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 thesecond kind on a finite interval \((0, \tau )\) (which is also called the truncated Wiener–Hopf equation) anda factorization problem (which is also called a vector Riemann–Hilbert boundary value problem ora vector Riemann boundary value problem). The factorization problem is associated with a familyof truncated Wiener–Hopf equations depending on the parameter \(\tau \in (0,\infty )\) . The well-posed solvability of this family of equations is shown depending onthe existence of a canonical factorization of some matrix function. In addition, various possibleapplications of the factorization problem and truncated Wiener–Hopf equations are considered.