Special functions and systems in Hermitian Clifford analysis

TL;DR

This paper explores new special functions such as Hermite polynomials, Bessel functions, and generalized powers within Hermitian Clifford analysis, providing insights into Dirac-like systems in complex variables and deriving a Vekua system for solutions.

Contribution

It introduces new special functions in Hermitian Clifford analysis and derives a Vekua system for solutions in axially symmetric domains.

Findings

Introduction of Hermite polynomials, Bessel functions, and generalized powers in Hermitian Clifford analysis

Derivation of a Vekua system for solutions in axially symmetric domains

Enhanced understanding of Dirac-like systems in several complex variables

Abstract

In this paper we study some new special functions that arise naturally within the framework of Hermitian Clifford analysis, which concerns the study of Dirac-like systems in several complex variables. In particular we focus on Hermite polynomials, Bessel functions and generalized powers. We also derive a Vekua system for solutions of Hermitian systems in axially symmetric domains.