About Wiener–Hopf Factorization of Functionally Commutative Matrix Functions

Abstract

An algorithm of an explicit solution of the Wiener–Hopf factorization problem is proposed for functionally commutative matrix functions of a special kind. Elementary facts of the representation theory of finite groups are used. Symmetry of the matrix function that is factored out allows to diagonalize it by a constant linear transformation. Thus, the problem is reduced to the scalar case.