Dunkl-Poisson Equation and Related Equations in Superspace

Abstract

In this paper, we investigate the Almansi expansion for solutions of Dunkl-polyharmonic equations by the 0-normalized system for the Dunkl-Laplace operator in superspace. Moreover, applying the 0-normalized system, we construct solutions to the Dunkl-Helmholtz equation, the Dunkl-Poisson equation, and the inhomogeneous Dunkl-polyharmonic equation in superspace.

Keywords

• normalized system
• super Dunkl-Laplace operator
• Dunkl-Helmholtz equation
• Dunkl-Poisson equation
• inhomogeneous Dunkl-polyharmonic equation