The growth of a semigroup and its Cayley transform

N.C. Besseling, Heiko J. Zwart

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    Abstract

    Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on a Hilbert space. We show that the powers of the Cayley transform of $A$ are bounded by a constant times $\log (n+1)$. The proof is based on Lyapunov equations.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages9
    Publication statusPublished - Apr 2011

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1941
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • MSC-34G10
    • IR-76707
    • METIS-278712
    • MSC-39A11
    • MSC-46N20
    • EWI-20080

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