Exact observability, square functions and spectral theory

Details Exact observability, square functions and spectral theory Exact observability, square functions and spectral theory

2011-02-16

arxiv.org/abs/1102.3268v1

Mathematics

Functional Analysis

17 pages

Scientific paper

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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