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Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 1/2, Pages 70–79 (Mi jmag483)  

A theorem on stability of the argument of characteristic function

A. I. Il'inskii

Kharkov State University, 4, Svobody Sq., 310077, Kharkov, Ukraine

Abstract: 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.

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Received: 08.12.1994
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Citation: A. I. Il'inskii, “A theorem on stability of the argument of characteristic function”, Mat. Fiz. Anal. Geom., 3:1/2 (1996), 70–79

Citation in format AMSBIB
\Bibitem{Ili96}
\by A.~I.~Il'inskii
\paper A theorem on stability of the argument of characteristic function
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 1/2
\pages 70--79
\mathnet{http://mi.mathnet.ru/jmag483}


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