Work

A New Systems Theory Perspective on Canonical Wiener-Hopf Factorization on the Unit Circle

Year: 2025

Type: article

Abstract: We establish left and right canonical factorizations of Hilbert-space operator-valued functions G ( z ) that are analytic on neighborhoods of the complex unit circle $${\mathbb {T}}$$ T and the origin 0 and that have the form $$G(z)=I+F(z)$$ G ( z ) = I + F ( z ) with F ( z ) taking strictly contractive values on $${\mathbb {T}}$$ T . Such functions can be realized as transfer functions of infinite dimensional dichotomous discrete-time linear systems, and we employ the strict bounded real lemma for this class of operators, together with associated Kreĭn space theory, to derive explicit formulas for the left and right canonical factorizations.

Source: Integral Equations and Operator Theory

DOI: 10.1007/s00020-025-02813-x

Authors: S. ter Horst, M. Kurula, A. C. M. Ran

Institutions: North-West University, Åbo Akademi 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: $3,290

Funders: National Research Foundation, Magnus Ehrnroothin Säätiö, North-West University