This volume introduces a unified and homogeneous exposition of the theory of almost automorphic functions and its applications to the fast-growing field of differential equations in abstract spaces (Banach and Hilbert spaces). It is based essentially on the work of M. Zaki, S. Zaidman, and the author during the last three decades of the 20th century. It is also the first one to present the theory of almost periodic functions in general topological vector spaces.
1 Introduction and Preliminaries.- 2 Almost Automorphic Functions with Values in a Banach Space.- 3 Almost Periodic Functions with Values in a Linear Topological Space.- 4 The Equation x?(t) = Ax(t) + f(t).- 5 The Equation x? = f(t, x).- 6 A Case of One-to-One Correspondence between Almost Automorphic and Asymptotically Almost Automorphic Solutions.- 7 Almost Periodic Solutions of the Equation x? = Ax + f in Locally Convex Spaces.- 8 Almost Periodic Solutions of Differential Equations in Normed Spaces.- References.