A Generalization of Fueter's Theorem in Dunkl-Clifford Analysis

TL;DR

This paper extends Fueter's Theorem within Dunkl-Clifford analysis to higher orders and incorporates an extra homogeneous Dunkl-monogenic polynomial, broadening its applicability.

Contribution

It introduces a higher order version of Fueter's Theorem in Dunkl-Clifford analysis and generalizes it with an additional polynomial factor.

Findings

Extended Fueter's Theorem to higher order cases.

Proved a generalized version with an extra polynomial.

Enhanced understanding of Dunkl-Clifford analysis applications.

Abstract

In this paper we first offer an alternative approach to extend the original Fueter's Theorem in Dunkl-Clifford analysis to a version of the higher order case. Then this result is used to prove a generlized version of Fueter's Theorem with an extra homogeneous Dunkl-monogenic polynomial $P_n(x_0,\underline{x})$ in $\R_1^d$ instead of the classical factor $P_n(\underline{x})$ in $\R^d$.