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Fourier transform of composed functions (2412.00075v1)
Published 26 Nov 2024 in math.GM
Abstract: We prove an explicit formula for the Fourier transform of $f(u(t))$, given the Fourier transform of $f(t)$, assuming $f\in L2(-\infty,\infty)$ and $u$ sufficiently well behaved. We illustrate its usefulness by calculating the Fourier transform of $(a2 + \sinh(bt)2){-1}$.
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