About a theorem of Wiener on the Bessel-Kingman Hypergroup

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 .