# Estimiate Fourier transform coefficients of optimial $L1$ function?

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 $$f^*$$?