Abstract and Applied Analysis
Volume 2006 (2006), Article ID 31641, 16 pages
Exponential dichotomy for evolution families on the real line
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 . We show that the admissibility of the pair is equivalent to the uniform exponential dichotomy of an evolution family if and only if . As applications we obtain characterizations for uniform exponential dichotomy of semigroups.