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- W1506708145 abstract "Given a Hilbert space and the generator A of a strongly continuous, exponentially stable, semigroup on this Hilbert space. For any g( s) 2 H1 we show that there exists an inf nite-time admissible output operator g(A). If g is rational, then this operator is bounded, and equals the normal def nition of g(A). In particular, when g(s) = 1/(s + �), � 2 C + , then this admissible output operator equals (�I A) 1 . Although in general g(A) may be unbounded, we always have that g(A) multiplied by the semigroup is a bounded operator for every (strictly) positive time instant. Furthermore, when there exists an admissible output operator C such that (C,A) is exactly observable, then g(A) is bounded for all g's with g( s) 2 H1. I. I NTRODUCTION" @default.
- W1506708145 created "2016-06-24" @default.
- W1506708145 creator A5041102285 @default.
- W1506708145 date "2010-07-01" @default.
- W1506708145 modified "2023-10-18" @default.
- W1506708145 title "An H∞ calculus of admissible operators" @default.
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