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arXiv · 2406.09472

Wiener-Hopf indices of unimodular functions on the imaginary axis

A. E. Frazho·A. C. M. Ran·F. van Schagen
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Abstract

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.

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BibTeXRIS

A. E. Frazho, A. C. M. Ran, F. van Schagen. 2024-06-13. Wiener-Hopf indices of unimodular functions on the imaginary axis. https://arxiv.org/abs/2406.09472

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