Journal article
Wiener's theorem on hypergroups
Annals of Functional Analysis, Vol.6(4), pp.30-59
2015
Abstract
The following theorem on the circle group T is due to Norbert Wiener: If f∈L1(T) has non-negative Fourier coefficients and is square integrable on a neighbourhood of the identity, then f∈L2(T). This result has been extended to even exponents including p=∞, but shown to fail for all other p∈(1,∞]. All of this was extended further (appropriately formulated) well beyond locally compact abelian groups. In this paper we prove Wiener's theorem for even exponents for a large class of commutative hypergroups. In addition, we present examples of commutative hypergroups for which, in sharp contrast to the group case, Wiener's theorem holds for all exponents p∈[1,∞]. For these hypergroups and the Bessel-Kingman hypergroup with parameter 12 we characterise those locally integrable functions that are of positive type and square-integrable near the identity in terms of amalgam spaces.
Details
- Title
- Wiener's theorem on hypergroups
- Authors/Creators
- W.R. Bloom (Author/Creator)J.J.F. Fournier (Author/Creator)M. Leinert (Author/Creator)
- Publication Details
- Annals of Functional Analysis, Vol.6(4), pp.30-59
- Publisher
- Duke University Press
- Identifiers
- 991005544247607891
- Murdoch Affiliation
- School of Engineering and Information Technology
- Language
- English
- Resource Type
- Journal article
Metrics
127 File views/ downloads
101 Record Views