Introduction to Hypercomplex Analysis

In this paper, we give a basic introduction to hypercomplex analysis, in particular its functional analytic and function theoretical foundations. As it is well known, there is no function theory in higher dimensions that incorporates all tools from complex analysis. Here, we use an approach where the field of complex numbers is replaced by Clifford algebras. The main advantage of this approach consists of the possibility to combine many of the algebraic and geometrical properties of complex numbers. After a short introduction, we develop the necessary tools from a functional analytic and function theoretical point of view.