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Fourier algebras on locally compact hypergroups

✍ Scribed by M. Lashkarizadeh Bami; M. Pourgholamhossein; H. Samea

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 153 KB
Volume: 282
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200610719

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✦ Synopsis

Abstract

In the present paper we introduce a new definition for the Fourier space A (K) of a locally compact Hausdorff hypergroup K and prove that it is a Banach subspace of B (K). This definition coincides with that of Amini and Medghalchi in the case where K is a tensor hypergroup, and also with that of Vrem which is given only for compact hypergroups. We prove that A~p~ (K)* = PM~q~ (K), where q is the exponent conjugate to p, in particular A (K)* = VN (K). Also we show that for Pontryagin hypergroups, A (K) = L^2^(K) * L^2^(K) = F (L^1^($ \hat K $)), where F stands for the Fourier transform on $ \hat K $. Furthermore there is an equivalent norm on A (K) which makes A (K) into a Banach algebra isomorphic with L^1^($ \hat K $). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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