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Admissible observation operators for the right-shift semigroup. (English) Zbl 0966.93033
The main result in this paper is that if $$A$$ is a generator of the right-shift semigroup on $$L^2[0,\infty]$$ and $$C$$ is an observation operator, mapping $$D(A)$$ into the complex numbers, then $$C$$ is infinite-time admissible if and only if $$\|C(sI- A)^{-1}\|\leq m/\sqrt{\text{Re }s}$$ for all $$s$$ in the open right half-plane. The authors proved this theorem by using Fefferman’s theorem on bounded mean oscillation and Hankel operators. This result solves a special case of a more general conjecture which says that the same equivalence is true for any strongly continuous semigroup acting on a Hilbert space. For a normal semigroup the conjecture is known to be true and then it is equivalent to the Carleson measure theorem.
Reviewer: J.Y.Park (Pusan)

##### MSC:
 93B25 Algebraic methods 93B07 Observability 93C25 Control/observation systems in abstract spaces
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