Sokhotski–Plemelj theorem
= Sokhotski–Plemelj theorem
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As distributions on the real line,
$$
\frac1{x\pm i0}
=\operatorname{PV}\frac1x\mp i\pi\delta(x).
$$
The Sokhotski--Plemelj formula relates the two boundary values of a Cauchy transform across its contour and fixes the spectral delta functions generated by retarded and advanced prescriptions.
= Sokhotski–Plemelj formula
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