Article
| Title: | On almost periodicity defined via non-absolutely convergent integrals (English) |
| Author: | Bugajewski, Dariusz |
| Author: | Nawrocki, Adam |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 193-214 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | almost periodic function in view of the Lebesgue measure |
| Keyword: | barrelled space |
| Keyword: | Bohr almost periodic function |
| Keyword: | Denjoy-Bochner almost periodic function |
| Keyword: | Denjoy-Perron integral |
| Keyword: | Henstock-Kurzweil integral |
| Keyword: | linear differential equation |
| MSC: | 26A39 |
| MSC: | 34A30 |
| MSC: | 42A75 |
| DOI: | 10.21136/CMJ.2024.0014-23 |
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| Date available: | 2025-03-11T16:01:02Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152904 |
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