Discrete Vekua equations with constant coefficients in the complex and quaternionic case
Gürlebeck, K. ; Hommel, A.
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 689-703 / Harvested from Project Euclid
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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.
Publié le : 2005-03-14
Classification:  finite difference equations,  complex and quaternionic Vekua equations,  discrete holomorphic functions,  inhomogeneous equations,  30G20,  30G25,  39A10 
@article{1110205627,
     author = {G\"urlebeck, K. and Hommel, A.},
     title = {Discrete Vekua equations with constant coefficients in the complex and
quaternionic case},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 689-703},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1110205627}
}

Gürlebeck, K.; Hommel, A. Discrete Vekua equations with constant coefficients in the complex and
quaternionic case. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  689-703. http://gdmltest.u-ga.fr/item/1110205627/