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Proceedings of the American Mathematical Society

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



Functions which are Fourier-Stieltjes transforms

Author: Stephen H. Friedberg
Journal: Proc. Amer. Math. Soc. 28 (1971), 451-452
MSC: Primary 42.52
MathSciNet review: 0278006
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Abstract: Let $ G$ be a locally compact abelian group, $ \hat G$ the dual group, $ M(G)$ the algebra of regular bounded Borel measures on $ G$, and $ M{(G)^\wedge}$ the algebra of Fourier-Stieltjes transforms. The purpose of this paper is to characterize those continuous functions on $ \hat G$ which belongs to $ M(X)^\wedge$, where $ X$ is a closed subset of $ G$ and $ M(X) = \{ \mu \in M(G)$: the support of $ \mu $ is contained in $ X\} $.

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Keywords: Locally compact abelian group, dual group, Fourier-Stieltjes transform, Grothendieck's completion theorem, Eberlein's theorem, Bohr compactification
Article copyright: © Copyright 1971 American Mathematical Society