Orthogonal polynomial interpretation of Δ-Toda equations
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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 |
dc.relation.none.fl_str_mv |
https://doi.org/10.1088/1751-8113/48/40/405206 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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) 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 |
|
_version_ |
1822183477723791360 |
dc.identifier.doi.none.fl_str_mv |
10.1088/1751-8113/48/40/405206 |