Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials

Detalhes bibliográficos
Autor(a) principal: Branquinho, A.
Data de Publicação: 2017
Outros Autores: Moreno, Ana Foulquié, Mendes, A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/21344
Resumo: In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, generalized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattice
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spelling Dynamics and interpretation of some integrable systems via matrix orthogonal polynomialsMatrix orthogonal polynomialsLinear functionalRecurrence relationOperator theoryMatrix Sylvester differential equationsIn this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, generalized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type latticeTaylor & Francis2018-01-05T15:49:07Z2017-01-01T00:00:00Z2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/21344eng1065-246910.1080/10652469.2016.1250082Branquinho, A.Moreno, Ana FoulquiéMendes, A.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:RCAAP2024-02-22T11:41:47Zoai:ria.ua.pt:10773/21344Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:55:45.835570Repositório 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 Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
title Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
spellingShingle Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
Branquinho, A.
Matrix orthogonal polynomials
Linear functional
Recurrence relation
Operator theory
Matrix Sylvester differential equations
title_short Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
title_full Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
title_fullStr Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
title_full_unstemmed Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
title_sort Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
author Branquinho, A.
author_facet Branquinho, A.
Moreno, Ana Foulquié
Mendes, A.
author_role author
author2 Moreno, Ana Foulquié
Mendes, A.
author2_role author
author
dc.contributor.author.fl_str_mv Branquinho, A.
Moreno, Ana Foulquié
Mendes, A.
dc.subject.por.fl_str_mv Matrix orthogonal polynomials
Linear functional
Recurrence relation
Operator theory
Matrix Sylvester differential equations
topic Matrix orthogonal polynomials
Linear functional
Recurrence relation
Operator theory
Matrix Sylvester differential equations
description In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, generalized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattice
publishDate 2017
dc.date.none.fl_str_mv 2017-01-01T00:00:00Z
2017
2018-01-05T15:49:07Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/21344
url http://hdl.handle.net/10773/21344
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1065-2469
10.1080/10652469.2016.1250082
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 Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
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