Let $f\in L^1(\mathbb{R})\cap L^2(\mathbb{R})$. Evaluate
$$\int_{-\infty}^{\infty} \hat{f}(\xi)\overline{\hat{f}(\xi)}e^{-i\xi t}d\xi.$$
I have no idea how to proceed. Any hints?
2026-04-07 22:59:44.1775602784
Evaluate the following integral involving the product of a fourier transform and its conjugate
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