Abstract
This paper is concerned with the Wiener-Hopf indices of unitary-valued 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 unitary-valued 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 unitary-valued functions on the unit circle and corresponding Toeplitz operators.
Original language | English |
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Article number | 156 |
Pages (from-to) | 1-37 |
Number of pages | 37 |
Journal | Complex Analysis and Operator Theory |
Volume | 18 |
Early online date | 21 Sept 2024 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:© The Author(s) 2024.
Funding
The work of the second author is supported in part by the National Research Foundation of South Africa (NRF), Grant Number 145688.
Funders | Funder number |
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National Research Foundation | 145688 |
Keywords
- 47A53
- 47A56
- 47A68
- 47B35
- Unitary rational matrix functions
- Wiener-Hopf indices
- Wiener-Hopf operators