Fischer decomposition by inframonogenic functions

Abstract

Let ∂_x denote the Dirac operator in â„^m. In this paper, we present a refinement of the biharmonic functions and at the same time an extension of the monogenic functions by considering the equation ∂_xf∂_x = 0. The solutions of this “sandwich” equation, which we call inframonogenic functions, are used to obtain a new Fischer decomposition for homogeneous polynomials in â„^m.