Sharp weyl law for signed counting function of positive interior transmission eigenvalues

Detalhes bibliográficos
Autor(a) principal: Lakshtanov, E.
Data de Publicação: 2015
Outros Autores: Vainberg, B.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/15202
Resumo: We consider the interior transmission eigenvalue (ITE) problem that arises when scattering by inhomogeneous media is studied. The ITE problem is not self-adjoint. We show that positive ITEs are observable together with plus or minus signs that are defined by the direction of motion of the corresponding eigenvalues of the scattering matrix (as they approach $z=1$). We obtain a Weyl-type formula for the counting function of positive ITEs, which are taken together with the ascribed signs. The results are applicable to the case when the medium contains an unpenetrable obstacle.
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spelling Sharp weyl law for signed counting function of positive interior transmission eigenvaluesInterior transmission eigenvaluesAnisotropic mediaShapiro-Lopatinski conditionWe consider the interior transmission eigenvalue (ITE) problem that arises when scattering by inhomogeneous media is studied. The ITE problem is not self-adjoint. We show that positive ITEs are observable together with plus or minus signs that are defined by the direction of motion of the corresponding eigenvalues of the scattering matrix (as they approach $z=1$). We obtain a Weyl-type formula for the counting function of positive ITEs, which are taken together with the ascribed signs. The results are applicable to the case when the medium contains an unpenetrable obstacle.Society for Industrial and Applied Mathematics2016-02-19T12:36:51Z2015-01-01T00:00:00Z2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15202eng0036-141010.1137/140966277Lakshtanov, E.Vainberg, B.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:28:02Zoai:ria.ua.pt:10773/15202Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:36.473743Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Sharp weyl law for signed counting function of positive interior transmission eigenvalues
title Sharp weyl law for signed counting function of positive interior transmission eigenvalues
spellingShingle Sharp weyl law for signed counting function of positive interior transmission eigenvalues
Lakshtanov, E.
Interior transmission eigenvalues
Anisotropic media
Shapiro-Lopatinski condition
title_short Sharp weyl law for signed counting function of positive interior transmission eigenvalues
title_full Sharp weyl law for signed counting function of positive interior transmission eigenvalues
title_fullStr Sharp weyl law for signed counting function of positive interior transmission eigenvalues
title_full_unstemmed Sharp weyl law for signed counting function of positive interior transmission eigenvalues
title_sort Sharp weyl law for signed counting function of positive interior transmission eigenvalues
author Lakshtanov, E.
author_facet Lakshtanov, E.
Vainberg, B.
author_role author
author2 Vainberg, B.
author2_role author
dc.contributor.author.fl_str_mv Lakshtanov, E.
Vainberg, B.
dc.subject.por.fl_str_mv Interior transmission eigenvalues
Anisotropic media
Shapiro-Lopatinski condition
topic Interior transmission eigenvalues
Anisotropic media
Shapiro-Lopatinski condition
description We consider the interior transmission eigenvalue (ITE) problem that arises when scattering by inhomogeneous media is studied. The ITE problem is not self-adjoint. We show that positive ITEs are observable together with plus or minus signs that are defined by the direction of motion of the corresponding eigenvalues of the scattering matrix (as they approach $z=1$). We obtain a Weyl-type formula for the counting function of positive ITEs, which are taken together with the ascribed signs. The results are applicable to the case when the medium contains an unpenetrable obstacle.
publishDate 2015
dc.date.none.fl_str_mv 2015-01-01T00:00:00Z
2015
2016-02-19T12:36:51Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/15202
url http://hdl.handle.net/10773/15202
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0036-1410
10.1137/140966277
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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