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Bibliographic Details
Main Authors: Frazho, A. E., Ran, A. C. M., van Schagen, F.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.09472
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Table of Contents:
  • This paper is concerned with the Wiener-Hopf indices of unimodular rational matrix functions on the imaginary axis. These indices play a role in the Fredholm theory for Wiener-Hopf integral operators. Our main result gives formulas for the Wiener-Hopf indices in terms of the matrices appearing in realizations of the factors in a Douglas-Shapiro-Shields factorization of the unimodular function. Two approaches to this problem are presented: one direct approach using operator theoretic methods, and a second approach using the Cayley transform which allows to use results for an analogous problem regarding unimodular functions on the unit circle and corresponding Toeplitz operators.