Orthogonal polynomial interpretation of Δ-Toda equations

Detalhes bibliográficos
Autor(a) principal: Area, Iván
Data de Publicação: 2015
Outros Autores: Branquinho, Amílcar, Foulquié Moreno, Ana, Godoy, Eduardo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
DOI: 10.1088/1751-8113/48/40/405206
Texto Completo: http://hdl.handle.net/10316/43945
https://doi.org/10.1088/1751-8113/48/40/405206
Resumo: In this paper a discretization of Toda equations is analyzed. The correspondence between these Δ-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. It is shown that the spectral measure of these operators evolve in t like ${(1+x)}^{1-t}\;{\rm{d}}\mu (x)$ where ${\rm{d}}\mu$ is a given positive Borel measure. The Lax pair for the Δ-Toda equations is derived and characterized in terms of linear functionals, where orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ appear in a natural way. In order to illustrate the results of the paper we work out two examples of Δ-Toda equations related with Jacobi and Laguerre orthogonal polynomials.
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spelling Orthogonal polynomial interpretation of Δ-Toda equationsIn this paper a discretization of Toda equations is analyzed. The correspondence between these Δ-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. It is shown that the spectral measure of these operators evolve in t like ${(1+x)}^{1-t}\;{\rm{d}}\mu (x)$ where ${\rm{d}}\mu$ is a given positive Borel measure. The Lax pair for the Δ-Toda equations is derived and characterized in terms of linear functionals, where orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ appear in a natural way. In order to illustrate the results of the paper we work out two examples of Δ-Toda equations related with Jacobi and Laguerre orthogonal polynomials.IOP Publishing2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43945http://hdl.handle.net/10316/43945https://doi.org/10.1088/1751-8113/48/40/405206https://doi.org/10.1088/1751-8113/48/40/405206enghttps://doi.org/10.1088/1751-8113/48/40/405206Area, IvánBranquinho, AmílcarFoulquié Moreno, AnaGodoy, Eduardoinfo: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:RCAAP2021-07-22T10:39:25Zoai:estudogeral.uc.pt:10316/43945Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:30.341502Repositório 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 Orthogonal polynomial interpretation of Δ-Toda equations
title Orthogonal polynomial interpretation of Δ-Toda equations
spellingShingle Orthogonal polynomial interpretation of Δ-Toda equations
Orthogonal polynomial interpretation of Δ-Toda equations
Area, Iván
Area, Iván
title_short Orthogonal polynomial interpretation of Δ-Toda equations
title_full Orthogonal polynomial interpretation of Δ-Toda equations
title_fullStr Orthogonal polynomial interpretation of Δ-Toda equations
Orthogonal polynomial interpretation of Δ-Toda equations
title_full_unstemmed Orthogonal polynomial interpretation of Δ-Toda equations
Orthogonal polynomial interpretation of Δ-Toda equations
title_sort Orthogonal polynomial interpretation of Δ-Toda equations
author Area, Iván
author_facet Area, Iván
Area, Iván
Branquinho, Amílcar
Foulquié Moreno, Ana
Godoy, Eduardo
Branquinho, Amílcar
Foulquié Moreno, Ana
Godoy, Eduardo
author_role author
author2 Branquinho, Amílcar
Foulquié Moreno, Ana
Godoy, Eduardo
author2_role author
author
author
dc.contributor.author.fl_str_mv Area, Iván
Branquinho, Amílcar
Foulquié Moreno, Ana
Godoy, Eduardo
description In this paper a discretization of Toda equations is analyzed. The correspondence between these Δ-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. It is shown that the spectral measure of these operators evolve in t like ${(1+x)}^{1-t}\;{\rm{d}}\mu (x)$ where ${\rm{d}}\mu$ is a given positive Borel measure. The Lax pair for the Δ-Toda equations is derived and characterized in terms of linear functionals, where orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ appear in a natural way. In order to illustrate the results of the paper we work out two examples of Δ-Toda equations related with Jacobi and Laguerre orthogonal polynomials.
publishDate 2015
dc.date.none.fl_str_mv 2015
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/10316/43945
http://hdl.handle.net/10316/43945
https://doi.org/10.1088/1751-8113/48/40/405206
https://doi.org/10.1088/1751-8113/48/40/405206
url http://hdl.handle.net/10316/43945
https://doi.org/10.1088/1751-8113/48/40/405206
dc.language.iso.fl_str_mv eng
language eng
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dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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
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dc.identifier.doi.none.fl_str_mv 10.1088/1751-8113/48/40/405206