The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n

Autores
Campos, Silvina Mabel; Saal, Linda Victoria
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We denote by $H_{n}$ the $2n+1$-dimensional Heisenberg group and study the spherical transform associated with the generalized Gelfand pair $(U(p,q) \rtimes H_{n},U(p,q))$, $p+q=n$, which is defined on the space of Schwartz functions on $H_{n}$, and we characterize its image. In order to do that, since the spectrum associated to this pair can be identified with a subset $\Sigma$ of the plane, we introduce a space ${\cal H}_{n}$ of functions defined on $\mathbb{R}^2$ and we prove that a function defined on $\Sigma$ lies in the image if and only if it can be extended to a function in ${\cal H}_{n}$. In particular, the spherical transform of a Schwartz function $f$ on $H_{n}$ admits a Schwartz extension on the plane if and only if its restriction to the vertical axis lies in ${\cal S}(\mathbb{R})$.
Fil: Campos, Silvina Mabel. 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, Astronomía y Física; Argentina
Fil: Saal, Linda Victoria. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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
Heisenberg Group
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:11336/32135
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=nCampos, Silvina MabelSaal, Linda VictoriaHeisenberg GroupSpherical Transformhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We denote by $H_{n}$ the $2n+1$-dimensional Heisenberg group and study the spherical transform associated with the generalized Gelfand pair $(U(p,q) \rtimes H_{n},U(p,q))$, $p+q=n$, which is defined on the space of Schwartz functions on $H_{n}$, and we characterize its image. In order to do that, since the spectrum associated to this pair can be identified with a subset $\Sigma$ of the plane, we introduce a space ${\cal H}_{n}$ of functions defined on $\mathbb{R}^2$ and we prove that a function defined on $\Sigma$ lies in the image if and only if it can be extended to a function in ${\cal H}_{n}$. In particular, the spherical transform of a Schwartz function $f$ on $H_{n}$ admits a Schwartz extension on the plane if and only if its restriction to the vertical axis lies in ${\cal S}(\mathbb{R})$.Fil: Campos, Silvina Mabel. 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, Astronomía y Física; ArgentinaFil: Saal, Linda Victoria. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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; ArgentinaHeldermann Verlag2014-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/32135Saal, Linda Victoria; Campos, Silvina Mabel; The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n ; Heldermann Verlag; Journal Of Lie Theory; 24; 3; 9-2014; 657-6850949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT24/JLT243/jlt24028.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 Técnicas2025-09-17T10:51:43Zoai:ri.conicet.gov.ar:11336/32135instacron: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:34982025-09-17 10:51:43.534CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
title The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
spellingShingle The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
Campos, Silvina Mabel
Heisenberg Group
Spherical Transform
title_short The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
title_full The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
title_fullStr The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
title_full_unstemmed The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
title_sort The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
dc.creator.none.fl_str_mv Campos, Silvina Mabel
Saal, Linda Victoria
author Campos, Silvina Mabel
author_facet Campos, Silvina Mabel
Saal, Linda Victoria
author_role author
author2 Saal, Linda Victoria
author2_role author
dc.subject.none.fl_str_mv Heisenberg Group
Spherical Transform
topic Heisenberg Group
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 We denote by $H_{n}$ the $2n+1$-dimensional Heisenberg group and study the spherical transform associated with the generalized Gelfand pair $(U(p,q) \rtimes H_{n},U(p,q))$, $p+q=n$, which is defined on the space of Schwartz functions on $H_{n}$, and we characterize its image. In order to do that, since the spectrum associated to this pair can be identified with a subset $\Sigma$ of the plane, we introduce a space ${\cal H}_{n}$ of functions defined on $\mathbb{R}^2$ and we prove that a function defined on $\Sigma$ lies in the image if and only if it can be extended to a function in ${\cal H}_{n}$. In particular, the spherical transform of a Schwartz function $f$ on $H_{n}$ admits a Schwartz extension on the plane if and only if its restriction to the vertical axis lies in ${\cal S}(\mathbb{R})$.
Fil: Campos, Silvina Mabel. 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, Astronomía y Física; Argentina
Fil: Saal, Linda Victoria. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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 We denote by $H_{n}$ the $2n+1$-dimensional Heisenberg group and study the spherical transform associated with the generalized Gelfand pair $(U(p,q) \rtimes H_{n},U(p,q))$, $p+q=n$, which is defined on the space of Schwartz functions on $H_{n}$, and we characterize its image. In order to do that, since the spectrum associated to this pair can be identified with a subset $\Sigma$ of the plane, we introduce a space ${\cal H}_{n}$ of functions defined on $\mathbb{R}^2$ and we prove that a function defined on $\Sigma$ lies in the image if and only if it can be extended to a function in ${\cal H}_{n}$. In particular, the spherical transform of a Schwartz function $f$ on $H_{n}$ admits a Schwartz extension on the plane if and only if its restriction to the vertical axis lies in ${\cal S}(\mathbb{R})$.
publishDate 2014
dc.date.none.fl_str_mv 2014-09
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/11336/32135
Saal, Linda Victoria; Campos, Silvina Mabel; The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n ; Heldermann Verlag; Journal Of Lie Theory; 24; 3; 9-2014; 657-685
0949-5932
CONICET Digital
CONICET
url http://hdl.handle.net/11336/32135
identifier_str_mv Saal, Linda Victoria; Campos, Silvina Mabel; The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n ; Heldermann Verlag; Journal Of Lie Theory; 24; 3; 9-2014; 657-685
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/JLT24/JLT243/jlt24028.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
_version_ 1843606143195152384
score 13.001348

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