HAAK, Bernhard H.; KUNSTMANN, Peer Christian

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

HAAK, Bernhard H.
INSTITUT FUER ANALYSIS
Institut de Mathématiques de Bordeaux [IMB]

KUNSTMANN, Peer Christian
INSTITUT FUER ANALYSIS

Idioma

Article de revue

Este ítem está publicado en

Integral Equations and Operator Theory. 2006, vol. 55, n° 4, p. 497--533

Springer Verlag

Resumen en inglés

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 $\partial\Omega$.< Leer menos

Palabras clave en inglés

control theory

linear systems

admissibility

$H^\infty$--calculus

square-function estimates

Metadatos

Compartir este ítem

Licencia de uso del documento

Admissibility of unbounded operators and wellposedness of linear systems in Banach spaces

Idioma

Este ítem está publicado en

Resumen en inglés

Palabras clave en inglés

URI

Orígen

Centros de investigación