Fischer decomposition by inframonogenic functions

Abstract

Let D denote the Dirac operator in the Euclidean space R^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 DfD=0. The solutions of this "sandwich" equation, which we call inframonogenic functions, are used to obtain a new Fischer decomposition for homogeneous polynomials in R^m.

10 pages, accepted for publication in CUBO, A Mathematical Journal

Cited by in corpus (1)

• The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces