Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators

We consider a family of matrix-valued orthogonal polynomials of size 2 × 2, which are common eigenfunctions of a differential operator of hypergeometric type, in connection with the problem of time-and-band limiting. The problem in question is as follows: given a global operator, defined by an integ...

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Detalles Bibliográficos
Autores: Castro Smirnova, Mirta María, Foulquié Moreno, Ana, Fradi, A.
Tipo de recurso: capítulo de libro
Estado:Versión aceptada para publicación
Fecha de publicación:2024
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/167311
Acceso en línea:https://hdl.handle.net/11441/167311
https://doi.org/10.1090/conm/807/16164
Access Level:acceso abierto
Palabra clave:Time-band limiting
Matrix valued orthogonal polynomials
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spelling Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operatorsCastro Smirnova, Mirta MaríaFoulquié Moreno, AnaFradi, A.Time-band limitingMatrix valued orthogonal polynomialsWe consider a family of matrix-valued orthogonal polynomials of size 2 × 2, which are common eigenfunctions of a differential operator of hypergeometric type, in connection with the problem of time-and-band limiting. The problem in question is as follows: given a global operator, defined by an integral kernel or a full matrix, one looks for a local operator given by a second order differential operator or a block tridiagonal matrix respectively, commuting with the global one. We apply the techniques for the construction of the commuting local operator introduced in a previous work by A. Gr¨unbaum, I. Pacharoni and I. Zurrian in the matrix-valued setting, where the role of bispectrality is crucial. This constitutes an illustrative example of an extension to a situation involving matrix orthogonality, of a scalar result that originates in a series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the sixties.American Mathematical SocietyMatemática Aplicada IIFQM262: Teoría de la AproximaciónMinisterio de Ciencia e Innovación (MICIN). EspañaJunta de Andalucía2024info:eu-repo/semantics/bookPartinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/167311https://doi.org/10.1090/conm/807/16164reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésRecent Progress in Special FunctionsRecent Progress in Special Functions: https://doi.org/10.1090/conm/807PID2021-124332NB-C21FQM-262https://www.ams.org/books/conm/807/Rhode Island, USAinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1673112026-06-17T12:51:07Z
dc.title.none.fl_str_mv Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
title Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
spellingShingle Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
Castro Smirnova, Mirta María
Time-band limiting
Matrix valued orthogonal polynomials
title_short Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
title_full Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
title_fullStr Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
title_full_unstemmed Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
title_sort Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
dc.creator.none.fl_str_mv Castro Smirnova, Mirta María
Foulquié Moreno, Ana
Fradi, A.
author Castro Smirnova, Mirta María
author_facet Castro Smirnova, Mirta María
Foulquié Moreno, Ana
Fradi, A.
author_role author
author2 Foulquié Moreno, Ana
Fradi, A.
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
FQM262: Teoría de la Aproximación
Ministerio de Ciencia e Innovación (MICIN). España
Junta de Andalucía
dc.subject.none.fl_str_mv Time-band limiting
Matrix valued orthogonal polynomials
topic Time-band limiting
Matrix valued orthogonal polynomials
description We consider a family of matrix-valued orthogonal polynomials of size 2 × 2, which are common eigenfunctions of a differential operator of hypergeometric type, in connection with the problem of time-and-band limiting. The problem in question is as follows: given a global operator, defined by an integral kernel or a full matrix, one looks for a local operator given by a second order differential operator or a block tridiagonal matrix respectively, commuting with the global one. We apply the techniques for the construction of the commuting local operator introduced in a previous work by A. Gr¨unbaum, I. Pacharoni and I. Zurrian in the matrix-valued setting, where the role of bispectrality is crucial. This constitutes an illustrative example of an extension to a situation involving matrix orthogonality, of a scalar result that originates in a series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the sixties.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
info:eu-repo/semantics/acceptedVersion
format bookPart
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/167311
https://doi.org/10.1090/conm/807/16164
url https://hdl.handle.net/11441/167311
https://doi.org/10.1090/conm/807/16164
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Recent Progress in Special Functions
Recent Progress in Special Functions: https://doi.org/10.1090/conm/807
PID2021-124332NB-C21
FQM-262
https://www.ams.org/books/conm/807/
Rhode Island, USA
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 15,812429

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