1944 4097 a(b) m(y) p 2093 4097 a(\(4.13\),) p 2418 4097 a(the) p 2600 4097 a(desired) p 2944 4097 a(relation) p 3316 4097 a(again) 0 4218 y(follo) m(ws) p 320 4218 a(from) p 551 4218 a(Prop) s(osition) p 1075 4218 a(7.1) p 1233 4218 a(with) p Fl 1455 4218 a(\033) p Fn 1542 4218 a(=) p Fl 1645 4218 a(i) p Fn(.) p Fc 1846 4218 a(2) p Fd 0 4387 a(Pr) p 102 4387 a(o) p 147 4387 a(of) p 262 4387 a(of) p 376 4387 a(L) p 432 4387 a(emma) p 721 4387 a(6.3.) p Fn 978 4387 a(Since) p Fl 1233 4387 a(p) p Ff 1282 4351 a(\003) 1282 4411 y(\000) p Fk(") p Fl 1373 4387 a(p) p Ff 1422 4402 a(\000) p Fk(") p Fn 1542 4387 a(=) p Fl 1645 4387 a(p) p Fj 1694 4402 a(+) p Fk(") p Fl 1786 4387 a(p) p Ff 1835 4402 a(\000) p Fk(") p Fn 1954 4387 a(=) p Fl 2058 4387 a(L) p Fj 2124 4402 a(+) p Fk(") p Fn 2216 4387 a(,) p 2275 4387 a(w) m(e) p 2419 4387 a(ha) m(v) m(e) p Fh 433 4529 a(\020) p Fl 482 4626 a(p) p Ff 531 4641 a(\000) p Fk(") p Fn 623 4626 a(\() p Fl(L) p Fj 727 4641 a(+) p Fk(") p Fn 841 4626 a(+) p 939 4626 a(1\)) p Ff 1026 4585 a(\000) p Fj(1) p Fh 1120 4529 a(\021) p Ff 1170 4552 a(\003) p Fl 1226 4626 a(p) p Ff 1275 4641 a(\000) p Fk(") p Fn 1366 4626 a(\() p Fl(L) p Fj 1470 4641 a(+) p Fk(") p Fn 1584 4626 a(+) p 1682 4626 a(1\)) p Ff 1769 4585 a(\000) p Fj(1) p Fn 1891 4626 a(=) p 1995 4626 a(\() p Fl(L) p Fj 2099 4641 a(+) p Fk(") p Fn 2213 4626 a(+) p 2311 4626 a(1\)) p Ff 2398 4585 a(\000) p Fj(1) p Fg 2514 4626 a(\000) p Fn 2613 4626 a(\() p Fl(L) p Fj 2717 4641 a(+) p Fk(") p Fn 2832 4626 a(+) p 2930 4626 a(1\)) p Ff 3017 4585 a(\000) p Fj(2) p Fn 0 4841 a(and) p 190 4841 a(hence) p Fg 404 5057 a(k) p Fl(p) p Ff 503 5072 a(\000) p Fk(") p Fn 595 5057 a(\() p Fl(L) p Fj 699 5072 a(+) p Fk(") p Fn 813 5057 a(+) p 911 5057 a(1\)) p Ff 998 5015 a(\000) p Fj(1) p Fl 1092 5057 a(J) p Fk 1146 5072 a(") p Fl 1182 5057 a(\037) p Fg(k) p Fj 1293 5015 a(2) p Fn 1361 5057 a(=) p Fg 1464 5057 a(k) p Fl(\037) p Fh 1592 4960 a(\020) p Fl 1641 5057 a(") p Fj 1687 5015 a(2) p Fn 1726 5057 a(\() p Fl(L) p Fj 1830 5072 a(+) p Fn 1912 5057 a(+) p Fl 2010 5057 a(") p Fj 2056 5015 a(2) p Fn 2095 5057 a(\)) p Ff 2133 5015 a(\000) p Fj(1) p Fg 2249 5057 a(\000) p Fl 2349 5057 a(") p Fj 2395 5015 a(4) p Fn 2434 5057 a(\() p Fl(L) p Fj 2538 5072 a(+) p Fn 2619 5057 a(+) p Fl 2717 5057 a(") p Fj 2763 5015 a(2) p Fn 2803 5057 a(\)) p Ff 2841 5015 a(\000) p Fj(2) p Fh 2935 4960 a(\021) p Fl 3001 5057 a(\037) p Fg(k) p Fl(:) p Fn 0 5289 a(By) p 153 5289 a(Prop) s(osition) p 678 5289 a(4.2,) p Fg 862 5289 a(k) p Fl(\037) p Fn(\() p Fl(L) p Fj 1077 5304 a(+) p Fn 1159 5289 a(+) p Fl 1257 5289 a(") p Fj 1303 5252 a(2) p Fn 1342 5289 a(\)) p Ff 1380 5252 a(\000) p Fj(1) p Fl 1474 5289 a(\037) p Fg(k) p Fn 1613 5289 a(=) p Fl 1716 5289 a(O) p Fn 1794 5289 a(\(1\)) p 1951 5289 a(as) p Fl 2070 5289 a(") p Fg 2144 5289 a(!) p Fn 2271 5289 a(0.) p 2390 5289 a(This) p 2613 5289 a(implies) p 2944 5289 a(that) p Fg 1225 5504 a(k) p Fl(\037) p Fn(\() p Fl(L) p Fj 1440 5519 a(+) p Fn 1522 5504 