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Exponential dichotomy for evolution families on the real line

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  • Adina Luminiţa Sasu

Abstract

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair ( L p ( ℝ , X ) , L q ( ℝ , X ) ) . We show that the admissibility of the pair ( L p ( ℝ , X ) , L q ( ℝ , X ) ) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p ≥ q . As applications we obtain characterizations for uniform exponential dichotomy of semigroups.

Suggested Citation

  • Adina Luminiţa Sasu, 2006. "Exponential dichotomy for evolution families on the real line," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-16, April.
    • Handle: RePEc:hin:jnlaaa:031641
    DOI: 10.1155/AAA/2006/31641
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    Cited by:

    1. Sasu, Adina Luminiţa & Sasu, Bogdan, 2020. "Admissibility criteria for nonuniform dichotomic behavior of nonautonomous systems on the whole line," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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