This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001.
Inhalt
1. Introduction and Preliminaries.- 2. Almost Automorphic Functions.- 3. Almost Automorphy of the Function f(t,x).- 4. Differentiation and Integration.- 5. Pseudo Almost Automorphy.- 6. Stepanov-like Almost Automorphic Functions.- 7. Dynamical Systems and C0-Semigroups.- 8. Almost Periodic Functions with Values in a Locally Convex Space.- 9. Almost Period Functions with Values in a Non-Locally Convex Space.- 10. The Equation x'(t)=A(t)x(t)+f(t).- 11. Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces.- Bibliography.