Informace o publikaci
A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function
| Autoři | |
|---|---|
| Rok publikování | 2023 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Czechoslovak Mathematical Journal |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://doi.org/10.21136/CMJ.2023.0257-22 |
| Doi | http://dx.doi.org/10.21136/CMJ.2023.0257-22 |
| Klíčová slova | Fourier transform; Henstock-Kurzweil integral; bounded variation function |
| Popis | The paper is concerned with integrability of the Fourier sine transform function when f ? BV0(R), where BV0(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 ? L1(R). We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory. |
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