Wiener-Hopf indices of unimodular functions on the imaginary axis

2024/06/13 by A. E. Frazho, Frazho, A. E., André C. M. Ran +3
Mathematics · #47A53 #47A56 #47A68 #47B35 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.09472

openalex publication_date 2024/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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