The analytic Schwarz kernel function the real part of which is the harmonic Poisson kernel was generalized to a polyanalytic Schwarz kernel in a joint work with G. N. Hile [Rocky Mountain J. Math. 27 (1997) 669--706], see also H. Begehr [Complex Analytic Methods for Partial Differential Equations. An Introductory Text, Singapore: World Scientific 1994]. It is here used to give some higher order Cauchy-Schwarz-Pompeiu representations and to solve the Schwarz problem for the Poisson, the inhomogeneous Bitsadze and the inhomogeneous polyanalytic equation.
Cite this article
Heinrich Begehr, Dieter Schmersau, The Schwarz Problem for Polyanalytic Functions. Z. Anal. Anwend. 24 (2005), no. 2, pp. 341–351DOI 10.4171/ZAA/1244