1.3.8 Embedding Theorems for Hölder Spaces1.3.9 The Dual Space; 1.3.10 The Schauder Fixed-Point Theorem; 1.3.11 Leray-Schauder Alternative; 1.4 Hilbert Spaces; 1.4.1 Basic Definitions; 1.4.2 Examples of Hilbert Spaces; 1.5 Exercises; 1.6 Comments; 2 Operator Theory; 2.1 Bounded Linear Operators; 2.1.1 Basic Definitions; 2.1.2 Some Classes of Bounded Operators; 2.2 Unbounded Linear Operators; 2.2.1 Basic Definitions; 2.2.2 Examples of Unbounded Operators; 2.2.3 The Adjoint Operator in Banach Spaces; 2.2.4 Spectral Theory; 2.2.5 Sectorial Operators; 2.2.6 Examples of Sectorial Operators

2.3 Exercises2.4 Comments; 3 Semi-Group of Linear Operators; 3.1 Introduction; 3.2 Semi-Group of Operators; 3.2.1 Basic Definitions; 3.2.2 Analytic Semi-Groups; 3.2.3 Hyperbolic Semi-Groups; 3.3 Evolution Families; 3.3.1 Basic Definitions; 3.3.2 Acquistapace-Terreni Conditions; 3.3.2.1 Estimates for U(t,s); 3.4 Exercises; 3.5 Comments; 4 Almost Periodic Functions and Sequences; 4.1 Introduction; 4.2 Almost Periodic Functions; 4.2.1 Basic Definitions; 4.2.2 Fourier Series Representation; 4.2.3 Composition of Almost Periodic Functions; 4.3 Asymptotically Almost Periodic Functions

4.3.1 Basic Definitions and Properties4.3.2 Composition of Asymptotically Almost Periodic Functions; 4.4 Almost Periodic Sequences; 4.4.1 Basic Definitions; 4.4.2 Properties of Almost Periodic Sequences; 4.4.3 Composition of Almost Periodic Sequences; 4.5 Asymptotically Almost Periodic Sequences; 4.5.1 Basic Definitions; 4.5.2 Properties of Asymptotically Almost Periodic Sequences; 4.6 Exercises; 4.7 Comments; 5 Nonautonomous Difference Equations; 5.1 Introduction; 5.2 Discrete Exponential Dichotomy; 5.3 The Beverton-Holt Model with Overlapping Generations; 5.4 Exercises; 5.5 Comments

6 Singular Difference Equations6.1 Introduction; 6.2 The Case of a Linear Equation; 6.2.1 Existence of a Bohr Almost Periodic Solution; 6.2.2 Existence of Besicovitch Almost Periodic Solution; 6.3 The Semilinear Equation; 6.4 Second-Order Singular Difference Equations; 6.5 Exercises; 6.6 Comments; 7 Fractional Integro-Differential Equations; 7.1 Introduction; 7.2 Preliminaries and Notations; 7.3 Main Results; 7.3.1 Existence and Uniqueness; 7.3.2 Estimates for Solutions; 7.3.3 Global Asymptotic Stability of Solutions; 7.4 Example; 7.5 Comments; 8 First-Order Semilinear Evolution Equations