[Sur le comportement des séries entières en lʼabsence de lacunes de Hadamard–Ostrowski]
Nous montrons que les sommes partielles dʼune série entière f de rayon de convergence 1 tendent vers ∞ en capacité sur les ensembles compacts (arbitrairement grands) du complémentaire du disque unité fermé si f ne contient pas de lacunes de Hadamard–Ostrowski. Tenant compte dʼun résultat récent de Gardiner, ceci couvre une grande classe de fonctions f holomorphes sur le disque unité.
We show that the partial sums of a power series f with radius of convergence one tend to ∞ in capacity on (arbitrarily large) compact subsets of the complement of the closed unit disk, if f does not have so-called Hadamard–Ostrowski gaps. Regarding a recent result of Gardiner, this covers a large class of functions f holomorphic in the unit disk.
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@article{CRMATH_2013__351_7-8_255_0,
author = {Kalmes, Thomas and M\"uller, J\"urgen and Nie{\ss}, Markus},
title = {On the behaviour of power series in the absence of {Hadamard{\textendash}Ostrowski} gaps},
journal = {Comptes Rendus. Math\'ematique},
pages = {255--259},
publisher = {Elsevier},
volume = {351},
number = {7-8},
year = {2013},
doi = {10.1016/j.crma.2013.04.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.04.012/}
}
TY - JOUR AU - Kalmes, Thomas AU - Müller, Jürgen AU - Nieß, Markus TI - On the behaviour of power series in the absence of Hadamard–Ostrowski gaps JO - Comptes Rendus. Mathématique PY - 2013 SP - 255 EP - 259 VL - 351 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.04.012/ DO - 10.1016/j.crma.2013.04.012 LA - en ID - CRMATH_2013__351_7-8_255_0 ER -
%0 Journal Article %A Kalmes, Thomas %A Müller, Jürgen %A Nieß, Markus %T On the behaviour of power series in the absence of Hadamard–Ostrowski gaps %J Comptes Rendus. Mathématique %D 2013 %P 255-259 %V 351 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.04.012/ %R 10.1016/j.crma.2013.04.012 %G en %F CRMATH_2013__351_7-8_255_0
Kalmes, Thomas; Müller, Jürgen; Nieß, Markus. On the behaviour of power series in the absence of Hadamard–Ostrowski gaps. Comptes Rendus. Mathématique, Tome 351 (2013) no. 7-8, pp. 255-259. doi : 10.1016/j.crma.2013.04.012. http://www.numdam.org/articles/10.1016/j.crma.2013.04.012/
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