Eigenvalues with respect to a weight for general boundary value problems on networks

In this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the boundary with a Neumann condition is always considered. We first characterize when the energy is positive semi-definite on the space of functions satisfying the null boundary co...

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Detalles Bibliográficos
Autores: Carmona Mejías, Ángeles|||0000-0001-7713-1066, Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373, Mitjana Riera, Margarida|||0000-0002-6563-5512
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/336840
Acceso en línea:https://hdl.handle.net/2117/336840
https://dx.doi.org/10.1016/j.laa.2020.03.046
Access Level:acceso abierto
Palabra clave:Schrödinger operators
Eigenvalues
Green operators
Positive semi-definiteness
Discrete trace
Mercer theorem
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::34 Ordinary differential equations::34B Boundary value problems
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::16 Associative rings and algebras
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
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repository_id_str
spelling Eigenvalues with respect to a weight for general boundary value problems on networksCarmona Mejías, Ángeles|||0000-0001-7713-1066Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373Mitjana Riera, Margarida|||0000-0002-6563-5512Schrödinger operatorsEigenvaluesGreen operatorsPositive semi-definitenessDiscrete traceMercer theoremClassificació AMS::39 Difference and functional equations::39A Difference equationsClassificació AMS::34 Ordinary differential equations::34B Boundary value problemsClassificació AMS::15 Linear and multilinear algebramatrix theoryClassificació AMS::16 Associative rings and algebrasClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadísticaIn this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the boundary with a Neumann condition is always considered. We first characterize when the energy is positive semi-definite on the space of functions satisfying the null boundary conditions. To do this, the fundamental tools are the Doob transform and the discrete version of the trace function. Then, we raise eigenvalue problems with respect to a weight for general boundary value problems and we prove the discrete version of the Mercer Theorem. Finally, we apply the obtained results to a Dirichlet-Robin boundary value problem on a star-like network.Peer ReviewedElsevier20212021-04-0120212021-02-03journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/336840https://dx.doi.org/10.1016/j.laa.2020.03.046reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3368402026-05-27T15:37:01Z
dc.title.none.fl_str_mv Eigenvalues with respect to a weight for general boundary value problems on networks
title Eigenvalues with respect to a weight for general boundary value problems on networks
spellingShingle Eigenvalues with respect to a weight for general boundary value problems on networks
Carmona Mejías, Ángeles|||0000-0001-7713-1066
Schrödinger operators
Eigenvalues
Green operators
Positive semi-definiteness
Discrete trace
Mercer theorem
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::34 Ordinary differential equations::34B Boundary value problems
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::16 Associative rings and algebras
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Eigenvalues with respect to a weight for general boundary value problems on networks
title_full Eigenvalues with respect to a weight for general boundary value problems on networks
title_fullStr Eigenvalues with respect to a weight for general boundary value problems on networks
title_full_unstemmed Eigenvalues with respect to a weight for general boundary value problems on networks
title_sort Eigenvalues with respect to a weight for general boundary value problems on networks
dc.creator.none.fl_str_mv Carmona Mejías, Ángeles|||0000-0001-7713-1066
Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Mitjana Riera, Margarida|||0000-0002-6563-5512
author Carmona Mejías, Ángeles|||0000-0001-7713-1066
author_facet Carmona Mejías, Ángeles|||0000-0001-7713-1066
Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Mitjana Riera, Margarida|||0000-0002-6563-5512
author_role author
author2 Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Mitjana Riera, Margarida|||0000-0002-6563-5512
author2_role author
author
dc.subject.none.fl_str_mv Schrödinger operators
Eigenvalues
Green operators
Positive semi-definiteness
Discrete trace
Mercer theorem
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::34 Ordinary differential equations::34B Boundary value problems
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::16 Associative rings and algebras
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Schrödinger operators
Eigenvalues
Green operators
Positive semi-definiteness
Discrete trace
Mercer theorem
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::34 Ordinary differential equations::34B Boundary value problems
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::16 Associative rings and algebras
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
description In this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the boundary with a Neumann condition is always considered. We first characterize when the energy is positive semi-definite on the space of functions satisfying the null boundary conditions. To do this, the fundamental tools are the Doob transform and the discrete version of the trace function. Then, we raise eigenvalue problems with respect to a weight for general boundary value problems and we prove the discrete version of the Mercer Theorem. Finally, we apply the obtained results to a Dirichlet-Robin boundary value problem on a star-like network.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-04-01
2021
2021-02-03
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/336840
https://dx.doi.org/10.1016/j.laa.2020.03.046
url https://hdl.handle.net/2117/336840
https://dx.doi.org/10.1016/j.laa.2020.03.046
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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