Parseval identity
= Parseval identity
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{wiki}
= Parseval's identity
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{synonym}
For $f,g\in L^2(\mathbb R^n)$ and the convention $\widehat f(\xi)=\int f(x)e^{-ix\cdot\xi}\,dx$,
$$
\int_{\mathbb R^n}f(x)\overline{g(x)}\,dx
=\frac1{(2\pi)^n}\int_{\mathbb R^n}\widehat f(\xi)\overline{\widehat g(\xi)}\,d\xi.
$$