The Nehari problem for the Pritchard-Salamon class of infinite- dimensional linear systems: A direct approach
type: Item
instance of: scholarly article
title: The Nehari problem for the Pritchard-Salamon class of infinite- dimensional linear systems: A direct approach
zbMATH Open document ID: 0807.47011
DOI: 10.1007/BF01192456
author: Ruth Curtain
author: Hans Zwart
published in: Integral Equations and Operator Theory
publication date: 1994-07-12T00:00:00Z
review text: The authors give an elementary derivation for the solution of the Nehari- problem for the symbol \(G(s)= C(sI- A)^{-1} B\), where \(\Sigma(A,B,C)\) is a regular Pritchard-Salamon system with \(A\) the infinitesimal generator of an exponentially stable \(C_ 0\)-semigroup on the separable Hilbert spaces \(V\), \(W\) and \(Z\). This allows for the possibility that \(B\) and \(C\) be unbounded and have infinite rank. The approach exploits properties of regular Pritchard-Salamon systems and a new idea on \(J\)- spectral factorizations due to Green et al. The approach reduces the problem to the solution of an equivalent \(J\)-spectral factorization problem for this particular realization.
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 604799
zbMATH Keywords: Nehari-problem
zbMATH Keywords: regular Pritchard-Salamon system
zbMATH Keywords: infinitesimal generator of an exponentially stable \(C_ 0\)-semigroup
zbMATH Keywords: \(J\)-spectral factorizations
zbMATH Keywords: \(J\)-spectral factorization problem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01192456
OpenAlex ID: W2109476054
description: scientific article; zbMATH DE number 604799