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 ...

Let (X, ω) be a symplectic orbifold which is locally like the quotient of a Z2 action on R . Let A ((~)) X be a deformation quantization of X constructed via the standard Fedosov method with characteristic class being ω. In this paper, we construct a universal deformation of the algebra A ((~)) X parametrized by codimension 2 components of the associated inertia orbifold X̃ . This partially conf...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

By using the symmetry of Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and logarithmic Sobolev for transform. Combining these inequalities, obtain new, short proof Heisenberg-type uncertainty principles in setting. Moreover, by combining Nash’s inequality, Carlson’s Sobolev’s embedding theorems transform, new inequalities involving L∞-norm. Finally, Lp-spaces, from which de...

Abstract Recently, deformed quantum systems have received lots of attention in the literature. Dunkl formalism differs from others by containing difference-differential and reflection operator. It is one most interesting deformations since it let us discuss solutions according to even odd solutions. In this work, we studied ideal Bose gas blackbody radiation via formalism. To end, made a liaiso...