Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
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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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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1799137611317510144 |