Semigroup Methods for Systems With Unbounded Control and Observation Operators.

Let S(t) be a strongly continuous semigroup on the Hilbert space H. Let <INNOPIPE>·<INNOPIPE> 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(1.1)$$ <INNOPIPE><INNOPIPE>h<INNOPIPE><INNOPIPE>_A^2 = <INNOPIPE>h<INNOPIPE>^2 + <INNOPIPE>Ah<INNOPIPE>^2 ,{\text{ }}h \in D(A), $$ it becomes a Hilbert space and (1.2)$$ A:D(A \to H $$ is a continuous linear operator. [ABSTRACT FROM AUTHOR]