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Exact observability, square functions and spectral theory

Abstract : In the first part of this article we introduce the notion of a backward-forward conditioning (BFC) system that generalises the notion of zero-class admissibiliy introduced in [Xu,Liu,Yung]. We can show that unless the spectum contains a halfplane, the BFC property occurs only in siutations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact observability in Banach spaces that is designed for infinite-dimensional output spaces and general strongly continuous semigroups. To obtain this we make use of certain weighted square function estimates. Specialising to the Hilbert space situation we obtain a result for contraction semigroups without an analyticity condition on the semigroup.
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https://hal.archives-ouvertes.fr/hal-00566394
Contributor : Bernhard H. Haak Connect in order to contact the contributor
Submitted on : Wednesday, February 16, 2011 - 9:57:20 AM
Last modification on : Saturday, December 4, 2021 - 3:42:46 AM
Long-term archiving on: : Tuesday, May 17, 2011 - 2:47:46 AM

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  • HAL Id : hal-00566394, version 1
  • ARXIV : 1102.3268

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Bernhard Hermann Haak, El-Maati Ouhabaz. Exact observability, square functions and spectral theory. Journal of Functional Analysis, Elsevier, 2012, 262 (6), pp.2903-2927. ⟨hal-00566394⟩

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