On the Existence of Almost Automorphic Solutions to Some Abstract Hyperbolic Differential Equations (Report‪)‬

1 Introduction Let (X, [parallel]*[parallel]) be a Banach space and let [X.sub.[alpha]], for [alpha] [member of] (0,1), be an abstract intermediate Banach space between D(A), the domain of a linear operator A defined on X, and X. Examples of those [X.sub.[alpha]] include, among others, the fractional spaces D([(-A).sup.[alpha]]), the reel interpolation spaces [D.sub.A]([alpha], [infinity]) due to both Lions and Peetre, and the Holder spaces [D.sub.A]([alpha]), which coincide with the continuous interpolation spaces that had been introduced in the literature by Da Prato and Grisvard.