Meromorphic Factorization Revisited and Application to Some Groups of Matrix Functions

Abstract

Some properties and applications of meromorphic factorization of matrix functions are studied. It is shown that a meromorphic factorization of a matrix function G allows one to characterize the kernel of the Toeplitz op- erator with symbol G without actually having to previously obtain a Wiener- Hopf factorization. A method to turn a meromorphic factorization into a Wiener-Hopf one which avoids having to factorize a rational matrix that ap- pears, in general, when each meromorphic factor is treated separately, is also presented. The results are applied to some classes of matrix functions for which the existence of a canonical factorization is studied and the factors of a Wiener-Hopf factorization are explicitly determined. Mathematics Subject Classification (2000). Primary 47A68; Secondary 47B35.