The Biregular Functions of Clifford Analysis: Some Special Topics

Abstract

In this paper we intend to show that certain features encountered in the theory of holomorphic functions of several complex variables, also occur in the theory of biregular functions, which are regular functions of two variables of arbitrary dimension with values in a Clifford algebra. For these functions there exist integral representations with regular and non-regular kernels, just as in the complex case. We will give a representation formula of the second kind using differential forms. Another topic is the study of the domains of bi- regularity which are the analogues of the domains of holomorphy of complex analysis. We will make it clear that multi-valued functions cannot be avoided in this study. Some examples of domains of biregula- rity will be given, by constructing biregular functions in the domains which cannot be extended to any larger domain.