J. Gil-Pelaez authored the 1951 Note on the inversion theorem by J. Gil-Pelaez, giving a way to recover a distribution function from its characteristic function. The primary journal byline supplies the verified initials.[ref]
Note on the inversion theorem by J. Gil-Pelaez. Biometrika 38, pp. 481–482
The inversion integrates an oscillatory expression involving the characteristic function. At a discontinuity, the formula naturally returns the midpoint of the two one-sided distribution values. Keeping this convention explicit matters for discrete laws as well as continuous ones: an inversion formula is not automatically a pointwise identity at every jump.[ref]
Note on the inversion theorem by J. Gil-Pelaez. Inversion identity, pp. 481–482
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