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Abstract

Notation. Throughout this chapter, U, X and Y are complex Hilbert spaces which are identified with their duals. \( \mathbb{T} \) is a strongly continuous semigroup on X, with generator A : D(A)→X and growth bound ω0 (\( \mathbb{T} \)). Remember that we use the notation A and \( \mathbb{T}_t \) also for the extension of the original generator to X and for the extension of the original semigroup to X−1. Recall also that X 1 d is D(A*) with the norm \( ||z||_1^d = ||(\bar \beta I - A*)z|| \) and X −1 d is the completion of X with respect to the norm \( ||z||_{ - 1}^d = ||(\bar \beta I - A*)^{ - 1} z|| \). Recall that X−1 is the dual of X 1 d with respect to the pivot space X.

Keywords

Weak Solution Control Operator Input Function Input Space 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 Verlag AG 2009

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