Dunkl Hyperbolic Equations

Hypoelliptic Dunkl equations in the space of distributions on R

In this paper we define and study the Dunkl convolution product and the Dunkl transform on spaces of distributions on R. By using the main results obtained, we study the hypoelliptic Dunkl convolution equations in the space of distributions.

Nonlocal Operational Calculi for Dunkl Operators

The one-dimensional Dunkl operator Dk with a non-negative parameter k, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of Dk, satisfying this condition is studied. An operational calculus of Mikusiński type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value ...

Numerical ‎S‎olution of Two-Dimensional Hyperbolic Equations with Nonlocal Integral Conditions Using Radial Basis Functions‎

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

Asymptotic Analysis for the Dunkl Kernel

This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain. The obtained results are based on the asymptotic analysis of an associated system of ordinary differential equ...

M ar 1 99 4 Elliptic Dunkl operators , root systems , and functional equations