$\alpha$-admissibility of observation and control operators
| hal.structure.identifier | INSTITUT FUER ANALYSIS | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HAAK, Bernhard H. | |
| hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
| dc.contributor.author | LE MERDY, Christian | |
| dc.date.accessioned | 2024-04-04T02:53:05Z | |
| dc.date.available | 2024-04-04T02:53:05Z | |
| dc.date.issued | 2005 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192137 | |
| dc.description.abstractEn | If $T(t) = e^{-tA}$ is a bounded strongly continuous semigroup on some Banach space $X$, and if $C\colon D(A^m)\to Y$ is a continuous mapping valued in some Banach space $Y$, we say that $C$ is $\alpha$-admissible if it satisfies an estimate of the form $\int_{0}^{\infty} t^{\alpha}\norm{CT(t)x}^2\, dt\leq M^2\norm{x}^2$. This extends the usual notion of admissibility, which corresponds to $\alpha=0$. In the case when $T(t)$ is a bounded analytic semigroup and $A$ has a `square function estimate', the second named author showed the validity of the so-called Weiss conjecture: $C$ is admissible if and only if $\{ t^{\frac{1}{2}} C(t+A)^{-1}\, :\, t>0 \}$ is a bounded set. In this paper, we extend that characterisation to our new setting. We show (under the same conditions on $T(t)$ and $A$) that $\alpha$-admissibility is equivalent to an appropriate resolvent estimate. | |
| dc.language.iso | en | |
| dc.subject.en | Control theory | |
| dc.subject.en | admissibility | |
| dc.subject.en | semigroups | |
| dc.subject.en | functional calculus | |
| dc.title.en | $\alpha$-admissibility of observation and control operators | |
| dc.type | Article de revue | |
| bordeaux.journal | Houston Journal of Mathematics | |
| bordeaux.page | 1153-1167 | |
| bordeaux.volume | 31 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00281617 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00281617v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Houston%20Journal%20of%20Mathematics&rft.date=2005&rft.volume=31&rft.issue=4&rft.spage=1153-1167&rft.epage=1153-1167&rft.au=HAAK,%20Bernhard%20H.&LE%20MERDY,%20Christian&rft.genre=article |
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