Comptes Rendus
no. 2
Potential theory/Complex analysis
Boundary behaviour of universal Taylor series
[Comportement à la frontière des séries de Taylor universelles]

Présenté par : Jean-Pierre Kahane

Stephen J. Gardiner1 ; Dmitry Khavinson2
1 School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
2 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 99-103.

Une série entière qui converge sur le disque unité D est appelée universelle si tout polynôme peut être approximé, sur tout compact de C\D ayant un complémentaire connexe, par ses sommes partielles. Cet article montre que ces séries croissent fortement et possèdent une propriété du type Picard près de chaque point de la frontière.

A power series that converges on the unit disc D is called universal if its partial sums approximate arbitrary polynomials on arbitrary compacta in C\D that have connected complement. This paper shows that such series grow strongly and possess a Picard-type property near each boundary point.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.12.008
Stephen J. Gardiner 1 ; Dmitry Khavinson 2

1 School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
2 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA 
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Stephen J. Gardiner; Dmitry Khavinson. Boundary behaviour of universal Taylor series. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 99-103. doi : 10.1016/j.crma.2013.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.008/

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☆ The first author was supported by Science Foundation Ireland under Grant 09/RFP/MTH2149, and the second author by NSF grant DMS 0855597.

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