Power series with fast decreasing coefficients
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 167-175
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $f(x)=\sum_{n=0}^\infty a_nx^n$ be an analytic function in the unit disc such that for
some $\lambda>1$, $C_0,C_1,C_2,C_3>0$ we have
$$
|f(x)|\le C_0\exp(-C_1|\log(1-x)|^\lambda),\qquad\frac121
$$
and
$$|a_n|\le C_2\exp\biggl(-C_3\frac{\sqrt n}{\log(n+2)}\biggr),\qquad n\ge0.
$$
Then $f\equiv0$. Bibl. – 5 titles.
@article{ZNSL_2010_376_a6,
author = {A. M. Chirikov},
title = {Power series with fast decreasing coefficients},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {167--175},
publisher = {mathdoc},
volume = {376},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a6/}
}
A. M. Chirikov. Power series with fast decreasing coefficients. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 167-175. http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a6/