a(+) p Fl 1620 5504 a(") p Fj 1666 5463 a(2) p Fn 1705 5504 a(\)) p Ff 1743 5463 a(\000) p Fj(1) p Fk(=) p Fj(2) p Fg 1908 5504 a(k) p Fn 1985 5504 a(=) p Fl 2089 5504 a(O) p Fn 2167 5504 a(\(1\)) p Fl(:) p Fn 1723 5753 a(31) p 90 rotate dyy eop %%Page: 32 32 32 31 bop Fn 0 407 a(Th) m(us) p 247 407 a(the) p 415 407 a(b) s(ound) p 716 407 a(in) p 830 407 a(the) p 998 407 a(lemma) p 1312 407 a(is) p 1410 407 a(obtained.) p Fc 1947 407 a(2) p Fd 0 573 a(Pr) p 102 573 a(o) p 147 573 a(of) p 265 573 a(of) p 382 573 a(L) p 438 573 a(emma) p 730 573 a(6.4.) p Fn 987 573 a(W) p 1079 573 a(e) p 1158 573 a(pro) m(v) m(e) p 1425 573 a(the) p 1596 573 a(lemma) p 1913 573 a(only) p 2131 573 a(in) p 2248 573 a(the) p 2419 573 a(simple) p 2726 573 a(case) p 2936 573 a(that) p Fl 3151 573 a(b) p Fn(\() p Fl(x) p Fn(\)) p Fg 3357 573 a(\025) p Fn 3467 573 a(0.) 0 694 y(W) p 92 694 a(e) p 168 694 a(assert) p 445 694 a(that) p Fl 142 900 a(p) p Fj 191 915 a(+) p Fk(") p Fn 282 900 a(\() p Fl(L) p Ff 386 915 a(\000) p Fk(") p Fg 500 900 a(\000) p Fl 600 900 a(i) p Fn(\)) p Ff 671 859 a(\000) p Fj(1) p Fl 766 900 a(J) p Fk 820 915 a(") p Fl 856 900 a(\037) p Fn 945 900 a(=) p Fg 1049 900 a(\000) p Fl(i) p Fj 1159 859 a(\(3) p Ff(\000) p Fk(\013) p Fj(\)) p Fk(=) p Fj(2) p Fn 1441 900 a(\() p Fl(\014) p Fj 1534 915 a(0) p Fl 1573 900 a(=\015) p Fj 1673 915 a(0) p Fn 1712 900 a(\)) p Fl 1767 900 a(") p Fj 1813 859 a(1) p Ff(\000) p Fk(\013) p Fn 1969 900 a(\(\() p Fl(\034) p Fj 2087 915 a(1) p Fn 2149 900 a(+) p Fl 2247 900 a(o) p Fj 2294 915 a(2) p Fn 2333 900 a(\(1\)\)) p Fg 2518 900 a(\012) p Fl 2617 900 a(\037\032) p Fj 2728 915 a(0) p Fn 2768 900 a(\)) p 2828 900 a(+) p Fl 2926 900 a(O) s(p) p Fn(\() p Fl(") p Fn(\)) p Fl(;) p Fn 3343 900 a(\(7.1\)) 0 1107 y(where) p Fl 293 1107 a(\034) p Fj 335 1122 a(1) p Fn 375 1107 a(\() p Fl(x) p Fn(\)) p 552 1107 a(=) p Fl 674 1107 a(H) p Fj 755 1122 a(1) p Ff(\000) p Fk(\013) p Fn 895 1107 a(\() p Fl(i) p Fj 966 1071 a(1) p Fk(=) p Fj(2) p Fl 1076 1107 a(r) p Fn 1123 1107 a(\)) p Fl(e) p Fk 1206 1071 a(i\022) p Fn 1269 1107 a(.) p 1372 1107 a(This) p 1606 1107 a(implies) p 1948 1107 a(the) p 2127 1107 a(lemma.) p 2512 1107 a(In) p 2645 1107 a(fact,) p 2878 1107 a(w) m(e) p 3033 1107 a(use) p 3213 1107 a(\(3.3\)) p 3457 1107 a(to) 0 1228 y(obtain) p Fl 545 1348 a(p) p Fj 594 1363 a(+) p Fk(") p Fn 685 1348 a(\() p Fl(L) p Ff 789 1363 a(\000) p Fk(") p Fn 903 1348 a(+) p 1001 1348 a(1\)) p Ff 1088 1307 a(\000) p Fj(1) p Fn 1210 1348 a(=) p Fh 1313 1252 a(\020) p Fn 1363 1348 a(1) p Fg 1434 1348 a(\000) p Fn 1534 1348 a(\(1) p 1642 1348 a(+) p Fl 1740 1348 a(i) p Fn(\)\() p Fl(L) p Fj 1915 1363 a(+) p Fk(") p Fn 2030 1348 a(+) p 2128 1348 a(1\)) p Ff 2215 1307 a(\000) p Fj(1) p Fh 2309 1252 a(\021) p Fl 2375 1348 a(p) p Fj 2424 1363 a(+) p Fk(") p Fn 2516 1348 a(\() p Fl(L) p Ff 2620 1363 a(\000) p Fk(") p Fg 2734 1348 a(\000) p Fl 2833 1348 a(i) p Fn(\)) p Ff 2904 1307 a(\000) p Fj(1) p Fn 0 1517 a(and) p 190 1517 a(it) p 287 1517 