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.

In this paper, we define subspaces of L by differences using the Dunkl translation operators that we call Besov-Dunkl spaces. We provide characterization of these spaces by the Dunkl convolution.

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 ...

We continue a program generalizing classical results from the analysis on symmetric cones to Dunkl setting for root systems of type A A ...

In the present paper, we define for the Dunkl tranlation operators on the real line, the Besov–Dunkl space of functions for which the remainder in the generalized Taylor’s formula has a given order. We provide characterization of these spaces by the Dunkl convolution.

In this paper, we show the inclusion and the density of the Schwartz space in Besov–Dunkl spaces and we prove an interpolation formula for these spaces by the real method. We give another characterization for these spaces by convolution. Finally, we establish further results concerning integrability of the Dunkl transform of function in a suitable Besov–Dunkl space.

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.

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh's theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(psi,p)$-Lipschitz Dunkl condition in the space $mathrm{L}_{p,alpha}=mathrm{L}^{p}(mathbb{R},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.