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.
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.
Accepted:
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Thomas Kalmes 1; Jürgen Müller 1; Markus Nieß 2
@article{CRMATH_2013__351_7-8_255_0, author = {Thomas Kalmes and J\"urgen M\"uller and Markus Nie{\ss}}, 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}, }
TY - JOUR AU - Thomas Kalmes AU - Jürgen Müller AU - Markus Nieß 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 DO - 10.1016/j.crma.2013.04.012 LA - en ID - CRMATH_2013__351_7-8_255_0 ER -
Thomas Kalmes; Jürgen Müller; Markus Nieß. On the behaviour of power series in the absence of Hadamard–Ostrowski gaps. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 255-259. doi : 10.1016/j.crma.2013.04.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.04.012/
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