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Proceedings of the American Mathematical Society

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



On a theorem of Figà-Talamanca

Author: Martin E. Walter
Journal: Proc. Amer. Math. Soc. 60 (1976), 72-74
MSC: Primary 43A30
MathSciNet review: 0420149
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Abstract: We give an example of a noncompact, unimodular group G with the property that $ B(G) \cap {C_0}(G) = A(G)$, where $ A(G)$ is the Fourier algebra of G, $ B(G)$ is the Fourier-Stieltjes algebra of G and $ {C_0}(G)$ is the set of all complex, continuous functions on G vanishing at infinity. This example answers negatively a question raised by A. Figà-Talamanca.

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Keywords: Fourier and Fourier-Stieltjes algebra, inverse Fourier transform for nonabelian groups, positive definite function, singular Fourier-Stieltjes series
Article copyright: © Copyright 1976 American Mathematical Society