Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)

Autores
Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of spherical functions, we take these diagonals as a matrix-valued function, which are the full spherical functions. Their orthogonality is a consequence of the Schur orthogonality relations. From the full spherical functions, we obtain matrix-valued orthogonal polynomials of arbitrary size, and they satisfy a three-term recurrence relation which follows by considering tensor product decompositions. An explicit expression for the weight and the complete block-diagonalization of the matrix-valued orthogonal polynomials is obtained. From the explicit expression, we obtain right-hand-sided differential operators of first and second order for which the matrix-valued orthogonal polynomials are eigenfunctions. We study the low-dimensional cases explicitly, and for these cases additional results, such as the Rodrigues' formula and being eigenfunctions to first-order differential-difference and second-order differential operators, are obtained. © 2012 The Author(s).
Fil: Koelink, Erik. Radboud Universiteit, Nijmegen; Países Bajos
Fil: Van Pruijssen, Maarten. Radboud Universiteit, Nijmegen; Países Bajos
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Matrix valued spherical functions
Matrix valued orthogonal polynomials
Hypergeometric functions
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:11336/200296
Acceder
id CONICETDig_f050813b2b9c6bb578c56ad9bb5a0f26
oai_identifier_str oai:ri.conicet.gov.ar:11336/200296
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)Koelink, ErikVan Pruijssen, MaartenRomán, Pablo ManuelMatrix valued spherical functionsMatrix valued orthogonal polynomialsHypergeometric functionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of spherical functions, we take these diagonals as a matrix-valued function, which are the full spherical functions. Their orthogonality is a consequence of the Schur orthogonality relations. From the full spherical functions, we obtain matrix-valued orthogonal polynomials of arbitrary size, and they satisfy a three-term recurrence relation which follows by considering tensor product decompositions. An explicit expression for the weight and the complete block-diagonalization of the matrix-valued orthogonal polynomials is obtained. From the explicit expression, we obtain right-hand-sided differential operators of first and second order for which the matrix-valued orthogonal polynomials are eigenfunctions. We study the low-dimensional cases explicitly, and for these cases additional results, such as the Rodrigues' formula and being eigenfunctions to first-order differential-difference and second-order differential operators, are obtained. © 2012 The Author(s).Fil: Koelink, Erik. Radboud Universiteit, Nijmegen; Países BajosFil: Van Pruijssen, Maarten. Radboud Universiteit, Nijmegen; Países BajosFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaOxford University Press2012-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/200296Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag); Oxford University Press; International Mathematics Research Notices; 2012; 24; 1-2012; 5673-57301073-79281687-0247CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnr236info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2012/24/5673/725289info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:18:43Zoai:ri.conicet.gov.ar:11336/200296instacron: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:34982025-09-10 13:18:44.128CONICET 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), diag)
title Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
spellingShingle Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
Koelink, Erik
Matrix valued spherical functions
Matrix valued orthogonal polynomials
Hypergeometric functions
title_short Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
title_full Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
title_fullStr Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
title_full_unstemmed Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
title_sort Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
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 Matrix valued spherical functions
Matrix valued orthogonal polynomials
Hypergeometric functions
topic Matrix valued spherical functions
Matrix valued orthogonal polynomials
Hypergeometric functions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of spherical functions, we take these diagonals as a matrix-valued function, which are the full spherical functions. Their orthogonality is a consequence of the Schur orthogonality relations. From the full spherical functions, we obtain matrix-valued orthogonal polynomials of arbitrary size, and they satisfy a three-term recurrence relation which follows by considering tensor product decompositions. An explicit expression for the weight and the complete block-diagonalization of the matrix-valued orthogonal polynomials is obtained. From the explicit expression, we obtain right-hand-sided differential operators of first and second order for which the matrix-valued orthogonal polynomials are eigenfunctions. We study the low-dimensional cases explicitly, and for these cases additional results, such as the Rodrigues' formula and being eigenfunctions to first-order differential-difference and second-order differential operators, are obtained. © 2012 The Author(s).
Fil: Koelink, Erik. Radboud Universiteit, Nijmegen; Países Bajos
Fil: Van Pruijssen, Maarten. Radboud Universiteit, Nijmegen; Países Bajos
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of spherical functions, we take these diagonals as a matrix-valued function, which are the full spherical functions. Their orthogonality is a consequence of the Schur orthogonality relations. From the full spherical functions, we obtain matrix-valued orthogonal polynomials of arbitrary size, and they satisfy a three-term recurrence relation which follows by considering tensor product decompositions. An explicit expression for the weight and the complete block-diagonalization of the matrix-valued orthogonal polynomials is obtained. From the explicit expression, we obtain right-hand-sided differential operators of first and second order for which the matrix-valued orthogonal polynomials are eigenfunctions. We study the low-dimensional cases explicitly, and for these cases additional results, such as the Rodrigues' formula and being eigenfunctions to first-order differential-difference and second-order differential operators, are obtained. © 2012 The Author(s).
publishDate 2012
dc.date.none.fl_str_mv 2012-01
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/11336/200296
Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag); Oxford University Press; International Mathematics Research Notices; 2012; 24; 1-2012; 5673-5730
1073-7928
1687-0247
CONICET Digital
CONICET
url http://hdl.handle.net/11336/200296
identifier_str_mv Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag); Oxford University Press; International Mathematics Research Notices; 2012; 24; 1-2012; 5673-5730
1073-7928
1687-0247
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnr236
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2012/24/5673/725289
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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
_version_ 1842981022883381248
score 12.48226

Publicaciones similares