Multiparametric dissipative linear stationary dynamical scattering systems: Discrete case. II: Existence of conservative dilations
type: Item
instance of: scholarly article
title: Multiparametric dissipative linear stationary dynamical scattering systems: Discrete case. II: Existence of conservative dilations
zbMATH Open document ID: 0948.47013
DOI: 10.1007/BF01236289
published in: Integral Equations and Operator Theory
publication date: 2000-05-11T00:00:00Z
review text: The author studies multiparameter linear stationary dynamical systems (LSDSs). Such systems represent a generalization of LSDSs with discrete time \(t\in \mathbb Z\), in particular dissipative (contractive), and conservative (unitary) scattering systems, to the case \(t\in \mathbb Z^n\). The notion of a dilation of a multiparameter LSDS is introduced, and a criterion is given for existence of a conservative dilation of a dissipative system. The class of transfer functions of all dissipative scattering LSDSs (with given input and output spaces) possessing conservative dilations is characterized. It is a subclass of the generalized Schur class of operator-valued functions on the open unit polydisk.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 1417546
zbMATH Keywords: dilation
zbMATH Keywords: transfer function
zbMATH Keywords: generalized Schur class
zbMATH Keywords: multiparameter linear stationary dynamical systems
zbMATH Keywords: operator-valued functions
author: Dmitry Kaliuzhnyi-Verbovetskyi
MaRDI profile type: Publication
cites work: Q3278549
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description: scientific article; zbMATH DE number 1417546