Special functions and systems in Hermitian Clifford analysis

2012/05/24 by Nele De Schepper, De Schepper, Nele, Dixan Peña Peña +3
Mathematics · #Algebraic and Geometric Analysis #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #math.CV #msc:30G35 #msc:33C10 #msc:33C45

paper · pdf · doi:10.48550/arxiv.1205.5352

23 pages

arxiv created 2012/05/24 · arxiv updated 2012/05/25

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.

Related

• Hermitian Clifford Analysis and Its Connections with Representation\n Theory
• Vekua-type systems related to two-sided monogenic functions
• Hermite Polynomials in Dunkl-Clifford Analysis
• The Cauchy-Kovalevskaya Extension Theorem in Hermitean Clifford Analysis
• Holomorphic Cliffordian Functions