Fourier transform of composed functions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917852803497984 |
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| author | Venhoek, David |
| author_facet | Venhoek, David |
| contents | We prove an explicit formula for the Fourier transform of $f(u(t))$, given the Fourier transform of $f(t)$, assuming $f\in L^2(-\infty,\infty)$ and $u$ sufficiently well behaved. We illustrate its usefulness by calculating the Fourier transform of $(a^2 + \sinh(bt)^2)^{-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier transform of composed functions Venhoek, David General Mathematics 42A38 We prove an explicit formula for the Fourier transform of $f(u(t))$, given the Fourier transform of $f(t)$, assuming $f\in L^2(-\infty,\infty)$ and $u$ sufficiently well behaved. We illustrate its usefulness by calculating the Fourier transform of $(a^2 + \sinh(bt)^2)^{-1}$. |
| title | Fourier transform of composed functions |
| topic | General Mathematics 42A38 |
| url | https://arxiv.org/abs/2412.00075 |