Geodesic
Generalization of two theorems of M. I. Kadets concerning the indefinite integral of abstract almost periodic functions
Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 311-321 
R. Boles Basit. Generalization of two theorems of M. I. Kadets concerning the indefinite integral of abstract almost periodic functions. Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 311-321. http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a9/
@article{MZM_1971_9_3_a9,
     author = {R. Boles Basit},
     title = {Generalization of two theorems of {M.} {I.~Kadets} concerning the indefinite integral of abstract almost periodic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {311--321},
     year = {1971},
     volume = {9},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a9/}
}
TY  - JOUR
AU  - R. Boles Basit
TI  - Generalization of two theorems of M. I. Kadets concerning the indefinite integral of abstract almost periodic functions
JO  - Matematičeskie zametki
PY  - 1971
SP  - 311
EP  - 321
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a9/
LA  - ru
ID  - MZM_1971_9_3_a9
ER  - 
%0 Journal Article
%A R. Boles Basit
%T Generalization of two theorems of M. I. Kadets concerning the indefinite integral of abstract almost periodic functions
%J Matematičeskie zametki
%D 1971
%P 311-321
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a9/
%G ru
%F MZM_1971_9_3_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions are obtained for the almost periodicity (or almost automorphy) of an abstract function $f(t)$ on a group $G$ satisfying the difference equations $f(t\gamma)-f(t)=g_\gamma(t)$, where, for each $\gamma\in G$, the function $f(t)$ is almost periodic (or almost automorphic) (the difference problem). The investigation of the almost periodicity of the integral $\int_0^x\varphi(t)dt$ of an almost periodic function $\varphi(t)$ on the real line $R$ is reduced to a study of the difference problem.