On Conditions for the Well-Posed Solvability of a Factorization Problem and a Class of Truncated Wiener–Hopf Equations

Abstract

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.