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arXiv · 2412.00075

Fourier transform of composed functions

David Venhoek
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Abstract

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 $(a^2 + \sinh(bt)^2)^{-1}$.

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David Venhoek. 2024-11-26. Fourier transform of composed functions. https://arxiv.org/abs/2412.00075

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