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arXiv · 1102.3268

Exact observability, square functions and spectral theory

Bernhard Hermann Haak·El-Maati Ouhabaz
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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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Bernhard Hermann Haak, El-Maati Ouhabaz. 2011-02-16. Exact observability, square functions and spectral theory. https://arxiv.org/abs/1102.3268

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