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- W4205802929 abstract "Abstract In this paper, we consider an equivalence relation on the space $AP(mathbb {R},X)$ of almost periodic functions with values in a prefixed Banach space X . In this context, it is known that the normality or Bochner-type property, which characterizes these functions, is based on the relative compactness of the family of translates. Now, we prove that every equivalence class is sequentially compact and the family of translates of a function belonging to this subspace is dense in its own class, i.e., the condition of almost periodicity of a function $fin AP(mathbb {R},X)$ yields that every sequence of translates of f has a subsequence that converges to a function equivalent to f . This extends previous work by the same authors on the case of numerical almost periodic functions." @default.
- W4205802929 created "2022-01-25" @default.
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- W4205802929 date "2022-01-18" @default.
- W4205802929 modified "2023-10-18" @default.
- W4205802929 title "A note on spaces of almost periodic functions with values in Banach spaces" @default.
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- W4205802929 doi "https://doi.org/10.4153/s0008439522000042" @default.
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