Bispectrality for matrix Laguerre-Sobolev polynomials

In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transforma...

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Authors: Marcellán Español, Francisco, Zurrián, Ignacio Nahuel
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2024
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/160562
Online Access:https://hdl.handle.net/11441/160562
https://doi.org/10.1016/j.laa.2023.09.017
Access Level:Open access
Keyword:Standard orthogonal polynomials
Sobolev type orthogonal polynomials
Darboux transformations
Matrix orthogonal polynomials
Bispectrality
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spelling Bispectrality for matrix Laguerre-Sobolev polynomialsMarcellán Español, FranciscoZurrián, Ignacio NahuelStandard orthogonal polynomialsSobolev type orthogonal polynomialsDarboux transformationsMatrix orthogonal polynomialsBispectralityIn this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out.ElsevierMatemática Aplicada IIEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Ciencia e Innovación (MICIN). EspañaAgencia Estatal de Investigación. EspañaConsejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Argentina2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/160562https://doi.org/10.1016/j.laa.2023.09.017reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésLinear Algebra and its Applications, 697, 131-145.PID2021-122154NBI00EPUC3M23VI PPIT-UShttps://www.sciencedirect.com/science/article/pii/S0024379523003555info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1605622026-06-17T12:51:07Z
dc.title.none.fl_str_mv Bispectrality for matrix Laguerre-Sobolev polynomials
title Bispectrality for matrix Laguerre-Sobolev polynomials
spellingShingle Bispectrality for matrix Laguerre-Sobolev polynomials
Marcellán Español, Francisco
Standard orthogonal polynomials
Sobolev type orthogonal polynomials
Darboux transformations
Matrix orthogonal polynomials
Bispectrality
title_short Bispectrality for matrix Laguerre-Sobolev polynomials
title_full Bispectrality for matrix Laguerre-Sobolev polynomials
title_fullStr Bispectrality for matrix Laguerre-Sobolev polynomials
title_full_unstemmed Bispectrality for matrix Laguerre-Sobolev polynomials
title_sort Bispectrality for matrix Laguerre-Sobolev polynomials
dc.creator.none.fl_str_mv Marcellán Español, Francisco
Zurrián, Ignacio Nahuel
author Marcellán Español, Francisco
author_facet Marcellán Español, Francisco
Zurrián, Ignacio Nahuel
author_role author
author2 Zurrián, Ignacio Nahuel
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada II
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
Ministerio de Ciencia e Innovación (MICIN). España
Agencia Estatal de Investigación. España
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Argentina
dc.subject.none.fl_str_mv Standard orthogonal polynomials
Sobolev type orthogonal polynomials
Darboux transformations
Matrix orthogonal polynomials
Bispectrality
topic Standard orthogonal polynomials
Sobolev type orthogonal polynomials
Darboux transformations
Matrix orthogonal polynomials
Bispectrality
description In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/160562
https://doi.org/10.1016/j.laa.2023.09.017
url https://hdl.handle.net/11441/160562
https://doi.org/10.1016/j.laa.2023.09.017
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Linear Algebra and its Applications, 697, 131-145.
PID2021-122154NBI00
EPUC3M23
VI PPIT-US
https://www.sciencedirect.com/science/article/pii/S0024379523003555
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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