CONTENTS
Introduction.............................................................5
1. Notation, preliminaries, main definitions and solution of problem (D)...................6
1.1. Notation............................................................6
1.2. Preliminaries.......................................................7
1.3. Main definitions....................................................8
1.4. Problem (D).........................................................8
2. Examples of Λ-classes and Π-classes.....................................................9
2.1. Almost periodic, recurrent and almost automorphic functions.........9
2.2. Asymptotically recurrent and almost automorphic functions..........12
2.3. Eberlein almost periodic functions.................................14
2.4. Ergodic and totally ergodic functions..............................15
3. Problems concerning indefinite integral of TICSC-classes...............................16
3.1. Two theorems on indefinite integral and difference problem.........16
3.2. Weak classes.......................................................18
3.3. Some conditions for ergodicity.....................................19
4. Harmonic analysis for Λ-classes........................................................19
4.1. Definition and general properties of the spectrum with respect to a Λ-class $A ⊂ C_{ub}(\mathbb{J}X)$....................................20
4.2. Further properties of $σ_{A}(φ)$...................................21
5. Application to integro-differential difference equations...............................22
5.1. Reduction of equations on ℝ⁺ to equations on ℝ.....................23
5.2. Solution of problem (L) for integro-differential difference equations....................................23
References..............................................................24