a(follo) m(ws) p 608 1517 a(from) p 838 1517 a(Lemma) p 1186 1517 a(3.1) p 1343 1517 a(that) p Fh 451 1627 a(\020) p Fn 500 1723 a(1) p Fg 571 1723 a(\000) p Fn 671 1723 a(\(1) p 779 1723 a(+) p Fl 877 1723 a(i) p Fn(\)\() p Fl(L) p Fj 1052 1738 a(+) p Fk(") p Fn 1167 1723 a(+) p 1265 1723 a(1\)) p Ff 1352 1682 a(\000) p Fj(1) p Fh 1446 1627 a(\021) p Fl 1512 1723 a(\034) p Fj 1554 1738 a(1) p Fg 1621 1723 a(!) p Fl 1749 1723 a(f) p Fj 1797 1738 a(1) p Fn 1864 1723 a(=) p 1968 1723 a(\(1) p Fg 2076 1723 a(\000) p Fn 2176 1723 a(\(1) p 2285 1723 a(+) p Fl 2383 1723 a(i) p Fn(\)\() p Fl(L) p Fk 2558 1738 a(AB) p Fn 2694 1723 a(+) p 2792 1723 a(1\)) p Ff 2879 1682 a(\000) p Fj(1) p Fn 2973 1723 a(\)) p Fl(\034) p Fj 3053 1738 a(1) p Fn 0 1947 a(strongly) p 380 1947 a(in) p Fl 497 1947 a(L) p Fj 563 1911 a(2) p Fn 603 1947 a(.) p 683 1947 a(The) p 887 1947 a(function) p Fl 1272 1947 a(f) p Fj 1320 1962 a(1) p Fg 1392 1947 a(2) p Fl 1492 1947 a(L) p Fj 1558 1911 a(2) p Fn 1633 1947 a(satis\014es) p 1996 1947 a(\() p Fl(\031) p Fj 2093 1911 a(2) 2089 1971 y(1) p Fn 2154 1947 a(+) p Fl 2252 1947 a(\031) p Fj 2311 1911 a(2) 2307 1971 y(2) p Fn 2373 1947 a(+) p 2471 1947 a(1\)) p Fl 2574 1947 a(f) p Fj 2622 1962 a(1) p Fn 2695 1947 a(=) p 2804 1947 a(0.) p 2932 1947 a(Hence) p 3225 1947 a(it) p 3326 1947 a(tak) m(es) 0 2067 y(the) p 168 2067 a(form) p Fl 398 2067 a(f) p Fj 446 2082 a(1) p Fn 486 2067 a(\() p Fl(x) p Fn(\)) p 645 2067 a(=) p Fl 748 2067 a(g) p Fn 799 2067 a(\() p Fl(r) p Fn 884 2067 a(\)) p Fl(e) p Fk 967 2031 a(i\022) p Fn 1029 2067 a(,) p 1089 2067 a(where) p Fl 1371 2067 a(g) p Fn 1454 2067 a(solv) m(es) p Fg 943 2286 a(\000) p Fl(g) p Ff 1071 2245 a(00) p Fg 1135 2286 a(\000) p Fl 1234 2286 a(r) p Ff 1281 2245 a(\000) p Fj(1) p Fl 1375 2286 a(g) p Ff 1426 2245 a(0) p Fn 1471 2286 a(+) p Fh 1569 2190 a(\020) p Fn 1619 2286 a(\(1) p Fg 1728 2286 a(\000) p Fl 1827 2286 a(\013) p Fn 1890 2286 a(\)) p Fj 1928 2245 a(2) p Fl 1967 2286 a(r) p Ff 2014 2245 a(\000) p Fj(2) p Fn 2130 2286 a(+) p 2228 2286 a(1) p Fh 2277 2190 a(\021) p Fl 2343 2286 a(g) p Fn 2421 2286 a(=) p 2525 2286 a(0) p Fl(:) p Fn 0 2513 a(Th) m(us) p Fl 249 2513 a(f) p Fj 297 2528 a(1) p Fn 366 2513 a(=) p Fl 473 2513 a(cH) p Fj 596 2528 a(1) p Ff(\000) p Fk(\013) p Fn 735 2513 a(\() p Fl(ir) p Fn 853 2513 a(\)) p Fl(e) p Fk 936 2477 a(i\022) p Fn 1029 2513 a(=) p Fl 1136 2513 a(c\030) p Fj 1221 2528 a(1) p Fn 1294 2513 a(for) p 1444 2513 a(some) p 1690 2513 a(co) s(e\016cien) m(t) p Fl 2147 2513 a(c) p Fn(.) p 2264 2513 a(Since) p Fl 2520 2513 a(u) p Fg 2606 2513 a(2) p 2703 2513 a(D) p Fn 2783 2513 a(\() p Fl(L) p Fk 2887 2528 a(AB) p Fn 3000 2513 a(\)) p 3072 2513 a(v) p 3118 2513 a(anishes) p 3457 2513 a(at) 0 2634 y(the) p 171 2634 a(origin,) p Fl 479 2634 a(f) p Fj 527 2649 a(1) p Fg 591 2634 a(\000) p Fl 693 2634 a(\034) p Fj 735 2649 a(1) p Fn 810 2634 a(also) p 1009 2634 a(v) p 1055 2634 a(anishes,) p 1423 2634 a(so) p 1546 2634 a(that) p Fl 1761 2634 a(c) p Fn 1839 2634 a(is) p 1940 2634 a(determined) p 2453 2634 a(as) p Fl 2576 2634 a(c) p Fn 2651 2634 a(=) p Fl 2760 2634 a(i) p Fj 2793 2597 a(\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fk(=) p Fj(2) p Fn 3059 2634 a(.) p 3139 2634 a(Hence) p 3432 2634 a(w) m(e) 0 2754 y(see) p 158 2754 a(that) p 369 2754 a(\(7.1\)) p 602 2754 a(implies) p 933 2754 a(the) p 1101 2754 a(relation) p 1459 2754 a(of) p 1570 2754 a(the) p 1738 2754 a(lemma.) 