Correlations between the maximum modulus and maximum term of random entire functions (in Ukrainian) |
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| Author |
Lviv University, Department of Mechanics and Mathematics
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| Abstract |
Let $\{X_n\}$ be a uniformly bounded sequence of
independent random variables with the zero mean value. For entire
functions of the form $\Sigma a_n X_n(t) z^n $
it is proved that Wiman's inequality can be improved to
$M_f(r,t)\le \mu_f(t)~\ln^{1/4}\mu_f(r)~\ln^{1+\delta}\ln\mu_f(r)$,
for almost every~$t$ and all $r>1$ except a set $E(\delta,t)$ of
finite logarithmic measure.
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| Keywords |
uniformly bounded sequence, independent random variables, zero mean, entire functions, Wiman's inequality, maximal term, logarithmic measure
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| DOI |
doi:10.30970/ms.7.2.157-166
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Reference |
1. Ж.П. Кахан, Случайные функциональные ряды. — М.: Наука, 1973. 302с.
2. P.C. Rosenbloom, Probability and entire functions // Stud. Math. Anal. Related Topics. Stanford: Calif. Univ. Press. 1962. P.325–332. 3. P. Erdös, A.R ényi, On random entire functions // Zastos. Mat. – 1969. V.10. P.47–55. 4. J. Jakubowski, S. Kwapień, On multiplicative systems of functions // Bull. L'Acad. Pol. Sci. 1979. V.27. P.689–694. |
| Pages |
157-166
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| Volume |
7
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| Issue |
2
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| Year |
1997
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| Journal |
Matematychni Studii
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| Full text of paper | |
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