Exact observability, square functions and spectral theory
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:18:02Z | |
| dc.date.available | 2024-04-04T02:18:02Z | |
| dc.date.created | 2011 | |
| dc.date.issued | 2012 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189278 | |
| dc.description.abstractEn | 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 admissibility introduced in Xu et al. (2008) [30]. We can show that unless the spectrum contains a half-plane, the BFC property occurs only in situations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact and final state 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. | |
| dc.language.iso | en | |
| dc.subject.en | Exact observability | |
| dc.subject.en | Final state observability | |
| dc.subject.en | Admissibility | |
| dc.subject.en | Spectral theory of semigroups and groups | |
| dc.subject.en | H∞ functional calculus | |
| dc.subject.en | Square function estimates | |
| dc.title.en | Exact observability, square functions and spectral theory | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jfa.2012.01.007 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1102.3268 | |
| bordeaux.journal | J. Funct. Analysis | |
| bordeaux.page | 2903-2927 | |
| bordeaux.volume | 262 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 262 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00992229 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00992229v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=J.%20Funct.%20Analysis&rft.date=2012&rft.volume=262&rft.issue=262&rft.spage=2903-2927&rft.epage=2903-2927&rft.au=OUHABAZ,%20El%20Maati&rft.genre=article |
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