On the Relation between stability of continuous- and discrete-time evolution equations via the Cayley transform

B.Z. Guo, Heiko J. Zwart

    Research output: Contribution to journalArticleAcademicpeer-review

    24 Citations (Scopus)


    n this paper we investigate and compare the properties of the semigroup generated by $A$, and the sequence $A_d^n$, $n \in {\mathbb N}$, where $A_d= (I+A)(I-A)^{-1}$. We show that if $A$ and $A^{-1}$ generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then $A_d$ is power bounded. For analytic semigroups we can prove stronger results. If $A$ is the infinitesimal generator of an analytic semigroup, then power boundedness of $A_d$ is equivalent to the uniform boundedness of the semigroup generated by $A$.
    Original languageUndefined
    Article number10.1007/s00020-003-1350-9
    Pages (from-to)349-383
    Number of pages34
    JournalIntegral equations and operator theory
    Issue number2
    Publication statusPublished - 2006


    • MSC-34A30
    • IR-62874
    • METIS-238015
    • EWI-2774

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