Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 94-103
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I. P. Kamynin. A generalization of Marcinkiewich's theorem on integer characteristic functions of probability distributions. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 94-103. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a6/
@article{ZNSL_1979_85_a6,
author = {I. P. Kamynin},
title = {A~generalization of {Marcinkiewich's} theorem on integer characteristic functions of probability distributions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {94--103},
year = {1979},
volume = {85},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a6/}
}
TY - JOUR
AU - I. P. Kamynin
TI - A generalization of Marcinkiewich's theorem on integer characteristic functions of probability distributions
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1979
SP - 94
EP - 103
VL - 85
UR - http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a6/
LA - ru
ID - ZNSL_1979_85_a6
ER -
%0 Journal Article
%A I. P. Kamynin
%T A generalization of Marcinkiewich's theorem on integer characteristic functions of probability distributions
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 94-103
%V 85
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a6/
%G ru
%F ZNSL_1979_85_a6
The result of the paper is the following one: Let the function $\varphi(z)$ be analitic and of finite order $\rho>0$ in the upper half-plane. Suppose the function $\varphi(z)$ has no zeros and satisfies the following condition: $|\varphi(z)|\leq\varphi(i\operatorname{Im}z)$. Than $\rho\leq3$.
