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
it becomes a Hilbert space and
is a continuous linear operator.
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© 2007 Birkhäuser Boston
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(2007). Semigroup Methods for Systems With Unbounded Control and Observation Operators. In: Representation and Control of Infinite Dimensional Systems. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4581-6_6
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DOI: https://doi.org/10.1007/978-0-8176-4581-6_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4461-1
Online ISBN: 978-0-8176-4581-6
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