Some questions on the relationship of the factorization problem of matrix functions and the truncated Wiener—Hopf equation in the Wiener algebra

The paper studies the relationship between the equation in convolutions of the second kind on a finite interval (which is also called the truncated Wiener—Hopf equation) and the factorization problem (which is also called the Riemann—Hilbert boundary value problem or the Riemann boundary value problem). In our works published in 2020–2021 (Izv. vuz.), a new approach (method) was proposed to solve the Riemann boundary value problem in the Wiener algebra of order 2. The method is to reduce the Riemann problem to the truncated Wiener—Hopf equation. In this paper, the method is being developed. Here, in the factorization problem, a matrix-function of a sufficiently general form with an arbitrary total index is studied, more general formulas for the relationship between the solutions of the factorization problem and the corresponding truncated Wiener—Hopf equation are also found. In addition, new results are obtained in the theory of equations in convolutions based on the revealed relationship between the problems under consideration.