Associated Spaces in Clifford Analysis

In this paper we give a characterization of all linear first order partial differential operators with Clifford-algebra-valued coefficients that are associated to the generalized Cauchy-Riemann operator. In order to achieve our goal, we make use of a rule for D(u·v), where u and v are Clifford-algebra-valued functions. As an application, the solvability of initial value problems involving these operators is shown.