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Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.

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Poisson summation for solutions of the Burgers equation in the form 1/x

Long story short: I'm looking for a good way of showing that the Fourier transform of $1/x$ is a sign function. Motivation and why this has been a problem: I'm dealing with an equation similar to the …
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