Generalization of two theorems of M. I. Kadets concerning the indefinite integral of abstract almost periodic functions
Tóm tắt
Conditions are obtained for the almost periodicity (or almost automorphy) of an abstract functionf (t) on a group G satisfying the difference equationsf (tγ)−f(t)=gγ(t), where, for each γ ∃ G, the function ℕ(t) is almost periodic (or almost automorphic) (the difference problem). The investigation of the almost periodicity of the integral
$$\int\limits_0^x {\varphi (t){\text{ }}dt}$$
of an almost periodic function ϕ(t) on the real line R is reduced to a study of the difference problem.
Tài liệu tham khảo
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