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I am working on a research problem which leads to the following optimization problem: \begin{equation} \hat{M} = \operatorname*{arg\,max}_M \Bigl\lVert\sum_{k=0}^{M-1} {\mathbf y}_k \exp\left(-j 2\pi ...

What are the continuous functions $f$ such that on $\mathbb{R}^{+*}$: $$f(x) - \frac{C}{x} \hat{f}(\frac{1}{x}) =x^{\alpha}$$ Where $\hat{f}$ is the Fourier transform of $f(|x|)$ and $C$ a constant....