Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups
The Fourier transform of Schwartz functions on Chebli-Trimeche hypergroups is investigated in this paper in a systematic way, where the notions of Schwartz functions are adapted from spherical Schwartz functions on noncompact symmetric spaces. The results are based essentially on estimates for hypergroup characters due to Chebli, Trimeche, and later on Zeuner. Except for the basic properties of Schwartz spaces, the authors also discuss some connections with the Abel transform and specific approximate identities on various function spaces. Finally, hypergroup convolutions of tempered distributions and Schwartz functions are studied.
scientific article; zbMATH DE number 1145815