On the Volterra Factorization of the Wiener–Hopf Integral Operator

The problem of the factorization of the Wiener–Hopf integral operator in the form of the product of the upper and lower Volterra operators is considered. Conditions for the existence of such a factorization are obtained. The application of this factorization to Wiener–Hopf integral equations of the first kind can reduce the study of certain classes of such equations to that of the corresponding Volterra equations of the first kind.