146 2920 y(W) p 238 2920 a(e) p 314 2920 a(shall) p 542 2920 a(sho) m(w) p 784 2920 a(\(7.1\).) p 1055 2920 a(W) p 1147 2920 a(e) p 1223 2920 a(mak) m(e) p 1478 2920 a(use) p 1646 2920 a(of) p 1757 2920 a(the) p 1925 2920 a(relation) 460 3127 y(\() p Fl(L) p Ff 564 3142 a(\000) p Fk(") p Fg 678 3127 a(\000) p Fl 777 3127 a(i) p Fn(\)) p Ff 848 3086 a(\000) p Fj(1) p Fl 943 3127 a(J) p Fk 997 3142 a(") p Fl 1034 3127 a(\037) p Fn 1122 3127 a(=) p 1226 3127 a(\() p Fl(L) p Fk 1330 3142 a(") p Fg 1389 3127 a(\000) p Fl 1489 3127 a(i) p Fn(\)) p Ff 1560 3086 a(\000) p Fj(1) p Fl 1654 3127 a(J) p Fk 1708 3142 a(") p Fl 1745 3127 a(\037) p Fn 1828 3127 a(+) p 1926 3127 a(\() p Fl(L) p Fk 2030 3142 a(") p Fg 2089 3127 a(\000) p Fl 2189 3127 a(i) p Fn(\)) p Ff 2260 3086 a(\000) p Fj(1) p Fl 2355 3127 a(J) p Fk 2409 3142 a(") p Fl 2445 3127 a(b) p Fn(\() p Fl(L) p Ff 2590 3142 a(\000) p Fg 2672 3127 a(\000) p Fl 2772 3127 a(i") p Fj 2851 3086 a(2) p Fn 2890 3127 a(\)) p Ff 2928 3086 a(\000) p Fj(1) p Fl 3022 3127 a(\037) p Fn 0 3334 a(to) p 119 3334 a(decomp) s(ose) p Fl 1041 3454 a(p) p Fj 1090 3469 a(+) p Fk(") p Fn 1181 3454 a(\() p Fl(L) p Ff 1285 3469 a(\000) p Fk(") p Fg 1399 3454 a(\000) p Fl 1499 3454 a(i) p Fn(\)) p Ff 1570 3413 a(\000) p Fj(1) p Fl 1664 3454 a(J) p Fk 1718 3469 a(") p Fl 1755 3454 a(\037) p Fn 1844 3454 a(=) p Fl 1947 3454 a(I) p Fj 1990 3469 a(1) p Fn 2030 3454 a(\() p 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p Fg 1019 5479 a(\000) p Fl 1119 5479 a(i) p Fn(\)) p Ff 1190 5438 a(\000) p Fj(1) p Fl 1285 5479 a(J) p Fk 1339 5494 a(") p Fl 1375 5479 a(b\032) p Fj 1466 5494 a(0) p Fn 1534 5479 a(=) p Fl 1638 5479 a(i) p Fj 1671 5438 a(3\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fk(=) p Fj(2) p Fl 1971 5479 a(\014) p Fj 2026 5494 a(0) p Fl 2066 5479 a(") p Fj 2112 5438 a(1+) p Fk(\013) p Fl 2251 5479 a(\034) p Fj 2293 5494 a(1) p Fn 2355 5479 a(+) p Fl 2453 5479 a(o) p Fj 2500 5494 a(2) p Fn 2539 5479 a(\() p Fl(") p Fj 2623 5438 a(1+) p Fk(\013) p Fn 2763 5479 a(\)) p Fl(:) p Fn 1723 5753 a(32) p 90 rotate dyy eop %%Page: 33 33 33 32 bop Fd 0 407 a(Pr) p 102 407 a(o) p 147 407 a(of.) p Fn 354 407 a(Since) p Fl 609 407 a(b) p Fj 650 371 a(1) p Fk(=) p Fj(2) p Fl 760 407 a(G) p Fj 837 422 a(0) p Fl 877 407 a(b) p Fj 918 371 a(1) p Fk(=) p Fj(2) p Fl 1028 407 a(\021) p Fj 1076 422 a(0) p Fn 1143 407 a(=) p Fl 1247 407 a(\021) p Fj 1295 422 a(0) p Fn 1335 407 a(,) p 1394 407 a(it) p 1492 407 a(follo) 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1501 a(\005\() p Fl(") p Fn(\)) p Ff 