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

Abstract

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 (ℜ(n×n)). Left standard factorization of the coefficientU(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.