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Nonuniform exponential dichotomies and admissibility. (English) Zbl 1221.34141
The authors investigate the relation between the notions of exponential stability and admissibility, in the general context of nonuniform exponential behavior. It is shown that, with respect to certain adapted norms related to the nonuniform behavior, if any $L^p$ ($1<p\leq \infty$) space is admissible for a given evolution process, then this process is a nonuniform exponential dichotomy. For each nonuniform exponential dichotomy, the paper provides a collection of admissible Banach spaces.

34D09Dichotomy, trichotomy
34D08Characteristic and Lyapunov exponents
34C45Invariant manifolds (ODE)
34D10Stability perturbations of ODE
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