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arXiv · 2002.03202

Admissibility and general dichotomies for evolution families

Davor Dragicevic·Nevena Jurcevic Pecek·Nicolae Lupa
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Abstract

For an arbitrary noninvertible evolution family on the half-line and for $\rho \colon [0, \infty)\to [0, \infty)$ in a large class of rate functions, we consider the notion of a $\rho$-dichotomy with respect to a family of norms and characterize it in terms of two admissibility conditions. In particular, our results are applicable to exponential as well as polynomial dichotomies with respect to a family of norms. As a nontrivial application of our work, we establish the robustness of general nonuniform dichotomies.

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Davor Dragicevic, Nevena Jurcevic Pecek, Nicolae Lupa. 2020-02-08. Admissibility and general dichotomies for evolution families. https://arxiv.org/abs/2002.03202

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