Translation from Russian.

Includes bibliographical references.

General theorems on the factorization of matrix-valued functions. I. Fundamental theorem /; General theorems on the factorization of matrix-valued functions. II. Some tests and their consequences /; Functions with dominant mixed derivative satisfying a multiple Holder condition /; Approximation of functions in the mean by trigonometric polynomials /; decomposition of the space of quasi-polynomials (On the stability of linearized distributive systems) /; On a Tauberian theorem /; Theorems of Tauberian type in the spectral analysis of differential operators /; On the asymptotic behavior of the spectral function of a selfadjoint differential equation of the second order and on expansion in eigenfunctions /; On the spectral function of the equation " + (\lambda - q(x))y = 0 /; A limit theorem for difference operators / M. S. Budjanu and I. C. Gohberg; M. S. Budjanu and I. C. Gohberg; S. M. Nikolskii; S. M. Nikolskii; Ju. I. Neimark; M. V. Keldys; V. A. Marcenko; B. M. Levitan; B. M. Levitan; A. I. Zukov