Geodesic
On representation of the logarithm for arbitrary characteristic function on segments
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 262-281

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We consider a characteristic function of arbitrary probability law. We obtain analogs of the Lévy–Khintchine formula for it on any segment of the form $[-r,r]$ with finite $r>0$, where the characteristic function does not vanish. Using these representations we prove a criterion of belonging of the corresponding distribution function to the new wide class of so called quasi-infinitely divisible distribution functions. 
@article{ZNSL_2022_510_a15,
     author = {A. A. Khartov},
     title = {On representation of the logarithm for arbitrary characteristic function on segments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {262--281},
     publisher = {mathdoc},
     volume = {510},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a15/}
}
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A. A. Khartov. On representation of the logarithm for arbitrary characteristic function on segments. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 262-281. http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a15/