Our paper is focused on spaces of generalized almost periodic functions which, as in classical Fourier analysis, are associated with a Fourier series with real frequencies. In fact, based on a pertinent equivalence relation defined on the spaces of almost periodic functions in Bohr, Stepanov, Weyl and Besicovitch’s sense, we refine the Bochner-type property by showing that the condition of almost periodicity of a function in any of these generalized spaces can be interpreted in the way that, with respect to the topology of each space, the closure of its set of translates coincides with its corresponding equivalence class.

中文翻译：

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广义概周期函数空间上的Bochner型性质

我们的论文集中在广义的几乎周期函数的空间上，就像经典的傅立叶分析中那样，它们与具有实频率的傅立叶级数相关联。实际上，根据在Bohr，Stepanov，Weyl和Besicovitch的意义上定义的几乎周期函数的空间的相关等价关系，我们通过证明在这些广义函数中函数的几乎周期的条件来细化Bochner型性质就每个空间的拓扑而言，可以这样解释空间：其翻译集的关闭与其对应的等价类一致。