Some problems concerning different types of vector valued almost periodic functions

Bolis Basit

GDML_Books, (1995), p.

Résumé

CONTENTS   Introduction.............................................................51. 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).........................................................82. 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..............................153. 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.....................................194. 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 $σ_{A}(φ)$...................................215. 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

AbstractWe study some problems concerning derivatives and indefinite integrals of elements of wide classes of functions (including almost periodic, recurrent, almost automorphic and Eberlein almost periodic functions). We introduce a notion of a spectrum of a function with respect to a class of functions. This notion enables us to investigate almost periodicity of the bounded solutions of certain functional equations.

Détail

Zbl 0828.43004

EUDML-ID : urn:eudml:doc:268610