Hermite Polynomials in Dunkl-Clifford Analysis

TL;DR

This paper extends classical Hermite polynomials to Clifford-Dunkl analysis, establishing their properties, differential equations, and basis functions within a new algebraic framework.

Contribution

It introduces a generalized Hermite polynomial framework in Clifford-Dunkl analysis, including orthogonality, recurrence relations, and basis construction.

Findings

Hermite polynomials are generalized to Clifford-Dunkl operators.

Orthogonality relations and recurrence formulas are established.

An orthonormal basis for related Hilbert modules is constructed.

Abstract

In this paper we present a generalization of the classical Hermite polynomials to the framework of Clifford-Dunkl operators. Several basic properties, such as orthogonality relations, recurrence formulae and associated differential equations, are established. Finally, an orthonormal basis for the Hilbert modules arising from the corresponding weight measures is studied.