Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II

Autores
Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a previous paper we have introduced matrixvalued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2) × SU(2). In particular the matrix-size of the polynomials is arbitrarily large. In this paper, the matrix-valued orthogonal polynomials and the corresponding weight function are studied. In particular, we calculate the LDU-decomposition of the weight where the matrix entries of L are given in terms of Gegenbauer polynomials. The monic matrix-valued orthogonal polynomials P_n are expressed in terms of Tirao's matrix-valued hypergeometric function using the matrix-valued differential operators of first and second order of which the P_n's are eigenfunctions. From this result we obtain an explicit formula for coefficients in the three-term recurrence relation satisfied by the polynomials Pn. These differential operators are also crucial in expressing the matrix entries of P_nL as a product of a Racah and a Gegenbauer polynomial. We also present a group-theoretic derivation of the matrix-valued differential operators by considering the Casimir operators corresponding to SU(2) × SU(2).
Fil: Koelink, Erik. Radboud Universiteit; Países Bajos
Fil: Van Pruijssen, Maarten. Radboud Universiteit; Países Bajos
Fil: Román, Pablo Manuel. Universidad Nacional de Cordoba. Facultad de Matematica, Astronomia y Fisica. Seccion Matematica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Spherical Functions
Matrix Valued Orthogonal Polynomials
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/12273

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network_name_str CONICET Digital (CONICET)
spelling Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), IIKoelink, ErikVan Pruijssen, MaartenRomán, Pablo ManuelSpherical FunctionsMatrix Valued Orthogonal Polynomialshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In a previous paper we have introduced matrixvalued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2) × SU(2). In particular the matrix-size of the polynomials is arbitrarily large. In this paper, the matrix-valued orthogonal polynomials and the corresponding weight function are studied. In particular, we calculate the LDU-decomposition of the weight where the matrix entries of L are given in terms of Gegenbauer polynomials. The monic matrix-valued orthogonal polynomials P_n are expressed in terms of Tirao's matrix-valued hypergeometric function using the matrix-valued differential operators of first and second order of which the P_n's are eigenfunctions. From this result we obtain an explicit formula for coefficients in the three-term recurrence relation satisfied by the polynomials Pn. These differential operators are also crucial in expressing the matrix entries of P_nL as a product of a Racah and a Gegenbauer polynomial. We also present a group-theoretic derivation of the matrix-valued differential operators by considering the Casimir operators corresponding to SU(2) × SU(2).Fil: Koelink, Erik. Radboud Universiteit; Países BajosFil: Van Pruijssen, Maarten. Radboud Universiteit; Países BajosFil: Román, Pablo Manuel. Universidad Nacional de Cordoba. Facultad de Matematica, Astronomia y Fisica. Seccion Matematica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaKyoto Univ2013-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/12273Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 49; 2; 4-2013; 271-3120034-5318enginfo:eu-repo/semantics/altIdentifier/doi/10.4171/PRIMS/106info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=49&iss=2&rank=3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:04:48Zoai:ri.conicet.gov.ar:11336/12273instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:04:48.594CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
title Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
spellingShingle Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
Koelink, Erik
Spherical Functions
Matrix Valued Orthogonal Polynomials
title_short Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
title_full Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
title_fullStr Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
title_full_unstemmed Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
title_sort Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II
dc.creator.none.fl_str_mv Koelink, Erik
Van Pruijssen, Maarten
Román, Pablo Manuel
author Koelink, Erik
author_facet Koelink, Erik
Van Pruijssen, Maarten
Román, Pablo Manuel
author_role author
author2 Van Pruijssen, Maarten
Román, Pablo Manuel
author2_role author
author
dc.subject.none.fl_str_mv Spherical Functions
Matrix Valued Orthogonal Polynomials
topic Spherical Functions
Matrix Valued Orthogonal Polynomials
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In a previous paper we have introduced matrixvalued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2) × SU(2). In particular the matrix-size of the polynomials is arbitrarily large. In this paper, the matrix-valued orthogonal polynomials and the corresponding weight function are studied. In particular, we calculate the LDU-decomposition of the weight where the matrix entries of L are given in terms of Gegenbauer polynomials. The monic matrix-valued orthogonal polynomials P_n are expressed in terms of Tirao's matrix-valued hypergeometric function using the matrix-valued differential operators of first and second order of which the P_n's are eigenfunctions. From this result we obtain an explicit formula for coefficients in the three-term recurrence relation satisfied by the polynomials Pn. These differential operators are also crucial in expressing the matrix entries of P_nL as a product of a Racah and a Gegenbauer polynomial. We also present a group-theoretic derivation of the matrix-valued differential operators by considering the Casimir operators corresponding to SU(2) × SU(2).
Fil: Koelink, Erik. Radboud Universiteit; Países Bajos
Fil: Van Pruijssen, Maarten. Radboud Universiteit; Países Bajos
Fil: Román, Pablo Manuel. Universidad Nacional de Cordoba. Facultad de Matematica, Astronomia y Fisica. Seccion Matematica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In a previous paper we have introduced matrixvalued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2) × SU(2). In particular the matrix-size of the polynomials is arbitrarily large. In this paper, the matrix-valued orthogonal polynomials and the corresponding weight function are studied. In particular, we calculate the LDU-decomposition of the weight where the matrix entries of L are given in terms of Gegenbauer polynomials. The monic matrix-valued orthogonal polynomials P_n are expressed in terms of Tirao's matrix-valued hypergeometric function using the matrix-valued differential operators of first and second order of which the P_n's are eigenfunctions. From this result we obtain an explicit formula for coefficients in the three-term recurrence relation satisfied by the polynomials Pn. These differential operators are also crucial in expressing the matrix entries of P_nL as a product of a Racah and a Gegenbauer polynomial. We also present a group-theoretic derivation of the matrix-valued differential operators by considering the Casimir operators corresponding to SU(2) × SU(2).
publishDate 2013
dc.date.none.fl_str_mv 2013-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/12273
Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 49; 2; 4-2013; 271-312
0034-5318
url http://hdl.handle.net/11336/12273
identifier_str_mv Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 49; 2; 4-2013; 271-312
0034-5318
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/PRIMS/106
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=49&iss=2&rank=3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Kyoto Univ
publisher.none.fl_str_mv Kyoto Univ
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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