Computational Methods and Function Theory 10 (2010), No. 1, 249--263
Copyright Heldermann Verlag 2010
Sirkka-Liisa Eriksson
Sirkka-Liisa.Eriksson@tut.fi , Tampere University of Technology, Department of Mathematics, P.O. Box 527, FI-33101 Tampere, Finland.
Heikki Orelma
Heikki.Orelma@tut.fi , Tampere University of Technology, Department of Mathematics, P.O. Box 527, FI-33101 Tampere, Finland.
In this paper we study geometric algebra valued null solutions of the equation $$ D_\ell f-\frac{k}{x_0}Q_0f=0 $$ on the upper half $\mathbb{R}^{n+1}\cap\{x_0>0\}$, where $D_\ell$ is the Dirac operator and $Q_0$ is a projection-type mapping. Null solutions are called hypergenic functions. We will also study their local properties and integral representations.
Keywords: Hypergenic function, Cauchy formula, Borel-Pompeiu formula, multivector function.
MSC 2000: 30G35, 30A05.
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