Bulletin of the Belgian Mathematical Society - Simon Stevin

Discrete Vekua equations with constant coefficients in the complex and quaternionic case

K. Gürlebeck and A. Hommel

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 5 (2005), 689-703.

Dates
First available in Project Euclid: 7 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1110205627

Mathematical Reviews number (MathSciNet)
MR2130633

Zentralblatt MATH identifier
1071.30044

Subjects
Primary: 30G20: Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.) 30G25: Discrete analytic functions 39A10: Difference equations, additive

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

Citation

Gürlebeck, K.; Hommel, A. Discrete Vekua equations with constant coefficients in the complex and quaternionic case. Bull. Belg. Math. Soc. Simon Stevin 11 (2005), no. 5, 689--703. https://projecteuclid.org/euclid.bbms/1110205627.


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