Some questions on the relationship of the factorization problem of matrix functions and the truncated Wiener-Hopf equation in the Wiener algebra (Q2145054)

The factorization problems have a lot of applications in various branch of mathematics and other sciences. In this paper the author continues the study on the method to reduce the Riemann factorization problem of matrix functions to the truncated Wiener-Hopf equations. More general formulas for the relationship between the solutions of the factorization problem and the corresponding truncated Wiener-Hopf equation are also found. Also new results are obtained in the theory of equations in convolutions based on the revealed relationship between the problems under consideration. To do this, necessary notions, additional constructions and assumptions, and results on the topics are recalled. Then the main result (Theorem 2) is obtained on the method of reducing factorization problem to truncated Wiener-Hopf equation. Applying Theorem 2, new results are obtained in the theory of equations in convolutions on the basis of the established relationship between the considered problems.