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Consider vector X =( X_1 ... X_N), consider the discrete Fourier transform $Y=F(X)$. I am interested to minimize $|Y|_{\infty}$, by permutation of numbers X_i, how to do it ? Here $|Y|_{\infty}$ is ...

I would like to express the integral of the absolute value of a real-valued function $f$ (over a finite interval) in terms of the Fourier coefficients of $f$. Failing that, I would like to know of any ...