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Admissibility: Further Developments

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Admissibility and Hyperbolicity

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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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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Luís Barreira & Claudia Valls

  2. Department of Mathematics, University of Rijeka, Rijeka, Croatia

    Davor Dragičević

Authors
  1. Luís Barreira
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  2. Davor Dragičević
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  3. Claudia Valls
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Barreira, L., Dragičević, D., Valls, C. (2018). Admissibility: Further Developments. In: Admissibility and Hyperbolicity. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-90110-7_5

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