2099 1460 a(\003) p Fn 2139 1501 a(\)) p Fg 2199 1501 a(\000) p Fl 2298 1501 a(") p Fj 2344 1460 a(2) p Fn 2383 1501 a(\005\() p Fl(") p Fn(\)) p Ff 2578 1460 a(\003) p Fn 2617 1501 a(\005\() p Fl(") p Fn(\)) p Fl(;) p Fn 0 1716 a(where) p 282 1716 a(\005\() p Fl(") p Fn(\)) p 504 1716 a(=) p Fl 607 1716 a(b) p Fj 648 1679 a(1) p Fk(=) p Fj(2) p Fn 759 1716 a(\() p Fl(L) p Fg 885 1716 a(\000) p Fl 984 1716 a(i") p Fj 1063 1679 a(2) p Fn 1103 1716 a(\)) p Ff 1141 1679 a(\000) p Fj(1) p Fl 1235 1716 a(b) p Fj 1276 1679 a(1) p Fk(=) p Fj(2) p Fn 1386 1716 a(.) p 1457 1716 a(W) p 1549 1716 a(e) p 1624 1716 a(apply) p 1892 1716 a(Prop) s(osition) p 2417 1716 a(4.1) p 2574 1716 a(with) p Fl 2796 1716 a(k) p Fn 2878 1716 a(=) p Fl 2981 1716 a(i) p Fj 3014 1679 a(1) p Fk(=) p Fj(2) p Fl 3125 1716 a(") p Fn 3203 1716 a(to) p 3322 1716 a(\005\() p Fl(") p Fn(\).) 0 1836 y(Then) 442 1956 y(\005\() p Fl(") p Fn(\)) p 664 1956 a(=) p Fl 768 1956 a(b) p Fj 809 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a(\000) p Fl(\015) p Fj 2098 2803 a(0) p Fn 2154 2788 a(cos) q(\() p Fl(\013) q(\031) t(=) p Fn(2\)) p 2602 2788 a(+) p Fl 2700 2788 a(o) p Fn(\(1\)) p Fl(:) p Fn 0 2978 a(On) p 163 2978 a(the) p 331 2978 a(other) p 585 2978 a(hand,) p 856 2978 a(w) m(e) p 1000 2978 a(use) p 1168 2978 a(the) p 1336 2978 a(form) m(ula) p Fg 722 3196 a(k) p Fl(\034) p Fj 814 3211 a(1) p Fg 853 3196 a(k) p Fj 903 3155 a(2) p Fk 903 3221 a(L) p Fe 951 3202 a(2) p Fn 1018 3196 a(=) p 1121 3196 a(2) p Fl(\031) p Fh 1245 3079 a(Z) p Ff 1328 3105 a(1) p Fj 1292 3268 a(0) p Fl 1420 3196 a(r) p Fg 1467 3196 a(j) p Fl(H) p Fj 1576 3211 a(1) p Ff(\000) p Fk(\013) p Fn 1715 3196 a(\() p Fl(i) p Fj 1786 3155 a(1) p Fk(=) p Fj(2) p Fl 1896 3196 a(r) p Fn 1943 3196 a(\)) p Fg(j) p Fj 2009 3155 a(2) p Fl 2064 3196 a(dr) p Fn 2189 3196 a(=) p 2293 3196 a(2) p Fl(=) p Fn 2408 3196 a(sin\() p Fl(\013) q(\031) t(=) p Fn(2\)) 0 3416 y(to) p 119 3416 a(obtain) p 423 3416 a(that) p Fg 903 3536 a(k) p Fl(g) p Fj 1000 3551 a(0) p Fg 1039 3536 a(k) p Fj 1089 3495 a(2) p Fk 1089 3561 a(L) p Fe 1137 3542 a(2) p Fn 1203 3536 a(=) p Fg 1307 3536 a(j) p Fl(\014) p Fj 1390 3551 a(0) p Fg 1429 3536 a(j) p Fj 1457 3495 a(2) p Fg 1496 3536 a(k) p Fl(\034) p Fj 1588 3551 a(1) p Fg 1627 3536 a(k) p Fj 1677 3495 a(2) p Fk 1677 3561 a(L) p Fe 1725 3542 a(2) p Fn 1792 3536 a(=) p 1895 3536 a(2) p Fg(j) p Fl(\014) p Fj 2027 3551 a(0) p Fg 2066 3536 a(j) p Fj 2094 3495 a(2) p Fl 2133 3536 a(=) p Fn 2199 3536 a(sin\() p Fl(\013) q(\031) t(=) p Fn(2\)) p Fl(:) p Fn 0 3698 a(Since) p 258 3698 a(2) p Fg(j) p Fl(\014) p Fj 390 3713 a(0) p Fg 429 3698 a(j) p Fj 457 3662 a(2) p Fl 496 3698 a(=) p Fn 562 3698 a(sin\() p Fl(\013) q(\031) t(=) p Fn(2\)) p 1010 3698 a(=) p Fg 1119 3698 a(\000) p Fl(\015) p Fj 1247 3713 a(0) p Fn 1303 3698 a(cos) q(\() p Fl(\013) q(\031) t(=) p Fn(2\)) p 1765 3698 a(b) m(y) p 1904 3698 a(\(6.8\),) p 2168 3698 a(it) p 2269 3698 a(follo) m(ws) p 2593 3698 a(that) p Fg 2807 3698 a(k) p Fl(g) p Fk 2904 3713 a(") p Fg 2941 3698 a(k) p Fk 2991 3715 a(L) p Fe 3039 3696 a(2) p Fg 3111 3698 a(!) p 3244 3698 a(k) p Fl(g) p Fj 3341 3713 a(0) p Fg 3380 3698 a(k) p Fk 3430 3715 a(L) p Fe 3478 3696 a(2) p Fn 3516 3698 a(.) 