Optimal time-variant systems and factorization of operators. I: Minimal and optimal systems
type: Item
instance of: scholarly article
title: Optimal time-variant systems and factorization of operators. I: Minimal and optimal systems
zbMATH Open document ID: 0927.47006
DOI: 10.1007/BF01228099
author: D. R. Pik
author: Damir Z. Arov
author: Marinus Kaashoek
published in: Integral Equations and Operator Theory
publication date: 1999-12-06T00:00:00Z
review text: The notions of optimal, and star-optimal dissipative scattering (contractive) time-invariant systems were introduced by the first author [J. Oper. Theory 2, 95-126 (1979; Zbl 0461.47005)]. The investigation of such systems was continued in the paper [\textit{D. Z. Arov, M. A. Kaashoek} and \textit{D. R. Pik}, Integral Equations Oper. Theory 29, No. 2, 127-154 (1997; Zbl 0898.47005)]. In particular, two constructions both for a minimal and optimal, and for a minimal and star-optimal contractive system (realizations) were given for prescribed Schur-class (contractive analytic) operator-valued functions as their transfer functions. In the paper under review the authors introduce the notions of optimal, and star-optimal contractive discrete time-variant systems and extend their above-mentioned results to the time-variant setting. Instead of a Schur-class operator-valued function, a contractive block lower triangular operator acting between appropriate Hilbert space vector-valued \(\ell^2\) spaces is considered, and plays a role of the input-output map of a contractive time-variant system. Two different ways of construction both for a minimal and optimal, and for a minimal and star-optimal realization of a prescribed block-triangular contraction are described.
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 1204334
zbMATH Keywords: time-variant dissipative scattering systems
zbMATH Keywords: minimal and optimal realizations
zbMATH Keywords: block-triangular contraction
reviewed by: Dmitry Kaliuzhnyi-Verbovetskyi
MaRDI profile type: Publication
cites work: Q3910973
cites work: Minimal and optimal linear discrete time-invariant dissipative scattering systems
cites work: Q4843129
cites work: Q5534423
cites work: Discrete time-variant interpolation as classical interpolation with an operator argument
cites work: Classes of linear operators. Vol. II
cites work: Q4012900
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description: scientific article; zbMATH DE number 1204334