Fischer decomposition by inframonogenic functions

Helmuth R. Malonek; Dixan Peña; Frank Sommen

doi:10.4067/S0719-06462010000200012

Authors

Helmuth R. Malonek Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal.
Dixan Peña Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal.
Frank Sommen Department of Mathematical Analysis, Ghent University, 9000 Gent, Belgium.

DOI:

https://doi.org/10.4067/S0719-06462010000200012

Keywords:

Inframonogenic functions, Fischer decomposition

Abstract

Let âˆ‚_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 âˆ‚_xfâˆ‚_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.