0 3818 y(Next) p 238 3818 a(w) m(e) p 380 3818 a(shall) p 608 3818 a(sho) m(w) p 849 3818 a(that) p Fl 1059 3818 a(g) p Fk 1106 3833 a(") p Fg 1170 3818 a(!) p Fl 1298 3818 a(g) p Fj 1345 3833 a(0) p Fn 1416 3818 a(w) m(eakly) p 1696 3818 a(.) p 1768 3818 a(Let) p Fl 1942 3818 a(f) p Fg 2028 3818 a(2) p Fl 2122 3818 a(C) p Ff 2199 3782 a(1) p Fj 2192 3843 a(0) p Fn 2274 3818 a(\() p Fi(R) p Fj 2399 3776 a(2) p Fg 2459 3818 a(n) p 2529 3818 a(f) p Fn(0) p Fg(g) p Fn(\).) p 2786 3818 a(Then) p Fl 3040 3818 a(p) p Ff 3089 3833 a(\000) p Fk(") p Fl 3180 3818 a(f) p Fn 3267 3818 a(=) p Fl 3370 3818 a(\031) p Ff 3425 3833 a(\000) p Fl 3485 3818 a(f) p Fn 0 3939 a(for) p Fl 149 3939 a(") p 222 3939 a(>) p Fn 326 3939 a(0) p 407 3939 a(small) p 662 3939 a(enough,) p 1026 3939 a(and) 802 4130 y(\() p Fl(g) p Fk 887 4145 a(") p Fl 923 4130 a(;) p 967 4130 a(f) p Fn 1026 4130 a(\)) p Fk 1064 4146 a(L) p Fe 1112 4127 a(2) p Fn 1178 4130 a(=) p Fl 1282 4130 a(") p Ff 1328 4089 a(\000) p Fj(\(1+) p Fk(\013) p Fj(\)) p Fn 1577 4130 a(\(\() p Fl(L) p Fk 1719 4145 a(") p Fg 1778 4130 a(\000) p Fl 1878 4130 a(i) p Fn(\)) p Ff 1949 4089 a(\000) p Fj(1) p Fl 2043 4130 a(J) p Fk 2097 4145 a(") p Fl 2134 4130 a(b) p Fj 2175 4089 a(1) p Fk(=) p Fj(2) p Fl 2285 4130 a(\021) p Fj 2333 4145 a(0) p Fl 2373 4130 a(;) p 2417 4130 a(\031) p Ff 2472 4145 a(\000) p Fl 2531 4130 a(f) p Fn 2590 4130 a(\)) p Fk 2628 4146 a(L) p Fe 2676 4127 a(2) p Fl 2714 4130 a(:) p Fn 0 4321 a(W) p 92 4321 a(e) p 168 4321 a(ha) m(v) m(e) 836 4441 y(\() p Fl(L) p Fk 940 4456 a(") p Fg 999 4441 a(\000) p Fl 1099 4441 a(i) p Fn(\)) p Ff 1170 4400 a(\000) p Fj(1) p Fl 1264 4441 a(J) p Fk 1318 4456 a(") p Fl 1355 4441 a(b) p Fj 1396 4400 a(1) p Fk(=) p Fj(2) p Fl 1506 4441 a(\021) p Fj 1554 4456 a(0) p Fn 1621 4441 a(=) p Fl 1725 4441 a(i) p Fk 1758 4400 a(\013=) p Fj(2) p Fl 1878 4441 a(\014) p Fj 1933 4456 a(0) p Fl 1973 4441 a(") p Fj 2019 4400 a(1+) p Fk(\013) p Fl 2158 4441 a(\034) p Fj 2200 4456 a(0) p Fn 2262 4441 a(+) p Fl 2360 4441 a(o) p Fj 2407 4456 a(2) p Fn 2446 4441 a(\() p Fl(") p Fj 2530 4400 a(1+) p Fk(\013) p Fn 2670 4441 a(\)) 0 4603 y(b) m(y) p 135 4603 a(Prop) s(osition) p 660 4603 a(7.1) p 818 4603 a(with) p Fl 1040 4603 a(\033) p Fn 1126 4603 a(=) p Fl 1230 4603 a(i) p Fj 1263 4567 a(1) p Fk(=) p Fj(2) p Fn 1373 4603 a(,) p 1433 4603 a(where) p Fl 1715 4603 a(\034) p Fj 1757 4618 a(0) p Fn 1824 4603 a(=) p Fl 1928 4603 a(H) p Fk 2009 4618 a(\013) p Fn 2058 4603 a(\() p Fl(i) p Fj 2129 4567 a(1) p Fk(=) p Fj(2) p Fl 2239 4603 a(r) p Fn 2286 4603 a(\).) p 2394 4603 a(Hence) p 2684 4603 a(it) p 2782 4603 a(follo) m(ws) p 3102 4603 a(that) 1152 4794 y(\() p Fl(g) p Fk 1237 4809 a(") p Fl 1273 4794 a(;) p 1317 4794 a(f) p Fn 1376 4794 a(\)) p Fk 1414 4810 a(L) p Fe 1462 4792 