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Erschienen in:
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2018 | OriginalPaper | Buchkapitel

5. Admissibility: Further Developments

verfasst von : Luís Barreira, Davor Dragičević, Claudia Valls

Erschienen in: Admissibility and Hyperbolicity

Verlag: Springer International Publishing

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Abstract

In this chapter we consider various extensions of the results in the former chapters. In particular, we develop a general approach to the problem of constructing pairs of Banach spaces whose admissibility property can be used to characterize an exponential dichotomy. This generalizes and unifies some of the results in the former chapters. Moreover, we discuss what we call Pliss type theorems. These results deal with a weaker form of admissibility on the line not requiring the uniqueness condition and guarantee the existence of exponential dichotomies on both the positive and negative half-lines. Finally, we introduce the more general notion of a nonuniform exponential dichotomy and again we characterize it in terms of an appropriate admissibility property also for maps and flows.

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Vorheriges Kapitel Exponential Dichotomies: Continuous Time
Nächstes Kapitel Applications of Admissibility
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Metadaten
Titel
Admissibility: Further Developments
verfasst von
Luís Barreira
Davor Dragičević
Claudia Valls
Copyright-Jahr
2018
Buch
Admissibility and Hyperbolicity

Print ISBN: 978-3-319-90109-1

Electronic ISBN: 978-3-319-90110-7

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-90110-7_5