Exponential dichotomy for evolution families on the real line - Adina Luminiţa Sasu (Abstract and Applied Analysis)
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.