Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Convolutions of continuous measures and sets of nonsynthesis

Author: Sadahiro Saeki
Journal: Proc. Amer. Math. Soc. 60 (1976), 215-220
MSC: Primary 43A45; Secondary 43A05
MathSciNet review: 0430680
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Abstract: Let G be a nondiscrete LCA group, and $ A(G)$ the Fourier algebra of G. It is shown that if E is a closed subset of G such that $ (\mu \ast \nu )(E) \ne 0$ for some $ \mu $ and $ \nu \in {M_c}(G)$, then E is a set of analyticity and contains a set of nonsynthesis for $ A(G)$.

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Keywords: LCA group, Fourier algebra, set of analyticity, set of synthesis, independent set, continuous measure
Article copyright: © Copyright 1976 American Mathematical Society