In this paper, we develop a new method for studying the inhomogeneous vector Riemann–Hilbert boundary value problem (which is also called the Riemann boundary value problem) in the Wiener algebra of order two. The method consists in reducing the Riemann problem to a truncated Wiener–Hopf equation (to a convolution equation on a finite interval). The idea of the method was proposed by the author in a previous work. Here the method is applied to the inhomogeneous Riemann boundary value problem and to matrix functions of a more general form. The efficiency of the method is shown in the paper: new sufficient conditions for the existence of a canonical factorization of the matrix function in the Wiener algebra of order two are obtained. In addition, it was established that for the correct solvability of the inhomogeneous vector Riemann boundary value problem, it is necessary and sufficient to prove the uniqueness of the solution to the corresponding truncated homogeneous Wiener–Hopf equation.

在本文中，我们开发了一种新方法，用于研究二阶Wiener代数中的不均匀向量Riemann-Hilbert边值问题（也称为Riemann边值问题）。该方法包括将Riemann问题简化为截短的Wiener-Hopf方程（有限间隔上的卷积方程）。作者在先前的工作中提出了该方法的想法。在此，该方法适用于非均匀黎曼边值问题和更通用形式的矩阵函数。本文显示了该方法的有效性：获得了新的充分条件，用于存在阶数为2的维纳代数中的矩阵函数的规范分解。此外，