About a theorem of Wiener on the Bessel-Kingman Hypergroup

TL;DR

This paper extends Wiener's theorem on the Bessel-Kingman hypergroup for parameters greater than 1/2, broadening its applicability in harmonic analysis on hypergroups.

Contribution

It generalizes Wiener's theorem to Bessel-Kingman hypergroups with parameter alpha > 1/2, expanding previous results for alpha = 1/2.

Findings

Extended Wiener's theorem to alpha > 1/2 hypergroups

Broadened the class of hypergroups where the theorem applies

Enhanced understanding of harmonic analysis on Bessel-Kingman hypergroups

Abstract

A theorem of Wiener on the circle group was strengthened and extended by Fournier in [2] to locally compact abelian groups and extended further to the Bessel-Kingman hypergroup with parameter {\alpha} = 1 / 2 by Bloom/Fournier/Leinert in [1]. We further extend this theorem to Bessel-Kingman hypergroups with parameter {\alpha} > 1 / 2 .