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.
|Name||Memorandum Faculteit TW|
|Publisher||University of Twente, Department of Applied Mathematics|