Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 2, pp. 361  377 (1999) 

Iterated Integral Operators in Clifford AnalysisH. BegehrH. Begehr: Freie Universität Berlin, I. Math. Inst., Arnimallee 3, D14195 BerlinAbstract: Integral representation formulas of CauchyPompeiu type expressing Cliffordal\ge\bravalued functions in domains of $\R^m$ through its boundary values and its first order derivatives in form of the Dirac operator are iterated in order to get higher order CauchyPompeiu formulas. In the most general representation formulas obtained the Dirac operator is replaced by products of powers of the Dirac and the Laplace operator. Boundary values of lower order operators are involved too. In particular the integral operators provide particular solutions to the inhomogeneous equations $\pa^kw = f$, $\Delta^kw = g$ and $\pa\Delta^kw = h$. The main subject of this paper is to develop the representation formulas. Properties of the integral operators are not studied here. Keywords: CauchyPompeiu representations, Dirac operator, Laplace operator, Clifford analysis Full text of the article:
Electronic fulltext finalized on: 31 Jul 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
