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Functions of translation type and functorial properties of Segal algebras II

Authors:	Bürger Reinhard

Institution:	(1) Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria

Abstract:	In this paper we investigate functorial properties of the Segal algebra $\mathfrak{B}_0 (G)$ which consists of all functionsf in Wiener's algebra onG with Fourier transform $\hat f$ in Wiener's algebra on the dual group $\hat G$ . Especially $\mathfrak{B}_0 (G)$ may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE ₀(G) containing $\mathfrak{B}_0 (G)$ as a subspace, but still eachfE ₀(S) satisfies Poisson's formula.

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