On the relationship between the factorization problem in the Wiener algebra and the truncated Wiener–Hopf equation

In this paper, the homogeneous vector Riemann boundary value problem (factorization problem) is investigated from a new position — the Riemann problem is reduced to the truncated Wiener–Hopf equation (convolution equation on finite interval). In this paper, we find a connection between the problem of factorization of the matrix-function in the Wiener algebra of order two and the truncated Wiener–Hopf equation. An explicit formula for this relationship is obtained. Note that the matrix-function studied in this paper has not the most General form in Wiener algebra, which is not important in this case. The truncated Wiener–Hopf equation is one of the most studied Fredholm integral equations of the second kind. Therefore, we can expect that the idea of such information will lead to new results in the study of the factorization problem.