J. Aust. Math. Soc.  82 (2007), 59-83
Fourier algebra of a hypergroup. I

Varadharajan Muruganandam
  Department of Mathematics
  Pondicherry University
  Pondicherry 605 014

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.
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