The Cauchy-Riemann equation in Clifford analysis of several variables

Abstract

The aim of this article is to extend the theory of several complex variables to the non-commutativerealm. In this paper,we solve the non-homogeneous Cauchy-Riemann equation under the differential compatibility condition, find the explicit integral representation of the solution and derive the Hartogs theorem in Clifford analysis of several variables. This will generalize the corresponding results in several complex variables.