关于通过非绝对收敛积分定义的几乎周期性

Pub Date : 2024-04-02 DOI:10.21136/cmj.2024.0014-23

Dariusz Bugajewski, Adam Nawrocki

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引用次数: 0

摘要

.我们研究了通过 Denjoy-Perron（或等价于 Henstock-Kurzweil）积分定义的几乎周期函数的规范空间的一些性质。特别是，我们证明了这个空间是条形的，而不是完整的。我们还证明了一个线性二导方程，其非同调项为此类几乎周期性的函数，在所考虑的类中有一个解。

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On almost periodicity defined via non-absolutely convergent integrals

. We investigate some properties of the normed space of almost periodic functions which are deﬁned via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear diﬀerential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.

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