Exact observability, square functions and spectral theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Functional Analysis Année : 2012

Exact observability, square functions and spectral theory

Résumé

In the first part of this article we introduce the notion of a backward-forward conditioning (BFC) system that generalises the notion of zero-class admissibiliy introduced in [Xu,Liu,Yung]. We can show that unless the spectum contains a halfplane, the BFC property occurs only in siutations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact observability in Banach spaces that is designed for infinite-dimensional output spaces and general strongly continuous semigroups. To obtain this we make use of certain weighted square function estimates. Specialising to the Hilbert space situation we obtain a result for contraction semigroups without an analyticity condition on the semigroup.
Fichier principal
Vignette du fichier
ex-obs-Feb2011-HAL.pdf (237.14 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00566394 , version 1 (16-02-2011)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

Bernhard Hermann Haak, El-Maati Ouhabaz. Exact observability, square functions and spectral theory. Journal of Functional Analysis, 2012, 262 (6), pp.2903-2927. ⟨hal-00566394⟩
70 Consultations
110 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More