Hilbert boundary-value problem for a class of singular matrix-functions

We present a statement and a solution of a Hilbert boundary-value problem for $n\times n$ matrix-functions, the singularity of which is characterized by a given integral $n\times n$ matrix. For the homogeneous problem we find solvability conditions and the number of linearly independent solutions; for the nonhomogeneous problem we find conditions of solvability and the number of these solutions. We make essential use of the standard left factorization of the coefficient of the problem.