Hypermonogenic solutions and plane waves of the Dirac operator in Rp×Rq

Abstract In this paper we first define hypermonogenic solutions of the Dirac operator in R p × R q and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.