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Exact observability, square functions and spectral theory
Language
en
Article de revue
This item was published in
J. Funct. Analysis. 2012, vol. 262, n° 262, p. 2903-2927
English 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 admissibility introduced in Xu et al. (2008) [30]. We can show that unless ...Read more >
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 admissibility introduced in Xu et al. (2008) [30]. We can show that unless the spectrum contains a half-plane, the BFC property occurs only in situations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact and final state 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.Read less <
English Keywords
Exact observability
Final state observability
Admissibility
Spectral theory of semigroups and groups
H∞ functional calculus
Square function estimates
Origin
Hal imported