It's possible that I'm missing a constant. Is there any way to directly prove this without invoking the Fourier Inversion theorem?
2026-04-03 02:59:01.1775185141
Let $u\in C^\infty_0(\mathbb{R}^d)$, then show that $u(0)=\iint u(x)e^{-2\pi ix\cdot\xi}\,\mathrm{d}x\,\mathrm{d}\xi$.
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