Characterization of the Gelfand pair: Quasi Gelfand pair
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909074974572544 |
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| author | Malanda, Cornelie Mitcha |
| author_facet | Malanda, Cornelie Mitcha |
| contents | Let G be a locally compact group and let K be a compact subgroup of Aut(G), the group of automorphisms of G. The pair $(G, K )$ is a Gelfand pair if the algebra $L^{1}_{K}(G)$ of K-invariant integrable functions on G is commutative under convolution. In \cite{toure2008lie}, the charactezations of this algebra in the nilpotent case were studied, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in \cite{benson1990gel} and obtained a new criterion for Gelfand pairs. In this paper we describe the spherical function associated with this type of pair. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of the Gelfand pair: Quasi Gelfand pair Malanda, Cornelie Mitcha Classical Analysis and ODEs Functional Analysis 43A80, 22E25, 22E60 Let G be a locally compact group and let K be a compact subgroup of Aut(G), the group of automorphisms of G. The pair $(G, K )$ is a Gelfand pair if the algebra $L^{1}_{K}(G)$ of K-invariant integrable functions on G is commutative under convolution. In \cite{toure2008lie}, the charactezations of this algebra in the nilpotent case were studied, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in \cite{benson1990gel} and obtained a new criterion for Gelfand pairs. In this paper we describe the spherical function associated with this type of pair. |
| title | Characterization of the Gelfand pair: Quasi Gelfand pair |
| topic | Classical Analysis and ODEs Functional Analysis 43A80, 22E25, 22E60 |
| url | https://arxiv.org/abs/2401.08446 |