Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space

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    Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by a constant times $\log(t)$.
    Original languageEnglish
    Pages (from-to)487-494
    Number of pages8
    JournalSemigroup forum
    Issue number3
    Publication statusPublished - 2007


    • MSC-47D06
    • EWI-11962
    • IR-62177
    • METIS-247054

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