Disproof of two conjectures of George Weiss

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Jacob, B. and Zwart, H.J. (2000) Disproof of two conjectures of George Weiss. [Report]

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Abstract:
Two conjectures that were posed by Weiss almost ten years ago are shown not to hold. The first conjecture states that a scalar operator is admissible if and only a certain resolvent estimate holds. The second was posed by Weiss together with Russell and states that a system is exactly observable if and only if a test similar to the Hautus test for finite-dimensional systems holds. The $C_0$-semigroup in both counter-examples is analytic and possesses a basis of eigenfunctions.
Item Type:Report
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65733
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