Spherical Functions On Transitive Groupoids

Abstract

Let G be a topological locally compact, Hausdorff and second countable groupoid with a Haar system and K a compact subgroupoid of G with a Haar system too. (G,K) is a Gelfand pair if the algebra of K-biinvariant functions is commutative under convolution. In this paper, we study spherical functions on groupoids and generalize some well-known results on groups.