Exact observability, square functions and spectral theory
type: Item
instance of: scholarly article
title: Exact observability, square functions and spectral theory
zbMATH Open document ID: 1241.93010
author: Bernhard Haak
author: E. M. Ouhabaz
published in: Journal of Functional Analysis
publication date: 2012-03-22T00:00:00Z
review text: First, the paper introduces the notion of Backward-Forward Conditioning (BFC) system that occurs only in situations where the underlying semigroup extends to a group (unless the spectrum contains a half-plane) and generalises the notion of zero-class admissibility introduced in [\textit{G. Q. Xu}, \textit{C. Liu} and \textit{S. P. Yung}, Syst. Control Lett. 57, No.~3, 222--227 (2008; Zbl 1130.93019)]. Next, by using certain weighted square function estimates, a sufficient condition for exact and final state observability in Banach spaces is presented, that is designed for infinite-dimensional output spaces and general strongly continuous semigroups. In the case of Hilbert space, a result for contraction semigroups without an analyticity condition on the semigroup is derived.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 6017633
zbMATH Keywords: exact observability
zbMATH Keywords: final state observability
zbMATH Keywords: admissibility
zbMATH Keywords: spectral theory of semigroups and groups
zbMATH Keywords: \(H^{\infty }\) functional calculus
zbMATH Keywords: square function estimates
MaRDI profile type: Publication
full work available at URL: j.jfa.2012.01.007
OpenAlex ID: W2963539776
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DOI: 10.1016/J.JFA.2012.01.007
description: scientific article; zbMATH DE number 6017633