The strong conclusion of the F. and M. Riesz theorem on groups

Glicksberg, I.

doi:10.1090/S0002-9947-1984-0748839-2

The strong conclusion of the F. and M. Riesz theorem on groups
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Trans. Amer. Math. Soc. 285 (1984), 235-240 Request permission

Abstract:

Let $S$ be a closed proper generating subsemigroup of the dual $\Gamma$ of a locally compact abelian group $G$. Then there are Haar singular measures on $G$ orthogonal to $S$ unless $G = {\mathbf {R}} \times \Delta$ or ${\mathbf {T}} \times \Delta$ with $\Delta$ discrete, and then all $\mu$ orthogonal to $S$ are Haar absolutely continuous.

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Über die Randwerte einer Analytishcen Functionen

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