A new systems theory perspective on canonical Wiener-Hopf factorization on the unit circle

2024/09/25 by S. ter Horst, ter Horst, Sanne, Mikael Kurula +3 · 1 citation
Computer Science · Mathematics · #47A48 #47A56 #93B28 #93C05 #93D25 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Dynamics and Pattern Formation #Primary 47A68 #Secondary 47A63 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.17324

openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 and the origin 0, and that have the form G(z)=I+F(z) with F(z) taking strictly contractive values on the unit circle. 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 systems, together with associated Krein space theory, to derive explicit formulas for the left and right canonical factorizations.

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• Canonical Wiener-Hopf factorization on the unit circle: matching subspaces versus Riccati equations

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