On some constructive methods for the matrix Riemann–Hilbert boundary-value problem

Abstract

In this paper we consider the relations between the Riemann–Hilbert monodromy problem and the matrix Riemann–Hilbert boundary-value problem with piecewise continuous coefficient and construct the so-called canonical matrix for the boundary-value problem for a piecewise continuous matrix-function. The formula for the calculation of the index is also obtained.