On a Spatial Generalization of the Complex $\Pi$-Operator
Copyright policy )On a Spatial Generalization of the Complex $\Pi$-Operator
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.
- Bauhaus University, Weimar Germany
- University of Aveiro Portugal
Pompeiu operator, Functions of hypercomplex variables and generalized variables, Transform methods (e.g., integral transforms) applied to PDEs, \(\Pi\)-operator, Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.), Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Clifford analysis
Pompeiu operator, Functions of hypercomplex variables and generalized variables, Transform methods (e.g., integral transforms) applied to PDEs, \(\Pi\)-operator, Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.), Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Clifford analysis
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