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March 2005 Discrete Vekua equations with constant coefficients in the complex and quaternionic case
K. Gürlebeck, A. Hommel
Bull. Belg. Math. Soc. Simon Stevin 11(5): 689-703 (March 2005). DOI: 10.36045/bbms/1110205627

Abstract

A discrete version of complex Vekua type equations is considered. We construct a repre\-sentation formula for the solution of the homogeneous complex equation and investigate the inhomogeneous equation. Similar to the continuous case this representation formula is a product of two functions. We also factorize the solution of a homogeneous Vekua type equation in the quaternionic case. In the complex plane we analyse both factors in detail and study the relation between the non-holomorphic factors in the discrete and continuous case.

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K. Gürlebeck. A. Hommel. "Discrete Vekua equations with constant coefficients in the complex and quaternionic case." Bull. Belg. Math. Soc. Simon Stevin 11 (5) 689 - 703, March 2005. https://doi.org/10.36045/bbms/1110205627

Information

Published: March 2005
First available in Project Euclid: 7 March 2005

zbMATH: 1071.30044
MathSciNet: MR2130633
Digital Object Identifier: 10.36045/bbms/1110205627

Subjects:
Primary: 30G20 , 30G25 , 39A10

Keywords: complex and quaternionic Vekua equations , discrete holomorphic functions , finite difference equations , inhomogeneous equations

Rights: Copyright © 2005 The Belgian Mathematical Society

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Vol.11 • No. 5 • March 2005
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