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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2009
- DOI:
- 10.48550/arXiv.0911.0070
- arXiv:
- arXiv:0911.0070
- Bibcode:
- 2009arXiv0911.0070M
- Keywords:
-
- Mathematics - Complex Variables;
- 30G35;
- 31B30;
- 35G05
- E-Print:
- 10 pages, accepted for publication in CUBO, A Mathematical Journal