Partial Primitives for Clifford Algebra-Valued Functions

In this paper we generalize the concept of primitivation of monogenic functions taking values in a Clifford algebra, which is on its own a generalization to higher dimension of the primitivation problem for holomorphic functions in the complex plane. This problem can be stated as follows: given a monogenic function on , i.e. a solution for the generalized Cauchy-Riemann operator D on , construct a monogenic function such that . In view of the fact that, for monogenic functions g, this can be written as g = f, a straightforward generalization consists in replacing the scalar generator of translations in the x ₀-direction by a generator of another transformation group. In this paper we consider translations in more dimensions.