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Zeitschrift für Analysis und ihre Anwendungen

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Volume 24, Issue 2, 2005, pp. 341–351
DOI: 10.4171/ZAA/1244

Published online: 2005-06-30

The Schwarz Problem for Polyanalytic Functions

Heinrich Begehr[1] and Dieter Schmersau[2]

(1) Freie Universität Berlin, Germany
(2) Freie Universität Berlin, Germany

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.

Keywords: Schwarz kernel, Poisson equation, Bitsadze equation, polyanalytic equation, Schwarz boundary value problem

Begehr Heinrich, Schmersau Dieter: The Schwarz Problem for Polyanalytic Functions. Z. Anal. Anwend. 24 (2005), 341-351. doi: 10.4171/ZAA/1244