Holomorphic Cliffordian product

Abstract

Let $\mathbb R_{0,n}$ be the Clifford algebra of the antieuclidean vector space of dimension $n$. The aim is to built a function theory analogous to the one in the $\mathbb C$ case. In the latter case, the product of two holomorphic functions is holomorphic, this fact is, of course, of paramount importance. Then it is necessary to define a product for functions in the Clifford context. But, non-commutativity is inconciliable with product of functions. Here we introduce a product which is commutative and we compute some examples explicitely.