Abstract
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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We would like to thank the referees for their valuable comments which allowed us to improve the first version of this article.
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In memory of Professor Jaroslav Kurzweil
Open access funding provided by Adam Mickiewicz University.
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Bugajewski, D., Nawrocki, A. On almost periodicity defined via non-absolutely convergent integrals. Czech Math J (2024). https://doi.org/10.21136/CMJ.2024.0014-23
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DOI: https://doi.org/10.21136/CMJ.2024.0014-23
Keywords
- almost periodic function in view of the Lebesgue measure
- barrelled space
- Bohr almost periodic function
- Denjoy-Bochner almost periodic function
- Denjoy-Perron integral
- Henstock-Kurzweil integral
- linear differential equation