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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {1979},
     volume = {85},
     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/