Abstract and Applied Analysis
Volume 2006 (2006), Article ID 31641, 16 pages

Exponential dichotomy for evolution families on the real line

Adina Luminiţa Sasu

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Boulevard Vasile Pârvan No. 4, Timişoara 300223, Romania

Received 20 October 2004; Accepted 26 September 2005

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.


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