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, l]; then F operates in A(G) if and only if F is real-analytic in a neighborhood of the origin and F(0) = 0
DE MICHELE, L., Soardi, P. (1974). Functions which operate in the Fourier algebra of a discrete group. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 45(3), 389-392 [10.1090/S0002-9939-1974-0346419-3].
Functions which operate in the Fourier algebra of a discrete group
DE MICHELE, LEONEDE;SOARDI, PAOLO MAURIZIO
1974
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, l]; 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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