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Semigroup Methods for Systems With Unbounded Control and Observation Operators

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

Let S(t) be a strongly continuous semigroup on the Hilbert space H. Let |·| and (·, ·) be the norm and inner product in H. Denote by A the infinitesimal generator of S(t) and by D(A) its domain. When D(A) is endowed with the graph norm of A
$$ ||h||_A^2 = |h|^2 + |Ah|^2 ,{\text{ }}h \in D(A), $$
(1.1)
it becomes a Hilbert space and
$$ A:D(A \to H $$
(1.2)
is a continuous linear operator.

Keywords

Control Operator Real Hilbert Space Parabolic System Regularity Result Continuous Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2007

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