= Fourier inversion on a finite group
{c}
{title2=$f(x)=\sum_\rho d_\rho\operatorname{tr}(\widehat f(\rho)\rho(x)^*)$}
The <Fourier transform on a finite group> convention $\widehat f(\rho)=\mathbb E_xf(x)\rho(x)$ has the displayed inversion formula. The sum is over one representative from each equivalence class of <unitary irreducible representations>. It follows from the <Schur orthogonality relations> and the <regular representation> decomposition, and holds at every group element without a limiting argument.
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