A matrix-valued Choquet–Deny theorem

Abstract

Abstract. Let σ be a positive matrix-valued measure on a locally compact abelian group G such that σ(G) is the identity matrix. We give a necessary and sufficient condition on σ for the absence of a bounded non-constant matrixvalued function f on G satisfying the convolution equation f * σ = f . This extends Choquet and Deny's theorem for real-valued functions on G.