A novel approach through spherical functions in the characterization of invariant functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915548225339392 |
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| author | Martín, Rocío Díaz Saal, Linda |
| author_facet | Martín, Rocío Díaz Saal, Linda |
| contents | Given a compact subgroup K of the orthogonal group acting on the Euclidean space Rn, Gerald Schwarz proved that every smooth K-invariant function on Rn can be expressed as a smooth function of a generating set of $K$-invariant polynomials on n variables. The goal of this work is to provide an alternative and more straightforward proof of this result, based on Gelfand theory, with a particular focus on spherical functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A novel approach through spherical functions in the characterization of invariant functions Martín, Rocío Díaz Saal, Linda Functional Analysis Group Theory Spectral Theory 43A85, 43A90, 22E30 Given a compact subgroup K of the orthogonal group acting on the Euclidean space Rn, Gerald Schwarz proved that every smooth K-invariant function on Rn can be expressed as a smooth function of a generating set of $K$-invariant polynomials on n variables. The goal of this work is to provide an alternative and more straightforward proof of this result, based on Gelfand theory, with a particular focus on spherical functions. |
| title | A novel approach through spherical functions in the characterization of invariant functions |
| topic | Functional Analysis Group Theory Spectral Theory 43A85, 43A90, 22E30 |
| url | https://arxiv.org/abs/2510.01043 |