The Weiss conjecture on admissibility of observation operators for contraction semigroups

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

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Abstract

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.

Item Type:	Article
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.
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:	08 Feb 2013 17:02
Published Version:	http://www.springerlink.com/openurl.asp?genre=arti...
Status:	Published
Refereed:	Yes
Identification Number:	10.1007/BF01301467
URI:	http://eprints.whiterose.ac.uk/id/eprint/759

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