In this paper, we consider a q-analogue of the Dunkl operator on R, we define and study its associated Fourier transform which is a q-analogue of the Dunkl transform. In addition to several properties, we establish an inversion formula and prove a Plancherel theorem for this q-Dunkl transform. Next, we study the q-Dunkl intertwining operator and its dual via the q-analogues of the Riemann-Liouv...

In this article, we establish first a geometric Paley–Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the L p → L norm of Dunkl translations in dimension 1. Finally we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

Abstract Dunkl derivative enriches solutions by discussing parity due to its reflection operator. Very recently, one of the authors this manuscript presented most general forms that depends on three Wigner parameters have a better tuning. In manuscript, we employ latter generalized in relativistic equation examine two dimensional harmonic and anharmonic oscillators solutions. We obtain Nikiforo...

In the framework of theory Dunkl-deformed bosons, Bose-Einstein condensation two and three-dimensional Dunkl-boson gases confined in one-dimensional gravitational field is investigated. Using semi-classical approximation method, we calculate expressions Dunkl-critical temperature $T_{c}^{D}$, ground state population $\frac{N_{0}^{D}}{N}$ Dunkl-mean energy Dunkl-specific heat functions. Further ...