On solving the second four-element Riemann-type boundary-value problem on a disk

The paper is devoted to solving one of the main four-element Riemann-type boundary-value problems in classes of piecewise-bianalytic functions with unit circumference as jump line. We prove a theorem on reduction of solving the stated problem to solving two vector-matrix Riemann problems with respect to piecewise-analytic vector-functions. Using it, we obtain an algorithm for solving the problem and conditions under which one can get a constructive and explicit solution in terms of Cauchy-type integrals. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 377–385, July–September, 2006.