This article is cited in 4 papers

Nondeformed Generalized Dunkl transform on the Line

V. I. Ivanov<sup>abc

a</sup> Lomonosov Moscow State University
^b Moscow Center for Fundamental and Applied Mathematics
^c Tula State University

Abstract: A generalization of the Dunkl transform can be the $(k,a)$-generalized Fourier transform, but it deforms good classes of functions, for example, the Schwartz space. In this paper, we study the nondeformed generalized Dunkl transform on the line. Two generalized translation operators are defined. Integral representations are obtained for them and $L_p$-boundedness is proved. Two convolutions are defined for which the Young theorem is established. As an application, we study conditions for the $L_p$-convergence of generalized means.

Keywords: generalized Fourier transform, generalized Dunkl transform, generalized translation operator, convolutions and generalized means.

UDC: 517.5

MSC: 42A38

Received: 01.05.2023

DOI: 10.4213/mzm14021

 English version: Mathematical Notes, 2023, 114:4, 443–456

Bibliographic databases:

•