Work

Wiener-Hopf Indices of Unitary-Valued Functions on the Imaginary Axis

Year: 2024

Type: article

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.

Source: Complex Analysis and Operator Theory

DOI: 10.1007/s11785-024-01606-1

Authors: A. E. Frazho, A. C. M. Ran, F. van Schagen

Institutions: Purdue University West Lafayette, North-West University, Vrije Universiteit Amsterdam

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: National Research Foundation