Disproof of two conjectures of George Weiss

B. Jacob, Birgit Jacob, Heiko J. Zwart

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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.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages23
    Publication statusPublished - 2000

    Publication series

    NameMemorandum Faculteit TW
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1546
    ISSN (Print)0169-2690

    Keywords

    • METIS-141343
    • IR-65733
    • EWI-3366
    • MSC-93A05
    • MSC-93B07
    • MSC-93C25
    • MSC-47D60

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