Admissibility for nonuniform \((\mu,v)\) contraction and dichotomy
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.
scientific article; zbMATH DE number 6134158
scientific article