The aims of these lecture notes are twofold. On the one hand, they are meant as an
introduction to rational and trigonometric Dunkl theory, starting with the historical examples …

In this paper we study a translation operator associated with the n-dimensional (k, 1)-
generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In …

The-generalised Fourier transform is the unitary operator defined using the-deformed Dunkl
harmonic oscillator. The main aim of this paper is to prove-boundedness of-generalised …

In this paper, we present the basic k-Hankel wavelet theory. Next, we study the
boundedness and compactness of localization operators associated with k-Hankel wavelet …

We introduce the notion of the (k, a)-generalized wavelet multipliers. Particular cases of such
generalized wavelet multipliers are the classical and Dunkl wavelet multipliers. The …

Abstract For the kernel $ B_ {\kappa, a}(x, y) $ of the $(\kappa, a) $-generalized Fourier
transform $\mathcal {F} _ {\kappa, a} $, acting in $ L^{2}(\mathbb {R}^{d}) $ with the weight …

In this paper, we introduce the k-generalized Stockwell transform on R. We investigate for
this transform the main theorems of Harmonic analysis as Plancherel's, Calderón's, and …

In this paper, we introduce a family of one-dimensional maximal operators M κ, m, κ≥ 0 and
m∈ N∖{0}, which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 …

A product formula and a convolution structure for a k-Hankel transform on R - ScienceDirect Skip
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In this paper, we investigate the k-Hankel Gabor transform on R d in some problems of time–
frequency analysis. Firstly, we present the main theorems of Harmonic analysis as …