An extension of Bochner’s theorem

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

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Keywords

commutative triple, function of positive type, unitary representation, spherical function, lattice

Mathematical Subject Classification

Primary: 22E30, 43A05, 43A35, 43A90

Milestones

Received: 26 December 2024

Revised: 24 May 2025

Accepted: 8 July 2025

Published: 2 April 2026

Authors

Lamine Timité
Département des Sciences et Technologie École Normale Supérieure d’Abidjan Abidjan Ivory Coast

Ibrahima Touré
UFR de Mathématiques et Informatique Université Félix Houphouët-Boigny Abidjan Ivory Coast

Vol. 8, No. 2, 2026

Lamine Timité and Ibrahima Touré

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors