Partial primitives for Clifford algebra-valued functions (Q2457862)

The authors 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 \(f(x_{0}, \underline{x})\) on \(\mathbb{R}^{m+1}\), i.e. a solution for the generalized Cauchy-Riemann operator \(D\) on \(\mathbb{R}^{m+1}\), construct a monogenic function \(g(x_{0}, \underline{x})\) such that \(\overline{D}g=f\). In view of the fact that, for monogenic functions \(g\), this can be written as \(\partial_{x_{0}g}=f\), a straightforword generalization consists in replacing the scalar generator \(\partial_{x_{0}}\) of translations in the \(x_{0}\)-direction by a generator of another transformation group. In this paper they consider translations in more dimensions.