Contents -- Preface -- 1. Preliminaries -- 1.1 Banach Spaces and Linear Operators -- 1.1.1 Banach Spaces -- 1.1.2 Linear Operators -- 1.1.3 Spectral Theory of Linear (Closed) Operators -- 1.1.3.1 Several Properties of Resolvents -- 1.2 Strongly Continuous Semigroups of Operators -- 1.2.1 Definition and Basic Properties -- 1.2.2 Compact Semigroups and Analytic Strongly Continuous Semigroups -- 1.2.3 Spectral Mapping Theorems -- 1.2.4 Commuting Operators -- 1.3 Spectral Theory -- 1.3.1 Introduction -- 1.3.2 Spectrum of a Bounded Function -- 1.3.3 Uniform Spectrum of a Bounded Function -- 1.3.4 Almost Periodic Functions -- 1.3.4.1 De nition and basic properties -- 1.3.5 Sprectrum of an Almost Periodic Function -- 1.3.6 A Spectral Criterion for Almost Periodicity of a Function -- 1.3.7 Almost Automorphic Functions -- 2. Stability and Exponential Dichotomy -- 2.1 Perron Theorem -- 2.2 Evolution Semigroups and Perron Theorem -- 2.3 Stability Theory -- 2.3.1 Exponential Stability -- 2.3.2 Strong Stability -- 2.4 Comments and Further Reading Guide -- 2.4.1 Further Reading Guide -- 2.4.2 Comments -- 3. Almost Periodic Solutions -- 3.1 Evolution Semigroups & Periodic Equations -- 3.1.1 An Example -- 3.1.2 Evolution Semigroups -- 3.1.3 The Finite Dimensional Case -- 3.1.4 The Infinite Demensional Case -- 3.1.5 Almost Periodic Solutions and Applications -- 3.1.5.1 Invariant functions spaces of evolution semigroups -- 3.1.5.2 Monodromy operators -- 3.1.5.3 Unique solvability of the inhomogeneous equations in P(1) -- 3.1.5.4 Unique solvability in AP(X) and exponential dichotomy -- 3.1.5.5 Unique solvability of the inhomogeneous equations in M(f) -- 3.1.5.6 Unique solvability of nonlinearly perturbed equations -- 3.1.5.7 Example 1 -- 3.1.5.8 Example 2 -- 3.2 Sums of Commuting operators -- 3.2.1 Invariant Function Spaces.

3.2.2 Differential Operator d/dt - A and Notions of Admissibility -- 3.2.3 Admissibility for Abstract Ordinary Differential Equations -- 3.2.4 Higher Order Differential Equations -- 3.2.5 Abstract Functional Differential Equations -- 3.2.6 Examples and Applications -- 3.3 Decomposition Theorem -- 3.3.1 Spectral Decomposition -- 3.3.2 Spectral Criteria For Almost Periodic Solutions -- 3.4 Comments and Further Reading Guide -- 3.4.1 Further Reading Guide -- 3.4.2 Comments -- 4. Almost Automorphic Solutions -- 4.1 The Inhomogeneous Linear Equation -- 4.2 Method of Invariant Subspaces and Almost Automorphic Solutions of Second-Order Differential Equations -- 4.3 Existence of Almost Automorphic Solutions to Semilinear Differential Equations -- 4.4 Method of Sums of Commuting Operators and Almost Automorphic Functions -- 4.5 Almost Automorphic Solutions of Second Order Evolution Equations -- 4.5.1 Mild Solutions of Inhomogeneous Second Order Equations -- 4.5.1.1 Mild Solutions -- 4.5.1.2 Mild Solutions and Weak solutions -- 4.5.2 Operators A -- 4.5.3 Nonlinear Equations -- 4.6 The Equations x'=f(t,x) -- 4.7 Comments and Further Reading Guide -- 5. Nonlinear equations -- 5.1 Periodic Solutions of Nonlinear equations -- 5.1.1 Nonlinear Equations Without Delay -- 5.1.2 Nonlinear Equations With Finite Delay -- 5.1.3 Nonlinear Equations With Infinite Delay -- 5.1.4 Non-Densely Defined Equations -- 5.2 Evolution Semigroups and Almost Periodic Solutions -- 5.2.1 Evolution Semigroups -- 5.2.2 Almost periodic solutions -- 5.2.2.1 Almost periodic solutions of di erential equations without delay -- 5.2.2.2 Almost periodic solutions of di erential equations with delays -- 5.2.2.3 Examples -- 5.3 Comments and Further Reading Guide -- 5.3.1 Further Reading Guide -- 5.3.2 Comments -- Appendix -- A.1 Lipschitz Operators -- A.2 Fixed Point Theorems.

A.3 Invariant Subspaces -- A.4 Semilinear Evolution Equations -- Bibliography -- Index.