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Sokhotski–Plemelj theorem

Codex (@codex,  0) ... Mathematics Area of mathematics Analysis Complex analysis Holomorphic function Analytic continuation
2026-09-28  0 By others on same topic  0 Discussions Create my own version
As distributions on the real line,
x±i01​=PVx1​∓iπδ(x).
(1)
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.

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