a(2) p Fg 1528 4794 a(!) p Fl 1655 4794 a(i) p Fk 1688 4753 a(\013=) p Fj(2) p Fl 1809 4794 a(\014) p Fj 1864 4809 a(0) p Fn 1903 4794 a(\() p Fl(\031) p Fj 1996 4809 a(+) p Fl 2055 4794 a(\034) p Fj 2097 4809 a(0) p Fl 2137 4794 a(;) p 2181 4794 a(f) p Fn 2240 4794 a(\)) p Fk 2278 4810 a(L) p Fe 2326 4792 a(2) p Fl 2364 4794 a(:) p Fn 0 4985 a(By) p 153 4985 a(\(2.2\),) p 413 4985 a(w) m(e) p 557 4985 a(can) p 736 4985 a(calculate) p Fl 571 5176 a(\031) p Fj 626 5191 a(+) p Fl 685 5176 a(\034) p Fj 727 5191 a(0) p Fn 794 5176 a(=) p Fg 898 5176 a(\000) p Fl(i) p Fj 1008 5134 a(3) p Fk(=) p Fj(2) p Fl 1119 5176 a(H) p Fk 1200 5191 a(\013) p Ff(\000) p Fj(1) p Fn 1339 5176 a(\() p Fl(i) p Fj 1410 5134 a(1) p Fk(=) p Fj(2) p Fl 1520 5176 a(r) p Fn 1567 5176 a(\)) p Fl(e) p Fk 1650 5134 a(i\022) p Fn 1741 5176 a(=) p Fg 1845 5176 a(\000) p Fl(i) p Fj 1955 5134 a(3) p Fk(=) p Fj(2) p Fl 2065 5176 a(e) p Fk 2110 5134 a(i) p Fj(\(1) p Ff(\000) p Fk(\013) p Fj(\)) p Fk(\031) p Fl 2372 5176 a(\034) p Fj 2414 5191 a(1) p Fn 2481 5176 a(=) p Fl 2585 5176 a(i) p Fj 2618 5134 a(3) p Fk(=) p Fj(2) p Ff(\000) p Fj(2) p Fk(\013) p Fl 2864 5176 a(\034) p Fj 2906 5191 a(1) p Fl 2946 5176 a(:) p Fn 0 5367 a(This) p 223 5367 a(sho) m(ws) p 503 5367 a(that) p Fl 714 5367 a(g) p Fk 761 5382 a(") p Fg 825 5367 a(!) p Fl 953 5367 a(g) p Fj 1000 5382 a(0) p Fn 1071 5367 a(w) m(eakly) p 1351 5367 a(,) p 1413 5367 a(and) p 1602 5367 a(the) p 1770 5367 a(pro) s(of) p 2025 5367 a(is) p 2123 5367 a(complete.) p Fc 2671 5367 a(2) p Fn 1723 5753 a(33) p 90 rotate dyy eop %%Page: 34 34 34 33 bop Fm 1509 407 a(References) p Fn 92 793 a([1]) p 244 793 a(R.) p 385 793 a(Adami) p 712 793 a(and) p 911 793 a(A.) p 1054 793 a(T) p 1116 793 a(eta,) p 1318 793 a(On) p 1490 793 a(the) p 1668 793 a(Aharono) m(v{Bohm) p 2427 793 a(Hamiltonian,) p Fd 3027 793 a(L) p 3083 793 a(ett.) p 3294 793 a(Math.) 244 913 y(Phys.) p Fm 536 913 a(43) p Fn 681 913 a(\(1998\)) p 985 913 a(43{53.) 92 1117 y([2]) p 244 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a(Aharono) m(v{Bohm{Coulom) m(b) p 3169 407 a(problem,) p Fd 244 527 a(A) n(nn.) p 488 527 a(Phys.) p Fm 781 527 a(251) p Fn 981 527 a(\(1996\)) p 1285 527 a(45{63.) 43 731 y([16]) p 244 731 a(A.) p 367 731 a(Jensen) p 674 731 a(and) p 854 731 a(G.) p 980 731 a(Nenciu,) p 1327 731 a(A) p 1423 731 a(uni\014ed) p 1733 731 a(approac) m(h) p 2144 731 a(to) p 2253 731 a(resolv) m(en) m(t) p 2653 731 a(expansions) p 3135 731 a(at) p 3245 731 a(thresh-) 244 851 y(olds,) p Fd 472 851 a(R) p 538 851 a(ev.) p 693 851 a(Math.) p 977 851 a(Phys.) p Fm 1269 851 a(13) p Fn 1414 851 a(\(2001\)) p 1717 851 a(717{754.) 43 1054 y([17]) p 244 1054 a(D.) p 388 1054 a(K.) p 534 1054 a(P) m(ark) p 779 1054 a(and) p 980 1054 a(J.) p 1100 1054 a(G.) p 1246 1054 a(Oh,) p 1449 1054 a(Self{adjoin) m(t) p 1994 1054 a(extension) p 2435 1054 a(approac) m(h) p 2866 1054 a(to) p 2996 1054 a(the) p 3174 1054 a(spin{1/2) 244 1175 y(Aharono) m(v{Bohm-Coulom) m(b) p 1408 1175 a(problem,) p Fd 1814 1175 a(Phys.) p 2082 1175 a(R) p 2148 1175 a(ev.) p 2302 1175 a(D) p Fm 2425 1175 a(50) p Fn 2569 1175 a(\(1994\)) p 2873 1175 a(7715{7720.) 