On the factorization of matrix and operator Wiener–Hopf integral equations

Abstract

Let be a Wiener–Hopf operator, , , and let be the adjoint operator, , , where belongs to the Banach space of Bochner strongly integrable functions with values in a Banach algebra . We consider the canonical factorization problem , where is the identity operator and (resp. ) is a left (resp. right) triangular convolution operator such that the operators are invertible in the spaces , . We put forward a semi-inverse factorization method and prove that the canonical factorization exists if and only if the operators and are invertible in .