Fischer decomposition by inframonogenic functions

TL;DR

This paper introduces inframonogenic functions, solutions to a new Dirac operator equation, and uses them to develop a novel Fischer decomposition for homogeneous polynomials in Euclidean space.

Contribution

It presents a new class of functions called inframonogenic functions and derives a Fischer decomposition based on these functions, extending previous harmonic and monogenic function theories.

Findings

Defined inframonogenic functions as solutions to DfD=0

Established a new Fischer decomposition for homogeneous polynomials

Extended the theory of monogenic functions with this new framework

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.