Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators

Abstract

We provide new formulas for the Wiener-Hopf factorization indices of a rational matrix function which has neither poles nor zeros on the unit circle. In addition, we recover recent results on the Fredholm characteristics of the Toeplitz operator with symbol via the method of matricial coupling. Furthermore, we present an alternative formula for the index in terms of the Fourier coefficients of R