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Zeitschrift für Analysis und ihre Anwendungen


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Volume 6, Issue 1, 1987, pp. 75–82
DOI: 10.4171/ZAA/230

Published online: 1987-02-28

Martinelli–Bochner Type Formulae in Complex Clifford Analysis

Franciscus Sommen[1]

(1) Universiteit Gent, Belgium

Various types of solutions of the systems $(D_x + iD_y)f = 0$ are considered, where $D_x$ and $D_y$ are Dirac type operators in $\mathbb R^m$. Generalizing the classical Martinelli–Bochner formula for holomorphic functions, such a formula is proved for the $C_1$-solutions of this system. Martinelli–Bochner formulae are also obtained for other overdetermined systems occuring in Clifford analysis.

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Sommen Franciscus: Martinelli–Bochner Type Formulae in Complex Clifford Analysis. Z. Anal. Anwend. 6 (1987), 75-82. doi: 10.4171/ZAA/230