Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10316/43839 https://doi.org/10.1016/j.jmaa.2015.07.051 |
Resumo: | In this paper we introduce the Δ-Volterra lattice which is interpreted in terms of symmetric orthogonal polynomials. It is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like (1+x^2)^1−t μ(x) where μ is a given positive Borel measure. Moreover, the Δ-Volterra lattice is related to the Δ-Toda lattice from Miura or Bäcklund transformations. The main ingredients are orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ and the characterization of the point spectrum of a Jacobian operator that satisfies a Δ-Volterra equation (Lax type theorem). We also provide an explicit example of solutions of Δ-Volterra and Δ-Toda lattices, and connect this example with the results presented in the paper. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretationIn this paper we introduce the Δ-Volterra lattice which is interpreted in terms of symmetric orthogonal polynomials. It is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like (1+x^2)^1−t μ(x) where μ is a given positive Borel measure. Moreover, the Δ-Volterra lattice is related to the Δ-Toda lattice from Miura or Bäcklund transformations. The main ingredients are orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ and the characterization of the point spectrum of a Jacobian operator that satisfies a Δ-Volterra equation (Lax type theorem). We also provide an explicit example of solutions of Δ-Volterra and Δ-Toda lattices, and connect this example with the results presented in the paper.Elsevier2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43839http://hdl.handle.net/10316/43839https://doi.org/10.1016/j.jmaa.2015.07.051https://doi.org/10.1016/j.jmaa.2015.07.051enghttps://doi.org/10.1016/j.jmaa.2015.07.051Area, I.Branquinho, AmílcarFoulquié Moreno, A.Godoy, E.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:RCAAP2021-06-29T10:03:02Zoai:estudogeral.uc.pt:10316/43839Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:29.285590Repositório 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 |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
title |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
spellingShingle |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation Area, I. |
title_short |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
title_full |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
title_fullStr |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
title_full_unstemmed |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
title_sort |
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation |
author |
Area, I. |
author_facet |
Area, I. Branquinho, Amílcar Foulquié Moreno, A. Godoy, E. |
author_role |
author |
author2 |
Branquinho, Amílcar Foulquié Moreno, A. Godoy, E. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Area, I. Branquinho, Amílcar Foulquié Moreno, A. Godoy, E. |
description |
In this paper we introduce the Δ-Volterra lattice which is interpreted in terms of symmetric orthogonal polynomials. It is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like (1+x^2)^1−t μ(x) where μ is a given positive Borel measure. Moreover, the Δ-Volterra lattice is related to the Δ-Toda lattice from Miura or Bäcklund transformations. The main ingredients are orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ and the characterization of the point spectrum of a Jacobian operator that satisfies a Δ-Volterra equation (Lax type theorem). We also provide an explicit example of solutions of Δ-Volterra and Δ-Toda lattices, and connect this example with the results presented in the paper. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 |
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/10316/43839 http://hdl.handle.net/10316/43839 https://doi.org/10.1016/j.jmaa.2015.07.051 https://doi.org/10.1016/j.jmaa.2015.07.051 |
url |
http://hdl.handle.net/10316/43839 https://doi.org/10.1016/j.jmaa.2015.07.051 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1016/j.jmaa.2015.07.051 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1799133821597122560 |