Characterization of the Gelfand pair: Quasi Gelfand pair

2024/01/16 by Cornelie Mitcha Malanda, Malanda, Cornelie Mitcha
Mathematics · #22E25 #22E60 #43A80 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2401.08446

openalex publication_date 2024/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L¹_K(G) of K-invariant integrable functions on G is commutative under convolution. In \citetoure2008lie, the charactezations of this algebra in the nilpotent case were studied, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in \citebenson1990gel 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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