Abstract

Let $G$ be a locally compact group, $K$ be a compact subgroup of $G$ and $\delta$ be a class of unitary irreducible representations of $K$. The triple $(G,K,\delta )$ is commutative if the convolution algebra ${\mathcal{𝒞}}_c(G,F_{\delta },\delta ,\delta )$ of $\delta$-radial functions with compact support is commutative. We prove a Bochner-type theorem for commutative triples using some algebraic properties of $\delta$-radial functions of positive type. This work extends some results of Marouane Rabaoui.

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