Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 70-79
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A. I. Il'inskii. A theorem on stability of the argument of characteristic function. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 70-79. http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a6/
@article{JMAG_1996_3_1_a6,
author = {A. I. Il'inskii},
title = {A theorem on stability of the argument of characteristic function},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {70--79},
year = {1996},
volume = {3},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a6/}
}
TY - JOUR
AU - A. I. Il'inskii
TI - A theorem on stability of the argument of characteristic function
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 1996
SP - 70
EP - 79
VL - 3
IS - 1
UR - http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a6/
LA - en
ID - JMAG_1996_3_1_a6
ER -
%0 Journal Article
%A A. I. Il'inskii
%T A theorem on stability of the argument of characteristic function
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 1996
%P 70-79
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a6/
%G en
%F JMAG_1996_3_1_a6
Let $f(x)$ be the characteristic function of a probability distribution on the line. If $1-|f(t)|\le\varepsilon$ for $|t|\le a$ and, moreover, $\varepsilon\le C_1$, then $$ \min_{\beta\in R} \max_{|t|\leq a}|\arg f(t)-\beta t|\leq C_2\varepsilon^{3/4}, $$ where $C_1$, $C_2$ are suitable absolute constants.
