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

Artículo finalmente publicado en: Díaz Martín, R. y Levstein, F. (2018). Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group. Monatshefte fur Mathematik, 185 (4), 621-649. https://doi.org/10.1007/s00605-017-1123-1

Detalles Bibliográficos
Autores principales: Díaz Martín, Rocío Patricia, Levstein, Fernando
Otros Autores: https://orcid.org/0000-0002-3732-6296
Formato: submittedVersion article
Lenguaje:Inglés
Publicado: 2024
Materias:
Harmonic analysis
Strong gelfand pairs
Spherical transforms
Matrix spherical functions
Acceso en línea:http://hdl.handle.net/11086/551490
https://doi.org/10.48550/arXiv.1704.07336
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-551490
record_format dspace
spelling I10-R141-11086-5514902024-04-19T16:12:16Z Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group Díaz Martín, Rocío Patricia Levstein, Fernando https://orcid.org/0000-0002-3732-6296 Harmonic analysis Strong gelfand pairs Spherical transforms Matrix spherical functions Artículo finalmente publicado en: Díaz Martín, R. y Levstein, F. (2018). Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group. Monatshefte fur Mathematik, 185 (4), 621-649. https://doi.org/10.1007/s00605-017-1123-1 info:eu-repo/semantics/submittedVersion Fil: Díaz Martín, Rocío Patricia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Levstein, Fernando. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. 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)ˆ, 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 on 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. This work has been supported by a fellowship from Consejo Nacional de Investigaciones Cientı́ficas y Técnicas and reserch grants from Secretarı́a de Ciencia y Tecnologı́a, Universidad Nacional de Córdoba and Consejo Nacional de Investigaciones Cientı́ficas y Técnicas (Argentina). info:eu-repo/semantics/submittedVersion Fil: Díaz Martín, Rocío Patricia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Levstein, Fernando. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Matemática Pura 2024-04-19T12:32:05Z 2024-04-19T12:32:05Z 2018 article http://hdl.handle.net/11086/551490 https://doi.org/10.48550/arXiv.1704.07336 eng De la versión publicada: https://doi.org/10.1007/s00605-017-1123-1 Attribution-NonCommercial-NoDerivs 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Impreso; Electrónico y/o Digital e-ISSN: 1436-5081 ISSN: 0026-9255
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Harmonic analysis
Strong gelfand pairs
Spherical transforms
Matrix spherical functions
spellingShingle Harmonic analysis
Strong gelfand pairs
Spherical transforms
Matrix spherical functions
Díaz Martín, Rocío Patricia
Levstein, Fernando
Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
topic_facet Harmonic analysis
Strong gelfand pairs
Spherical transforms
Matrix spherical functions
description Artículo finalmente publicado en: Díaz Martín, R. y Levstein, F. (2018). Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group. Monatshefte fur Mathematik, 185 (4), 621-649. https://doi.org/10.1007/s00605-017-1123-1
author2 https://orcid.org/0000-0002-3732-6296
author_facet https://orcid.org/0000-0002-3732-6296
Díaz Martín, Rocío Patricia
Levstein, Fernando
format submittedVersion
article
author Díaz Martín, Rocío Patricia
Levstein, Fernando
author_sort Díaz Martín, Rocío Patricia
title Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
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
publishDate 2024
url http://hdl.handle.net/11086/551490
https://doi.org/10.48550/arXiv.1704.07336
work_keys_str_mv AT diazmartinrociopatricia sphericalanalysisonhomogeneousvectorbundlesofthe3dimensionaleuclideanmotiongroup
AT levsteinfernando sphericalanalysisonhomogeneousvectorbundlesofthe3dimensionaleuclideanmotiongroup
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