Exact observability, square functions and spectral theory
Langue
en
Article de revue
Ce document a été publié dans
Journal of Functional Analysis. 2012-03-15, vol. 262, n° 6, p. 2903-2927
Elsevier
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
spectral theory of semigroups and groups
square function estimates
$H^\infty$ functional calculus
Exact observability
admissibility
Origine
Importé de halUnités de recherche