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Segal algebras with functorial properties

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Abstract

We study the Segal algebrasE 0 (G) (G locally compact, abelian) introduced byR. Bürger. They serve as a domain for Poisson's formula. It is shown that ifH s a closed subgroup ofG, then functions inE 0 (H) can be extended toE 0 (G) and similarly, lifting fromE 0 (G/H) toE 0 (G) is possible. Moreover, it is shown that {E 0 (G)} is the largest family of Segal algebras that are invariant under Fourier transforms and have this extension and lifting property.

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  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Vienna, Austria

    Viktor Losert

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  1. Viktor Losert
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Losert, V. Segal algebras with functorial properties. Monatshefte für Mathematik 96, 209–231 (1983). https://doi.org/10.1007/BF01605489

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