Article
| Title: | The Fourier transform in Lebesgue spaces (English) |
| Author: | Talvila, Erik |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 179-191 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | For each $f\in L^p({\mathbb R)}$ ($1\leq p<\infty $) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each $p$, a norm is defined so that the space of Fourier transforms is isometrically isomorphic to $L^p({\mathbb R)}$. There is an exchange theorem and inversion in norm. (English) |
| Keyword: | Fourier transform |
| Keyword: | Lebesgue space |
| Keyword: | tempered distribution |
| Keyword: | generalised function |
| Keyword: | Banach space |
| Keyword: | continuous primitive integral |
| MSC: | 26A42 |
| MSC: | 42A38 |
| MSC: | 46B04 |
| MSC: | 46F10 |
| DOI: | 10.21136/CMJ.2024.0001-23 |
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| Date available: | 2025-03-11T16:00:23Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152903 |
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| Reference: | [14] Talvila, E.: Fourier transform inversion using an elementary differential equation and a contour integral.Am. Math. Mon. 126 (2019), 717-727. Zbl 1422.42007, MR 4009888, 10.1080/00029890.2019.1632629 |
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