Matrix valued spherical functions associated to the three dimensional hyperbolic space

Autores
Grünbaum, F. Alberto; Pacharoni, Maria Ines; Tirao, Juan Alfredo
Año de publicación
2002
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2, ℂ) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space ℍ = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of H in terms of Gauss' functions 2F1. Just as in the compact instance treated in [7], there is a useful role for a special class of generalized hypergeometric functions p+1Fp.
Fil: Grünbaum, F. Alberto. University of California at Berkeley; Estados Unidos
Fil: Pacharoni, Maria Ines. 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
Fil: Tirao, Juan Alfredo. 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
COUPLED SYSTEM
GENERALIZED HYPERGEOMETRIC FUNCTIONS
MATRIX VALUED BISPECTRAL PROPERTY
ORDINARY DIFFERENTIAL EQUATIONS
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:11336/129969
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Matrix valued spherical functions associated to the three dimensional hyperbolic spaceGrünbaum, F. AlbertoPacharoni, Maria InesTirao, Juan AlfredoCOUPLED SYSTEMGENERALIZED HYPERGEOMETRIC FUNCTIONSMATRIX VALUED BISPECTRAL PROPERTYORDINARY DIFFERENTIAL EQUATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2, ℂ) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space ℍ = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of H in terms of Gauss' functions 2F1. Just as in the compact instance treated in [7], there is a useful role for a special class of generalized hypergeometric functions p+1Fp.Fil: Grünbaum, F. Alberto. University of California at Berkeley; Estados UnidosFil: Pacharoni, Maria Ines. 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; ArgentinaFil: Tirao, Juan Alfredo. 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; ArgentinaWorld Scientific2002-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129969Grünbaum, F. Alberto; Pacharoni, Maria Ines; Tirao, Juan Alfredo; Matrix valued spherical functions associated to the three dimensional hyperbolic space; World Scientific; International Journal Of Mathematics; 13; 7; 9-2002; 727-7840129-167X1793-6519CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0129167X02001460info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0129167X02001460info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0203211info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:44:04Zoai:ri.conicet.gov.ar:11336/129969instacron: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 10:44:05.274CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Matrix valued spherical functions associated to the three dimensional hyperbolic space
title Matrix valued spherical functions associated to the three dimensional hyperbolic space
spellingShingle Matrix valued spherical functions associated to the three dimensional hyperbolic space
Grünbaum, F. Alberto
COUPLED SYSTEM
GENERALIZED HYPERGEOMETRIC FUNCTIONS
MATRIX VALUED BISPECTRAL PROPERTY
ORDINARY DIFFERENTIAL EQUATIONS
title_short Matrix valued spherical functions associated to the three dimensional hyperbolic space
title_full Matrix valued spherical functions associated to the three dimensional hyperbolic space
title_fullStr Matrix valued spherical functions associated to the three dimensional hyperbolic space
title_full_unstemmed Matrix valued spherical functions associated to the three dimensional hyperbolic space
title_sort Matrix valued spherical functions associated to the three dimensional hyperbolic space
dc.creator.none.fl_str_mv Grünbaum, F. Alberto
Pacharoni, Maria Ines
Tirao, Juan Alfredo
author Grünbaum, F. Alberto
author_facet Grünbaum, F. Alberto
Pacharoni, Maria Ines
Tirao, Juan Alfredo
author_role author
author2 Pacharoni, Maria Ines
Tirao, Juan Alfredo
author2_role author
author
dc.subject.none.fl_str_mv COUPLED SYSTEM
GENERALIZED HYPERGEOMETRIC FUNCTIONS
MATRIX VALUED BISPECTRAL PROPERTY
ORDINARY DIFFERENTIAL EQUATIONS
topic COUPLED SYSTEM
GENERALIZED HYPERGEOMETRIC FUNCTIONS
MATRIX VALUED BISPECTRAL PROPERTY
ORDINARY DIFFERENTIAL EQUATIONS
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 main purpose of this paper is to compute all irreducible spherical functions on G = SL(2, ℂ) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space ℍ = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of H in terms of Gauss' functions 2F1. Just as in the compact instance treated in [7], there is a useful role for a special class of generalized hypergeometric functions p+1Fp.
Fil: Grünbaum, F. Alberto. University of California at Berkeley; Estados Unidos
Fil: Pacharoni, Maria Ines. 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
Fil: Tirao, Juan Alfredo. 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 main purpose of this paper is to compute all irreducible spherical functions on G = SL(2, ℂ) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space ℍ = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of H in terms of Gauss' functions 2F1. Just as in the compact instance treated in [7], there is a useful role for a special class of generalized hypergeometric functions p+1Fp.
publishDate 2002
dc.date.none.fl_str_mv 2002-09
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/11336/129969
Grünbaum, F. Alberto; Pacharoni, Maria Ines; Tirao, Juan Alfredo; Matrix valued spherical functions associated to the three dimensional hyperbolic space; World Scientific; International Journal Of Mathematics; 13; 7; 9-2002; 727-784
0129-167X
1793-6519
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129969
identifier_str_mv Grünbaum, F. Alberto; Pacharoni, Maria Ines; Tirao, Juan Alfredo; Matrix valued spherical functions associated to the three dimensional hyperbolic space; World Scientific; International Journal Of Mathematics; 13; 7; 9-2002; 727-784
0129-167X
1793-6519
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0129167X02001460
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0129167X02001460
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0203211
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
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
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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score 13.070432

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