Generalization of two theorems of M.\,I.~Kadets concerning the indefinite integral of abstract almost periodic functions

R. Boles Basit

Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 311-321.

Résumé

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.