Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups
type: Item
instance of: scholarly article
title: Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups
zbMATH Open document ID: 0893.43001
DOI: 10.1007/BF01332821
author: Walter R. Bloom
author: Zengfu Xu
published in: Monatshefte für Mathematik
publication date: 1998-08-16T00:00:00Z
full work available at URL: https://eudml.org/doc/178801
review text: 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.
reviewed by: Michael Voit
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A32
zbMATH DE Number: 1145815
zbMATH Keywords: Fourier transform
zbMATH Keywords: Schwartz functions
zbMATH Keywords: Chebli-Trimeche hypergroups
zbMATH Keywords: Abel transform
zbMATH Keywords: tempered distributions
MaRDI profile type: Publication
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OpenAlex ID: W2033198446
description: scientific article; zbMATH DE number 1145815