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Proceedings of the American Mathematical Society

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

 

 

Functions which operate in the Fourier algebra of a discrete group


Authors: Leonede De-Michele and Paolo M. Soardi
Journal: Proc. Amer. Math. Soc. 45 (1974), 389-392
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0346419-3
MathSciNet review: 0346419
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Abstract: In this paper we prove the following theorem: let $ G$ be a discrete amenable group with nontrivial almost-periodic compactification, and let $ F$ be a complex-valued function defined in $ [ - 1,1]$; then $ F$ operates in $ A(G)$ if and only if $ F$ is real-analytic in a neighborhood of the origin and $ F(0) = 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0346419-3
Keywords: Fourier algebra, locally compact groups, functions which operate, real-analytic
Article copyright: © Copyright 1974 American Mathematical Society