{"title":"椭圆算子长程扰动的广义散射相位","authors":"Jean-Marc Bouclet","doi":"10.1016/S0764-4442(01)02144-9","DOIUrl":null,"url":null,"abstract":"<div><p>We show that limits on the real axis of arguments of regularized relative determinants for differential operators on <span><math><mtext>R</mtext><msup><mi></mi><mn>d</mn></msup></math></span>, exist in the weak sense. We call these limits generalized scattering phases. They extend, in the case of long range perturbations, the usual definition of scattering phase given by Birman–Krein theory. In Euclidean scattering, we give high energy expansions under a non-trapping assumption.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 845-850"},"PeriodicalIF":0.0000,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02144-9","citationCount":"1","resultStr":"{\"title\":\"Generalized scattering phase for long range perturbations of elliptic operators\",\"authors\":\"Jean-Marc Bouclet\",\"doi\":\"10.1016/S0764-4442(01)02144-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We show that limits on the real axis of arguments of regularized relative determinants for differential operators on <span><math><mtext>R</mtext><msup><mi></mi><mn>d</mn></msup></math></span>, exist in the weak sense. We call these limits generalized scattering phases. They extend, in the case of long range perturbations, the usual definition of scattering phase given by Birman–Krein theory. In Euclidean scattering, we give high energy expansions under a non-trapping assumption.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 9\",\"pages\":\"Pages 845-850\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02144-9\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021449\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021449","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalized scattering phase for long range perturbations of elliptic operators
We show that limits on the real axis of arguments of regularized relative determinants for differential operators on , exist in the weak sense. We call these limits generalized scattering phases. They extend, in the case of long range perturbations, the usual definition of scattering phase given by Birman–Krein theory. In Euclidean scattering, we give high energy expansions under a non-trapping assumption.
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