Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group

Autores
Díaz Martín, Rocío Patricia; Levstein, Fernando
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting problem consists in studying the set of bounded linear operators over the sections of Eτ that are invariant under the action of SO(3) ⋉ R3. Such operators are in correspondence with the End(Vτ) -valued, bi-τ-equivariant, integrable functions on R3 and they form a commutative algebra with the convolution product. We develop the spherical analysis on that algebra, explicitly computing the τ-spherical functions. We first present a set of generators of the algebra of SO(3) ⋉ R3-invariant differential operators non Eτ. We also give an explicit form for the τ-spherical Fourier transform, we deduce an inversion formula and we use it to give a characterization of End(Vτ) -valued, bi-τ-equivariant, functions on R3.
Fil: Díaz Martín, Rocío Patricia. Universidad Nacional de Córdoba; 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
Fil: Levstein, Fernando. Universidad Nacional de Córdoba; 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
HARMONIC ANALYSIS
MATRIX SPHERICAL FUNCTIONS
SPHERICAL TRANSFORMS
STRONG GELFAND PAIRS
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:11336/89299
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/89299
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion groupDíaz Martín, Rocío PatriciaLevstein, FernandoHARMONIC ANALYSISMATRIX SPHERICAL FUNCTIONSSPHERICAL TRANSFORMSSTRONG GELFAND PAIRShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting problem consists in studying the set of bounded linear operators over the sections of Eτ that are invariant under the action of SO(3) ⋉ R3. Such operators are in correspondence with the End(Vτ) -valued, bi-τ-equivariant, integrable functions on R3 and they form a commutative algebra with the convolution product. We develop the spherical analysis on that algebra, explicitly computing the τ-spherical functions. We first present a set of generators of the algebra of SO(3) ⋉ R3-invariant differential operators non Eτ. We also give an explicit form for the τ-spherical Fourier transform, we deduce an inversion formula and we use it to give a characterization of End(Vτ) -valued, bi-τ-equivariant, functions on R3.Fil: Díaz Martín, Rocío Patricia. Universidad Nacional de Córdoba; 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; ArgentinaFil: Levstein, Fernando. Universidad Nacional de Córdoba; 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; ArgentinaSpringer Wien2018-04info: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/11336/89299Díaz Martín, Rocío Patricia; Levstein, Fernando; Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group; Springer Wien; Monatshefete Fur Mathematik; 185; 4; 4-2018; 621-6490026-92551436-5081CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00605-017-1123-1info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00605-017-1123-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:33:02Zoai:ri.conicet.gov.ar:11336/89299instacron: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 15:33:03.226CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
title Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
spellingShingle Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
Díaz Martín, Rocío Patricia
HARMONIC ANALYSIS
MATRIX SPHERICAL FUNCTIONS
SPHERICAL TRANSFORMS
STRONG GELFAND PAIRS
title_short Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
title_full Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
title_fullStr Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
title_full_unstemmed Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
title_sort Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
dc.creator.none.fl_str_mv Díaz Martín, Rocío Patricia
Levstein, Fernando
author Díaz Martín, Rocío Patricia
author_facet Díaz Martín, Rocío Patricia
Levstein, Fernando
author_role author
author2 Levstein, Fernando
author2_role author
dc.subject.none.fl_str_mv HARMONIC ANALYSIS
MATRIX SPHERICAL FUNCTIONS
SPHERICAL TRANSFORMS
STRONG GELFAND PAIRS
topic HARMONIC ANALYSIS
MATRIX SPHERICAL FUNCTIONS
SPHERICAL TRANSFORMS
STRONG GELFAND PAIRS
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 consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting problem consists in studying the set of bounded linear operators over the sections of Eτ that are invariant under the action of SO(3) ⋉ R3. Such operators are in correspondence with the End(Vτ) -valued, bi-τ-equivariant, integrable functions on R3 and they form a commutative algebra with the convolution product. We develop the spherical analysis on that algebra, explicitly computing the τ-spherical functions. We first present a set of generators of the algebra of SO(3) ⋉ R3-invariant differential operators non Eτ. We also give an explicit form for the τ-spherical Fourier transform, we deduce an inversion formula and we use it to give a characterization of End(Vτ) -valued, bi-τ-equivariant, functions on R3.
Fil: Díaz Martín, Rocío Patricia. Universidad Nacional de Córdoba; 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
Fil: Levstein, Fernando. Universidad Nacional de Córdoba; 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 consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting problem consists in studying the set of bounded linear operators over the sections of Eτ that are invariant under the action of SO(3) ⋉ R3. Such operators are in correspondence with the End(Vτ) -valued, bi-τ-equivariant, integrable functions on R3 and they form a commutative algebra with the convolution product. We develop the spherical analysis on that algebra, explicitly computing the τ-spherical functions. We first present a set of generators of the algebra of SO(3) ⋉ R3-invariant differential operators non Eτ. We also give an explicit form for the τ-spherical Fourier transform, we deduce an inversion formula and we use it to give a characterization of End(Vτ) -valued, bi-τ-equivariant, functions on R3.
publishDate 2018
dc.date.none.fl_str_mv 2018-04
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/11336/89299
Díaz Martín, Rocío Patricia; Levstein, Fernando; Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group; Springer Wien; Monatshefete Fur Mathematik; 185; 4; 4-2018; 621-649
0026-9255
1436-5081
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89299
identifier_str_mv Díaz Martín, Rocío Patricia; Levstein, Fernando; Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group; Springer Wien; Monatshefete Fur Mathematik; 185; 4; 4-2018; 621-649
0026-9255
1436-5081
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00605-017-1123-1
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00605-017-1123-1
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 Springer Wien
publisher.none.fl_str_mv Springer Wien
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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