An extension theorem for multi-regular function in high dimensional Clifford analysis

Abstract

In the classical complex analysis of several variables Lars Hoermander had been proven for Hartog's extension theorem. His proof is based on solving the inhomogeneous Cauchy–Riemann system. However, it is difficult when generalizing this diagram to prove this problem in Clifford analysis because of the non-commutative property. In this paper we will propose a method to overcome this difficultly and we will prove the Hartog's extension theorem for multi-regular function taking valued in Clifford algebra