Abstract
Let $G$ be LCA group with dual $\Gamma$. Suppose $S\subseteq \Gamma$ is Borel set such that $S \cap (\gamma-S)$ has finite Haar measure for a dense set of $\gamma \epsilon \Gamma$ (or $S \cap (S-\gamma)$ does). If $\mu$ and $\nu$ are regular Borel measures whose Fourier-Stieltjes transforms vanish off $S$, then $|\mu|\ast|\nu|\epsilon|L^{1}(G)$ ($|\mu|$ denotes the total variation measure). This generalizes to non-metrizable groups a result of Glicksberg. Related results are given; the proofs are elementary.
Citation
Colin C. Graham. "Fourier-Stieltjes transforms with small supports." Illinois J. Math. 18 (4) 532 - 534, December 1974. https://doi.org/10.1215/ijm/1256051003
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