Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
Autor(a) principal: | |
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Data de Publicação: | 2022 |
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/10773/35075 |
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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7160 |
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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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1799137714926256128 |