Weakly admissible H-calculus on reflexive Banach spaces

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    Abstract

    We show that, given a reflexive Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction.
    Original languageEnglish
    Pages (from-to)796-815
    Number of pages20
    JournalIndagationes mathematicae
    Volume23
    Issue number4
    DOIs
    Publication statusPublished - Dec 2012

    Keywords

    • MSC-47A60
    • MSC-47B35
    • MSC-47D06
    • MSC-93C25
    • IR-82456
    • Weak admissibility
    • Operator semigroup
    • EWI-22631
    • METIS-296163
    • Functional calculus

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