Uncertainty principles for the weinstein transform

The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi’s theorem, Beurling’s theorem, and Donoho-Stark’s uncertainty principle are obtained for the Weinstein transform.     

A variant of Hardy's and Miyachi's theorems for the Bessel–Struve transform

In this paper, we establish new versions of Hardy's and Miyachi's theorems for the Bessel–Struve transform.     

An Lp-Lq-Version of Morgan’s Theorem for the Dunkl-Bessel Transform

In this paper, we give an L^p-L^q-version of Morgans theorem for the Dunkl-Bessel transform on More precisely, we prove that for all and then for all measurable function f on the conditions and imply f = 0, if and only if where are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004     

Dunkl heat semigroup and applications

In this article we characterize the Dunkl–Besov spaces and prove the embedding Sobolev theorems via the Dunkl heat semigroup. We also study the dispersive properties of the solutions of the Dunkl heat equation. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems on generalized functional spaces.     

Hypercyclic and Chaotic Convolution Associated with the Jacobi–Dunkl Operator

In this paper, we study the Jacobi–Dunkl convolution operators on some distribution spaces. We characterize the Jacobi–Dunkl convolution operators as those ones that commute with the Jacobi–Dunkl translations and with the Jacobi–Dunkl operators. Also we prove that the Jacobi–Dunkl convolution operators are hypercyclic and chaotic on the spaces under consideration and we give a universality property for the generalized heat equation associated with them.     

Global well-posedness and scattering for a class of nonlinear Dunkl–Schrödinger equations

In this paper, we introduce a class of nonlinear Schrödinger equations associated with the Dunkl operators. In this regard, we study local and global well-posedness, and the scattering theory associated with these equations.     

Strichartz estimates for the Dunkl wave equation and application

In this paper, we prove dispersive and Strichartz estimates associated for the Dunkl wave equation.