Wiener-Hopf indices of unimodular functions on the unit circle, revisited

TL;DR

This paper revisits the Wiener-Hopf indices of unimodular functions on the unit circle, offering an operator-theoretic approach that simplifies computation and provides deeper insight into these indices for rational matrix functions.

Contribution

It introduces a new operator-theoretic method to analyze Wiener-Hopf indices, improving understanding and simplifying calculations for unimodular rational matrix functions.

Findings

Provides a new operator-theoretic framework

Derives simpler formulas for Wiener-Hopf indices

Enhances understanding of unimodular matrix functions

Abstract

Inspired by the paper of Groenewald, Kaashoek and Ran (Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28, (2017), 649-710), we present an operator-theoretic approach to provide further insight and simpler computational formulas for the Wiener-Hopf indices of a rational matrix valued function taking unimodular values on the unit circle.