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I have a function $\phi(x): \mathbb{R} \to [0, 2 \pi)$, which describes phase of another function $$f = e^{i \phi(x)}. $$ I am interested in the following problem. If I know the function/distribution $...

Given the equation $(1-\Delta)u=f$ for $f \in S(\mathbb{R}^n)$ (rapidly decreasing functions) we get by taking the Fourier transform that $u = \left(\frac{1}{2\pi}\right)^{\frac{n}{2}}\mathcal{F}^{-...