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Let there be a loss function $h$ that takes an $L1$ function as input. Assume that $h$ has a finite global minima reached by a single $L1$ function $f^\ast$. In other words...

$$f^\ast = \operatorname{argmin}_{f \in L1} h(f)$$

How would we go about estimating the Fourier coefficients for the Fourier transform of $f^*$?

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