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
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| Format: | info:eu-repo/semantics/submittedVersion |
| Language: | eng |
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2024
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| Online Access: | http://hdl.handle.net/11086/551490 https://doi.org/10.48550/arXiv.1704.07336 |
| _version_ | 1801212324777820160 |
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| author | Díaz Martín, Rocío Patricia Levstein, Fernando |
| author2 | https://orcid.org/0000-0002-3732-6296 |
| author_facet | https://orcid.org/0000-0002-3732-6296 Díaz Martín, Rocío Patricia Levstein, Fernando |
| author_sort | Díaz Martín, Rocío Patricia |
| collection | Repositorio Digital Universitario |
| 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 |
| format | info:eu-repo/semantics/submittedVersion |
| id | rdu-unc.551490 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2024 |
| record_format | dspace |
| spelling | rdu-unc.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 |
| 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 |
| title | 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_short | 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 |
| topic | Harmonic analysis Strong gelfand pairs Spherical transforms Matrix spherical functions |
| 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 |