Admissibility for nonuniform \((\mu,v)\) contraction and dichotomy (Q1938290)
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scientific article; zbMATH DE number 6134158
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Admissibility for nonuniform \((\mu,v)\) contraction and dichotomy |
scientific article; zbMATH DE number 6134158 |
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Admissibility for nonuniform \((\mu,v)\) contraction and dichotomy (English)
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4 February 2013
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Summary: The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is shown that, if any of their associated \(\mathcal L^p\) spaces, with \(p \in (1, \infty]\), is admissible for a given evolution process, then this process is a nonuniform \((\mu, v)\)-contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform \((\mu, v)\)-contraction and dichotomy is provided.
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