Hilbert's boundary-value problem (with coefficients from the Wiener ring) for matrix-valued functions analytic in the unit disk

Hilbert's boundary-value problem is stated and solved for matrix-valued functions, analytic in the unit disk, under the condition that the coefficients and the free term belong to the Wiener ring $(\mathfrak{R}_{(n\times n)})$. Left standard factorization of the coefficient $\mathfrak{U}(t)$ leads to the determination of the number of linearly independent solutions of the homogeneous problem and the number and type of conditions under which the inhomogeneous problem is solvable.