Some problems concerning different types of vector valued almost periodic functions

Bolis Basit. Some problems concerning different types of vector valued almost periodic functions. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1995. <http://eudml.org/doc/268610>.

@book{BolisBasit1995,
abstract = {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..............................................................24AbstractWe 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.},
author = {Bolis Basit},
keywords = {almost periodicity; spectrum; indefinite intergral; intergo-differential equations; almost periodic; indefinite integral; differential-difference equation},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Some problems concerning different types of vector valued almost periodic functions},
url = {http://eudml.org/doc/268610},
year = {1995},
}

TY - BOOK
AU - Bolis Basit
TI - Some problems concerning different types of vector valued almost periodic functions
PY - 1995
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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..............................................................24AbstractWe 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.
LA - eng
KW - almost periodicity; spectrum; indefinite intergral; intergo-differential equations; almost periodic; indefinite integral; differential-difference equation
UR - http://eudml.org/doc/268610
ER -