J. Aust. Math. Soc.
82 (2007), 5983

Fourier algebra of a hypergroup. I

Varadharajan Muruganandam
Department of Mathematics
Pondicherry University
Pondicherry 605 014
India
vmuruganandam@gmail.com



Abstract

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, BesselKingman hypergroups.

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