Jacob, B. and Partington, J.R. (2001) The Weiss conjecture on admissibility of observation operators for contraction semigroups. Integral Equations and Operator Theory, 40 (2). pp. 231-243. ISSN 0378-620X
We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functional C is infinite-time admissible if and only if there is an M > 0 such that parallel to IC(sI - A)(-1)parallel to less than or equal to M/root Re s for all s in the open right half-plane. Here A denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators.
|Copyright, Publisher and Additional Information:||Copyright © 2001 Birkhauser Verlag. This is an author produced version of a paper published in Integral Equations and Operator Theory. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds)|
|Depositing User:||Sherpa Assistant|
|Date Deposited:||25 Oct 2005|
|Last Modified:||28 Oct 2016 23:34|