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arXiv · 2401.08446

Characterization of the Gelfand pair: Quasi Gelfand pair

Cornelie Mitcha Malanda
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Abstract

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.

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Cornelie Mitcha Malanda. 2024-01-16. Characterization of the Gelfand pair: Quasi Gelfand pair. https://arxiv.org/abs/2401.08446

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