Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group
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 s...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/89299 |
| Acesso em linha: | http://hdl.handle.net/11336/89299 |
| Access Level: | acceso abierto |
| Palavra-chave: | HARMONIC ANALYSIS MATRIX SPHERICAL FUNCTIONS SPHERICAL TRANSFORMS STRONG GELFAND PAIRS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | 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. |
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