Admissibility of unbounded operators and wellposedness of linear systems in Banach spaces
| hal.structure.identifier | INSTITUT FUER ANALYSIS | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HAAK, Bernhard H. | |
| hal.structure.identifier | INSTITUT FUER ANALYSIS | |
| dc.contributor.author | KUNSTMANN, Peer Christian | |
| dc.date.accessioned | 2024-04-04T02:53:03Z | |
| dc.date.available | 2024-04-04T02:53:03Z | |
| dc.date.issued | 2006 | |
| dc.identifier.issn | 0378-620X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192135 | |
| dc.description.abstractEn | We study linear systems, described by operators $A$, $B$, $C$ for which the state space $X$ is a Banach space. We suppose that $-A$ generates a bounded analytic semigroup and give conditions for admissibility of $B$ and $C$ corresponding to those in G. Weiss' conjecture. The crucial assumptions on $A$ are boundedness of an $H^\infty$--calculus or suitable square function estimates, allowing to use techniques recently developed by N. Kalton and L. Weis. For observation spaces $Y$ or control spaces $U$ that are not Hilbert spaces we are led to a notion of admissibility extending previous considerations by C. Le~Merdy. We also obtain a characterisation of wellposedness for the full system. We give several examples for admissible operators including point observation and point control. At the end we study a heat equation in $X=L^p(\Omega)$, $p \in(1,\infty)$, with boundary observation and control and prove its wellposedness for several function spaces $Y$ and $U$ on the boundary $\partial\Omega$. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | control theory | |
| dc.subject.en | linear systems | |
| dc.subject.en | admissibility | |
| dc.subject.en | $H^\infty$--calculus | |
| dc.subject.en | square-function estimates | |
| dc.title.en | Admissibility of unbounded operators and wellposedness of linear systems in Banach spaces | |
| dc.type | Article de revue | |
| bordeaux.journal | Integral Equations and Operator Theory | |
| bordeaux.page | 497--533 | |
| bordeaux.volume | 55 | |
| 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-00281621 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00281621v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Integral%20Equations%20and%20Operator%20Theory&rft.date=2006&rft.volume=55&rft.issue=4&rft.spage=497--533&rft.epage=497--533&rft.eissn=0378-620X&rft.issn=0378-620X&rft.au=HAAK,%20Bernhard%20H.&KUNSTMANN,%20Peer%20Christian&rft.genre=article |
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