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In the book Gaussian Measures in Finite and Infinite Dimensions by Stroock, there is a theorem with a comment The following remarkable theorem was discovered by Cramér and Lévy. So far as I know, ...

Let $\varphi(x)=\frac{1}{\sqrt{2\pi}}\exp(-x^2/2)$ be the Gaussian density and $f:\mathbb{R}\to\mathbb{R}$ another measurable function. Under what conditions can $f$ be recovered from its convolution ...