On almost automorphic solutions of linear operational-differential equations

for each t ∈R. When convergence in (1.1) and (1.2) is uniform in t ∈ R, f is said to be (Bochner) almost periodic. Almost periodic functions are characterized by the following so-called Bochner’s criterion. f : R→ X is almost periodic if and only if for every sequence of real numbers (s′ n), there exists a subsequence (sn) such that (f (t+sn)) is uniformly convergent in t ∈R. For more information on almost automorphic and almost periodic functions, see, for instance, [2, 4]. We consider both differential equations