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

  • Klaus Gürlebeck

    Bauhaus-Universität Weimar, Germany
  • Uwe Kähler

    Universidade de Aveiro, Portugal


The Π\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 Π\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 Π\Pi-operator to the solution of a hypercomplex Beltrami equation will be studied.

Cite this article

Klaus Gürlebeck, Uwe Kähler, On a Spatial Generalization of the Complex Π\Pi-Operator. Z. Anal. Anwend. 15 (1996), no. 2, pp. 283–297

DOI 10.4171/ZAA/700