The measure algebra of a locally compact hypergroup

Abstract

A hypergroup is a locally compact space on which the space of finite regular Borel measures has a convolution structure preserving the probability measures. This paper deals only with commutative hypergroups. §1 contains definitions, a discussion of invariant measures, and a characterization of idempotent probability measures. §2 deals with the characters of a hypergroup. §3 is about hypergroups, which have generalized translation operators (in the sense of Levitan), and subhypergroups of such. In this case the set of characters provides much information. Finally §4 discusses examples, such as the space of conjugacy classes of a compact group, certain compact homogeneous spaces, ultraspherical series, and finite hypergroups.