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Zeitschrift für Analysis und ihre Anwendungen

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Volume 27, Issue 1, 2008, pp. 53–66
DOI: 10.4171/ZAA/1343

Published online: 2008-03-31

On the Riemann–Hilbert Problem with a Piecewise Constant Matrix

Vladimir V. Mityushev[1] and Sergei V. Rogosin[2]

(1) Krakow Pedagogical Academy, Poland
(2) Belarusian State University, Minsk, Belarus

A constructive solution to the Riemann–Hilbert boundary value problem as well as to the C-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel–Schwarz transformation of the half-plane onto a circular polygon.

Keywords: Riemann–Hilbert boundary value problem, vector-matrix, C-linear conjugation problem, multiply connected domain, Christoffel–Schwarz transformation, functional equation

Mityushev Vladimir, Rogosin Sergei: On the Riemann–Hilbert Problem with a Piecewise Constant Matrix. Z. Anal. Anwend. 27 (2008), 53-66. doi: 10.4171/ZAA/1343