Abstract and Applied Analysis
Volume 2006 (2006), Article ID 31641, 16 pages
doi:10.1155/AAA/2006/31641
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
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.