ON THE KERNEL OF THE (κ,a)-GENERALIZED FOURIER TRANSFORM

作     者：Gorbachev, Dmitry V. Ivanov, V.I. Tikhonov, S.Y.U. 

作者机构：Tula State University Department of Applied Mathematics and Computer Science Tula300012 Russia Centre de Recerca Matemàtica Campus de Bellaterra Edifici C Bellaterra Barcelona08193 Spain ICREA Universitat Autònoma de Barcelona Pg. Lluís Companys 23 Barcelona08010 Spain 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Fourier transforms 

摘      要：For the kernel Bκ,a(x, y) of the (κ, a)-generalized Fourier transform Fκ,a, acting in L2(Rd) with the weight |x|a-2vκ(x), where vκ is the Dunkl weight, we study the important question of when kBκ,ak∞ = Bκ,a(0, 0) = 1. The positive answer was known for d ≥ 2 and a2 ∈ N. We investigate the case d = 1 and a2 ∈ N. Moreover, we give sufficient conditions on parameters for kBκ,ak∞ 1 to hold with d ≥ 1 and any a. We also study the image of the Schwartz space under the Fκ,a transform. In particular, we obtain that Fκ,a(S(Rd)) = S(Rd) only if a = 2. Finally, extending the Dunkl transform, we introduce non-deformed transforms generated by Fκ,a and study their main *** Codes 42B10, 33C45, 33C52 Copyright © 2022, The Authors. All rights reserved.