A matrix-valued Choquet–Deny theorem

Chu, Cho-Ho; Hilberdink, Titus; Howroyd, John

doi:10.1090/S0002-9939-00-05694-X

A matrix-valued Choquet–Deny theorem
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by Cho-Ho Chu, Titus Hilberdink and John Howroyd PDF

Proc. Amer. Math. Soc. 129 (2001), 229-235 Request permission

Abstract:

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

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