The monogenic Cauchy-Kovalevskaya extension in two vector variables

The Cauchy-Kovalevskaya extension for polynomials in several variables is a crucial result in Clifford analysis which describes theoretically how to construct simplicial monogenics in m dimensions starting from certain polynomial spaces in m - 1 dimensions, hereby using the so-called branching rules. In [13] it was shown that the Cauchy-Kovalevskaya extension map is an isomorphism of the kernel of the wedge operator onto the space of spherical monogenics in two variables. The aim of this paper is to show that this extension maps simplicial polynomials of the kernel of the wedge operator just onto the simplicial monogenics.