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Fourier algebra of a hypergroup. I

Part of: Commutative Banach algebras and commutative topological algebras Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Varadharajan Muruganandam
Varadharajan Muruganandam
Affiliation:
Department of Mathematics Pondicherry UniversityPondicherry 605 014India e-mail: vmuruganandam@gmail.com
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Abstract

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In this article we study the Fourier space of a general hypergroup and its multipliers. The main result of this paper characterizes commutative hypergroups whose Fourier space forms a Banach algebra under pointwise product with an equivalent norm. Among those hypergroups whose Fourier space forms a Banach algebra, we identify a subclass for which the Gelfand spectrum of the Fourier algebra is equal to the underlying hypergroup. This subclass includes for instance, Jacobi hypergroups, Bessel-Kingman hypergroups.

Keywords

hypergroupsFourier spacesmultipliersGelfand spectrum of a Fourier algebra

MSC classification

Secondary: 43A62: Hypergroups 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A10: Measure algebras on groups, semigroups, etc. 46J10: Banach algebras of continuous functions, function algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 1 , February 2007 , pp. 59 - 83
Copyright
Copyright © Australian Mathematical Society 2007

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