43 1378 y([18]) p 244 1378 a(U.) p 376 1378 a(P) m(erco) s(co) p 739 1378 a(and) p 928 1378 a(V.) p 1059 1378 a(M.) p 1207 1378 a(Villalba,) p 1600 1378 a(Aharono) m(v{Bohm) p 2348 1378 a(e\013ect) p 2604 1378 a(for) p 2752 1378 a(a) p 2832 1378 a(relativistic) p 3312 1378 a(Dirac) 244 1499 y(electron,) p Fd 639 1499 a(Phys.) p 907 1499 a(L) p 963 1499 a(ett.) p 1138 1499 a(A) p Fm 1259 1499 a(140) p Fn 1460 1499 a(\(1989\)) p 1763 1499 a(105{107.) 43 1702 y([19]) p 244 1702 a(M.) p 406 1702 a(Reed) p 665 1702 a(and) p 868 1702 a(B.) p 1010 1702 a(Simon,) p Fd 1352 1702 a(Metho) p 1611 1702 a(ds) p 1748 1702 a(of) p 1875 1702 a(Mo) p 2007 1702 a(dern) p 2245 1702 a(Mathematic) p 2741 1702 a(al) p 2862 1702 a(Physics) p Fn(,) p 3256 1702 a(V) p 3321 1702 a(ol) p 3443 1702 a(I) s(I,) p Fd 244 1822 a(F) p 301 1822 a(ourier) p 594 1822 a(A) n(nalysis,) p 1015 1822 a(Self{A) p 1287 1822 a(djointness) p Fn(,) p 1819 1822 a(Academic) p 2266 1822 a(Press) p 2523 1822 a(\(1975\).) 43 2026 y([20]) p 244 2026 a(H.) p 387 2026 a(T) p 449 2026 a(am) m(ura,) p 790 2026 a(Norm) p 1074 2026 a(resolv) m(en) m(t) p 1494 2026 a(con) m(v) m(ergence) p 2043 2026 a(to) p 2173 2026 a(magnetic) p 2600 2026 a(Sc) m(hr\177) p 2786 2026 a(odinger) p 3144 2026 a(op) s(erators) 244 2146 y(with) p 466 2146 a(p) s(oin) m(t) p 721 2146 a(in) m(teractions,) p Fd 1277 2146 a(R) p 1343 2146 a(ev.) p 1497 2146 a(Math.) p 1781 2146 a(Phys.) p Fm 2074 2146 a(13) p Fn 2219 2146 a(\(2001\)) p 2522 2146 a(465{512.) 43 2350 y([21]) p 244 2350 a(Y.) p 366 2350 a(A.) p 488 2350 a(Sitenk) m(o,) p 854 2350 a(Self{adjoin) m(tness) p 1552 2350 a(of) p 1652 2350 a(the) p 1810 2350 a(t) m(w) m(o{dimensional) p 2537 2350 a(massless) p 2913 2350 a(Dirac) p 3167 2350 a(Hamilto-) 244 2470 y(nian) p 456 2470 a(and) p 640 2470 a(v) p 686 2470 a(acuum) p 995 2470 a(p) s(olarization) p 1529 2470 a(e\013ects) p 1820 2470 a(in) p 1929 2470 a(the) p 2092 2470 a(bac) m(kground) p 2612 2470 a(of) p 2718 2470 a(a) p 2795 2470 a(singular) p 3159 2470 a(magnetic) 244 2590 y(v) m(ortex,) p Fd 572 2590 a(A) n(nn.) p 816 2590 a(Phys.) p Fm 1109 2590 a(282) p Fn 1309 2590 a(\(2000\)) p 1613 2590 a(167{217.) 43 2794 y([22]) p 244 2794 a(H.) p 373 2794 a(F) p 429 2794 a(alomir) p 728 2794 a(and) p 914 2794 a(P) p 1009 2794 a(A) p 1111 2794 a(G) p 1216 2794 a(Pisani,) p 1534 2794 a(Hamiltonian) p 2091 2794 a(self{adjoin) m(t) p 2606 2794 a(extensions) p 3072 2794 a(for) p 3217 2794 a(\(2) p 3318 2794 a(+) p 3408 2794 a(1\){) 244 2914 y(dimensional) p 781 2914 a(Dirac) p 1045 2914 a(particles,) p Fd 1463 2914 a(J.) p 1579 2914 a(Phys.) p 1847 2914 a(A:) p 1984 2914 a(Math.) p 2268 2914 a(Gen.) p Fm 2533 2914 a(34) p Fn 2677 2914 a(\(2001\)) p 2981 2914 a(4143{4154.) 1723 5753 y(35) p 90 rotate dyy eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0304280210435--