$α$-admissibility of the right-shift semigroup on $L^2(\mathbb{R}_+)$

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dc.creatorWynn, Andrew
dc.date2009-04-28
dc.date.accessioned2026-07-07T13:09:21Z
dc.date.available2026-07-07T13:09:21Z
dc.descriptionIt is shown that the right shift semigroup on $L^2(\mathbb{R}_+)$ does not satisfy the weighted Weiss conjecture for $α\in (0,1)$. In other words, $α$-admissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0-admissibility can be characterised by a simple growth bound. The result is proved by providing a link between discrete and continuous $α$-admissibility and then translating a counterexample for the unilateral shift on $H^2(\mathbb{D})$ to continuous time systems.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0904.4322
dc.identifierhttp://arxiv.org/abs/0904.4322
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228704
dc.subjectFunctional Analysis
dc.subject32A35, 32A36, 47D06
dc.title$α$-admissibility of the right-shift semigroup on $L^2(\mathbb{R}_+)$
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