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Functions which Operate in the Fourier Algebra of a Discrete Group

Leonede de Michele and Paolo M. Soardi
Proceedings of the American Mathematical Society
Vol. 45, No. 3 (Sep., 1974), pp. 389-392
DOI: 10.2307/2039963
Stable URL: http://www.jstor.org/stable/2039963
Page Count: 4
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Functions which Operate in the Fourier Algebra of a Discrete Group
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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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