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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 2, 1996, pp. 283–297
DOI: 10.4171/ZAA/700

Published online: 1996-06-30

On a Spatial Generalization of the Complex $\Pi$-Operator

Klaus Gürlebeck[1] and Uwe Kähler[2]

(1) Bauhaus-Universität Weimar, Germany
(2) Universidade de Aveiro, Portugal

The $\Pi$-operator plays a mayor role in complex analysis, especially in the theory of generalized analytic functions in the sense of Vekua. The present paper deals with a hyper-complex generalization of the complex $\Pi$-operator which turns out to have most of the useful properties of its complex origin such as mapping properties and invertibility. At the end an application of the generalized $\Pi$-operator to the solution of a hypercomplex Beltrami equation will be studied.

Keywords: Clifford analysis, integral transforms, $\Pi$-operator, hypercomplex Beltrami equation

Gürlebeck Klaus, Kähler Uwe: On a Spatial Generalization of the Complex $\Pi$-Operator. Z. Anal. Anwend. 15 (1996), 283-297. doi: 10.4171/ZAA/700