Weak admissibility does not imply admissibility for analytic semigroups
Zwart, Hans and Jacob, Birgit and Staffans, Olof (2003) Weak admissibility does not imply admissibility for analytic semigroups. Systems & control letters, 48 (34). pp. 341350. ISSN 01676911

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Abstract:  Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator defined on an infinitedimensional Hilbert space is an admissible control operator if for every element the vector defines an admissible control operator. The other conjecture says that is an admissible control operator if a certain resolvent estimate is satisfied. The examples given in this paper show that even for analytic semigroups the conjectures do not hold. In the last section we construct a semigroup example showing that the first estimate in the HilleYosida theorem is not sufficient to conclude boundedness of the semigroup. 
Item Type:  Article 
Copyright:  © 2003 Elsevier 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/68872 
Official URL:  http://dx.doi.org/10.1016/S01676911(02)002773 
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