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Exponential expansiveness and complete admissibility for evolution families. (English) Zbl 1080.34546

Summary: Connections between uniform exponential expansiveness and complete admissibility of the pair \((c_0({\mathbb N}, X),c_0({\mathbb N}, X))\) are studied. A discrete version for a theorem due to N.Van Minh, F.Räbiger and R.Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.

MSC:

34E05 Asymptotic expansions of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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