On conditions for the well-posed solvability of a factorization problem and a class of truncated Wiener—Hopf equations

This paper continues the study of the relationship between the convolution equation of the second kind on a finite interval $(0, \tau)$ (which is also called the truncated Wiener—Hopf equation) and a factorization problem (which is also called a vector Riemann—Hilbert boundary value problem or a vector Riemann boundary value problem). The factorization problem is associated with a family of truncated Wiener—Hopf equations depending on the parameter $\tau\in(0, \infty)$. The well-posed solvability of this family of equations is shown depending on the existence of a canonical factorization of some matrix function. In addition, various possible applications of the factorization problem and truncated Wiener—Hopf equations are considered.