Article
| Title: | A necessary condition for HK-integrability of the Fourier sine transform function (English) |
| Author: | Arredondo, Juan H. |
| Author: | Bernal, Manuel |
| Author: | Morales, Maria G. |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 69-84 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The paper is concerned with integrability of the Fourier sine transform function when $f\in {\rm BV}_0(\mathbb {R} )$, where ${\rm BV}_0(\mathbb {R} )$ is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of $f$ to be integrable in the Henstock-Kurzweil sense, it is necessary that $f /x \in L^1(\mathbb {R})$. We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory. (English) |
| Keyword: | Fourier transform |
| Keyword: | Henstock-Kurzweil integral |
| Keyword: | bounded variation function |
| MSC: | 26A39 |
| MSC: | 26A45 |
| MSC: | 42A38 |
| DOI: | 10.21136/CMJ.2023.0257-22 |
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| Date available: | 2025-03-11T15:56:37Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152897 |
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