Geodesic
Weak stability of I.~Marcinkievicz's theorem and some inequalities for characteristic functions
Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 193-196

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We investigate weak stability of the well known theorem due to I. Marcinkiewicz which asserts that $\exp P(t)$ ($P(t)$ is an algebraical polynomial) can be a characteristic function only if the degree of $P(t)$ is not greater than 2. Some other simple inequalities for characteristic functions are also established. 
@article{ZNSL_1979_85_a15,
     author = {N. A. Sapogov},
     title = {Weak stability of {I.~Marcinkievicz's} theorem and some inequalities for characteristic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {193--196},
     publisher = {mathdoc},
     volume = {85},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a15/}
}
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N. A. Sapogov. Weak stability of I.~Marcinkievicz's theorem and some inequalities for characteristic functions. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 193-196. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a15/