## 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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### References:

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