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2018 | OriginalPaper | Chapter

5. Admissibility: Further Developments

Authors : Luís Barreira, Davor Dragičević, Claudia Valls

Published in: Admissibility and Hyperbolicity

Publisher: 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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previous chapter Exponential Dichotomies: Continuous Time
next chapter Applications of Admissibility
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Metadata
Title
Admissibility: Further Developments
Authors
Luís Barreira
Davor Dragičević
Claudia Valls
Copyright Year
2018
Book
Admissibility and Hyperbolicity

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

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

Copyright Year: 2018

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

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