The Spherical Transform of any k-Type in a Locally Compact Group

Autores
Román, Pablo Manuel; Tirao, Juan Alfredo
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a locally compact group G and a compact subgroup K, we develop and study a spherical transform on the convolution algebra Cc;(G) of all continuous functions f with compact support on G such that f = f = f . Here denotes the character of a unitary irreducible representation of K times its dimension. We obtain an inversion formula for the spherical transform by using the Fourier inversion formula in G. The case of the group G = SU(2; 1) and the compact subgroup K = U(2) is discussed in detail. We give explicit expressions for the spherical transform and the corresponding inversion formula in terms of the matrix hypergeometric function 2H1.
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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina
Materia
Harmonic analysis
Matrix valued spherical functions
Spherical transform
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:11336/271929
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The Spherical Transform of any k-Type in a Locally Compact GroupRomán, Pablo ManuelTirao, Juan AlfredoHarmonic analysisMatrix valued spherical functionsSpherical transformhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a locally compact group G and a compact subgroup K, we develop and study a spherical transform on the convolution algebra Cc;(G) of all continuous functions f with compact support on G such that f = f = f . Here denotes the character of a unitary irreducible representation of K times its dimension. We obtain an inversion formula for the spherical transform by using the Fourier inversion formula in G. The case of the group G = SU(2; 1) and the compact subgroup K = U(2) is discussed in detail. We give explicit expressions for the spherical transform and the corresponding inversion formula in terms of the matrix hypergeometric function 2H1.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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección 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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; ArgentinaHeldermann Verlag2012-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/271929Román, Pablo Manuel; Tirao, Juan Alfredo; The Spherical Transform of any k-Type in a Locally Compact Group; Heldermann Verlag; Journal Of Lie Theory; 22; 2; 10-2012; 361-3950949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT22/JLT222/jlt22014.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:42:20Zoai:ri.conicet.gov.ar:11336/271929instacron: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:34982025-10-15 14:42:21.26CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Spherical Transform of any k-Type in a Locally Compact Group
title The Spherical Transform of any k-Type in a Locally Compact Group
spellingShingle The Spherical Transform of any k-Type in a Locally Compact Group
Román, Pablo Manuel
Harmonic analysis
Matrix valued spherical functions
Spherical transform
title_short The Spherical Transform of any k-Type in a Locally Compact Group
title_full The Spherical Transform of any k-Type in a Locally Compact Group
title_fullStr The Spherical Transform of any k-Type in a Locally Compact Group
title_full_unstemmed The Spherical Transform of any k-Type in a Locally Compact Group
title_sort The Spherical Transform of any k-Type in a Locally Compact Group
dc.creator.none.fl_str_mv Román, Pablo Manuel
Tirao, Juan Alfredo
author Román, Pablo Manuel
author_facet Román, Pablo Manuel
Tirao, Juan Alfredo
author_role author
author2 Tirao, Juan Alfredo
author2_role author
dc.subject.none.fl_str_mv Harmonic analysis
Matrix valued spherical functions
Spherical transform
topic Harmonic analysis
Matrix valued spherical functions
Spherical transform
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a locally compact group G and a compact subgroup K, we develop and study a spherical transform on the convolution algebra Cc;(G) of all continuous functions f with compact support on G such that f = f = f . Here denotes the character of a unitary irreducible representation of K times its dimension. We obtain an inversion formula for the spherical transform by using the Fourier inversion formula in G. The case of the group G = SU(2; 1) and the compact subgroup K = U(2) is discussed in detail. We give explicit expressions for the spherical transform and the corresponding inversion formula in terms of the matrix hypergeometric function 2H1.
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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina
description Given a locally compact group G and a compact subgroup K, we develop and study a spherical transform on the convolution algebra Cc;(G) of all continuous functions f with compact support on G such that f = f = f . Here denotes the character of a unitary irreducible representation of K times its dimension. We obtain an inversion formula for the spherical transform by using the Fourier inversion formula in G. The case of the group G = SU(2; 1) and the compact subgroup K = U(2) is discussed in detail. We give explicit expressions for the spherical transform and the corresponding inversion formula in terms of the matrix hypergeometric function 2H1.
publishDate 2012
dc.date.none.fl_str_mv 2012-10
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/11336/271929
Román, Pablo Manuel; Tirao, Juan Alfredo; The Spherical Transform of any k-Type in a Locally Compact Group; Heldermann Verlag; Journal Of Lie Theory; 22; 2; 10-2012; 361-395
0949-5932
CONICET Digital
CONICET
url http://hdl.handle.net/11336/271929
identifier_str_mv Román, Pablo Manuel; Tirao, Juan Alfredo; The Spherical Transform of any k-Type in a Locally Compact Group; Heldermann Verlag; Journal Of Lie Theory; 22; 2; 10-2012; 361-395
0949-5932
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT22/JLT222/jlt22014.htm
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 Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
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 12.891075

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