The Wiener property for a class of discrete hypergroups. (English) Zbl 0672.43004
Among important Banach algebras of measures on locally compact spaces, it is worth to study discrete hypergroups: they do, in fact, possess an (easily computable) Haar measure. Very important results are already available for discrete groups. We extend here, to begin with, the Wiener property to all discrete hypergroups of subexponential growth. As a consequence of the methods here developed, it is proved in a completely different way than was previously known, that commutative locally compact hypergroups are symmetric.
Reviewer: O.Gebuhrer
MSC:
| 43A20 | \(L^1\)-algebras on groups, semigroups, etc. |
| 60B15 | Probability measures on groups or semigroups, Fourier transforms, factorization |
| 46K10 | Representations of topological algebras with involution |
| 43A05 | Measures on groups and semigroups, etc. |
Keywords:
Banach algebras; measures on locally compact spaces; discrete hypergroups; Haar measure; Wiener property; commutative locally compact hypergroupsReferences:
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