Almost Periodic and Almost Automorphic Functions in Abstract Spaces

Description

Preface to the First Edition Preface to the Second Edition Contents 1 Introduction and Preliminaries 1 Banach Spaces 2 Lp Spaces 3 Linear Operators 4 Functions with Values in a Banach Space 5 Semigroups of Linear Operators 6 Topological Vector Spaces 7 The Exponential of a Bounded Linear Operator 8 Non-locally Convex Spaces 2 Almost Automorphic Functions 1 Almost Automorphic Functions in a Banach Space 2 Weak Almost Automorphy 3 Almost Automorphic Sequences 3.1 Kadets Theorem 4 Asymptotically Almost Automorphic Functions 3 Almost Automorphy of the Function f(t,x) 1 The Nemytskii's Operator 4 Differentiation and Integration 1 Differentiation in AA(X) 2 Integration in AA(X) 3 Differentiation in WAA(X) 4 Integration in AAA(X) 5 Pseudo Almost Automorphy 1 Pseudo Almost Automorphic Functions 2 μ-Pseudo Almost Automorphic Functions 6 Stepanov-like Almost Automorphic Functions 1 Definitions and Properties 7 Dynamical Systems and C0-Semigroups 1 Abstract Dynamical Systems 2 Complete Trajectories 8 Almost Periodic Functions with Values in a Locally Convex Space 1 Almost Periodic Functions 2 Weakly Almost Periodic Functions 3 Almost Periodicity of the Function f(t,x) 4 Equi-Asymptotically Almost Periodic Functions 9 Almost Periodic Functions with Values in a Non-locally Convex Space 1 Definitions and Properties 2 Weakly Almost Periodic Functions 3 Applications 10 The Equation x'(t)=A(t)x(t)+f(t) 1 The Equation x'(t)=A(t)x(t)+f(t) 11 Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces 1 Linear Equations 1.1 The Homogeneous Equation x'=Ax 1.2 The Inhomogeneous Case Appendix Appendix References