But how to get the Fourier transform of the zero? It seems
$$\hat{0}(x)=\int_{R} 0 e^{-2\pi i xy} dy=0$$
2026-04-14 03:30:02.1776137402
How about the Fourier transform of the constant zero?
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Wouldn't you have $$ \hat{0}(x) = \int_{\mathbb{R}} 0 e^{-2\pi i xy} dy = \int_{\mathbb{R}} 0 dy = 0 $$