On the Relationship Between the Factorization Problem in the Wiener Algebra and the Truncated Wiener–Hopf Equation

In this paper, we study the homogeneous vector Riemann boundary value problem (the factorization problem) from a new point of view. Namely, we reduce the Riemann problem to the truncated Wiener–Hopf equation (a convolution equation in a finite interval). We establish a connection between the problem of the factorization of a matrix function in the Wiener algebra of order two and the truncated Wiener–Hopf equation and obtain an explicit formula for this relationship. Note that the form of the matrix function considered in this paper differs from its most general form in the Wiener algebra; however, in this case, this is inessential. The truncated Wiener–Hopf equation is one of the most thoroughly studied Fredholm integral equations of the second kind. Therefore, the idea of the mentioned reduction can be expected to lead to new results in studying the factorization problem.