Journal of Mathematics of Kyoto University
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J. Math. Kyoto Univ. 48 (2008), no. 4,  p. 847 - 855
On lie algebras of K-invariant functions
Ibrahima Toure and Kinvi Kangni

Let $G$ be a locally compact group and let $K$ be a compact subgroup of $Aut(G)$, the group of automorphisms of $G$. $(G,K)$ is a Gelfand pair if the algebra $L_{K}^{1}(G)$ of K-invariant integrable functions on $G$ is commutative under convolution. In this paper, we give some charactezations of this algebra in the nilpotent case, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in [1] and obtain a new criterion for Gelfand pairs.

2000 Mathematics Subject Classification
Primary: 430A20, 17B30
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©2008 Department of Mathematics, Kyoto University