Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV

Detalhes bibliográficos
Autor(a) principal: Branquinho, Amílcar
Data de Publicação: 2022
Outros Autores: Moreno, Ana Foulquié, Fradi, Assil, Mañas, Manuel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/35075
Resumo: In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights—which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann–Hilbert problem, are derived. An explicit and general example is presented to illustrate the theoretical results of the work. The non-Abelian extensions of a family of discrete Painlevé IV equations are discussed.
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spelling Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IVRiemann–Hilbert problemsMatrix Pearson equationsMatrix biorthogonal polynomialsDiscrete integrable systemsNon-Abelian discrete Painlevé IV equationIn this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights—which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann–Hilbert problem, are derived. An explicit and general example is presented to illustrate the theoretical results of the work. The non-Abelian extensions of a family of discrete Painlevé IV equations are discussed.MDPI2022-11-02T15:54:49Z2022-04-07T00:00:00Z2022-04-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35075eng2227-739010.3390/math10081205Branquinho, AmílcarMoreno, Ana FoulquiéFradi, AssilMañas, Manuelinfo: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:RCAAP2024-02-22T12:07:04Zoai:ria.ua.pt:10773/35075Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:05:57.766117Repositório 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 Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
title Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
spellingShingle Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
Branquinho, Amílcar
Riemann–Hilbert problems
Matrix Pearson equations
Matrix biorthogonal polynomials
Discrete integrable systems
Non-Abelian discrete Painlevé IV equation
title_short Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
title_full Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
title_fullStr Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
title_full_unstemmed Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
title_sort Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
author Branquinho, Amílcar
author_facet Branquinho, Amílcar
Moreno, Ana Foulquié
Fradi, Assil
Mañas, Manuel
author_role author
author2 Moreno, Ana Foulquié
Fradi, Assil
Mañas, Manuel
author2_role author
author
author
dc.contributor.author.fl_str_mv Branquinho, Amílcar
Moreno, Ana Foulquié
Fradi, Assil
Mañas, Manuel
dc.subject.por.fl_str_mv Riemann–Hilbert problems
Matrix Pearson equations
Matrix biorthogonal polynomials
Discrete integrable systems
Non-Abelian discrete Painlevé IV equation
topic Riemann–Hilbert problems
Matrix Pearson equations
Matrix biorthogonal polynomials
Discrete integrable systems
Non-Abelian discrete Painlevé IV equation
description In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights—which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann–Hilbert problem, are derived. An explicit and general example is presented to illustrate the theoretical results of the work. The non-Abelian extensions of a family of discrete Painlevé IV equations are discussed.
publishDate 2022
dc.date.none.fl_str_mv 2022-11-02T15:54:49Z
2022-04-07T00:00:00Z
2022-04-07
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/10773/35075
url http://hdl.handle.net/10773/35075
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2227-7390
10.3390/math10081205
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 MDPI
publisher.none.fl_str_mv MDPI
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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