Exponential dichotomy for evolution families on the real line

Sasu, Adina Luminiţa

doi:https://doi.org/10.1155/AAA/2006/31641

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Volume 2006 | Article ID 031641 | https://doi.org/10.1155/AAA/2006/31641

Exponential dichotomy for evolution families on the real line

Adina Luminiţa Sasu¹

Received20 Oct 2004

Accepted26 Sept 2005

Published26 Apr 2006

Abstract

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)). We show that the admissibility of the pair (Lp(ℝ,X),Lq(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.

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Copyright © 2006 Adina Luminiţa Sasu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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