Semigroup Methods for Systems With Unbounded Control and Observation Operators

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


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
$$ ||h||_A^2 = |h|^2 + |Ah|^2 ,{\text{ }}h \in D(A), $$
it becomes a Hilbert space and
$$ A:D(A \to H $$
is a continuous linear operator.


Control Operator Real Hilbert Space Parabolic System Regularity Result Continuous Semigroup 


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Copyright information

© Birkhäuser Boston 2007

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