Functions which operate in the Fourier algebra of a discrete group

De-Michele, Leonede; Soardi, Paolo M.

doi:10.1090/S0002-9939-1974-0346419-3

Functions which operate in the Fourier algebra of a discrete group
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by Leonede De-Michele and Paolo M. Soardi PDF

Proc. Amer. Math. Soc. 45 (1974), 389-392 Request permission

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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