The -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 -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 -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 -Operator. Z. Anal. Anwend. 15 (1996), no. 2, pp. 283–297DOI 10.4171/ZAA/700