no. 1
Universal Taylor series, conformal mappings and boundary behaviour
[Séries de Taylor universelles, transformations conformes et comportement à la frontière]
Gardiner, Stephen J.1
1 School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.
Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 327-339.

On dit qu’une fonction f, qui est holomorphe sur un domaine simplement connexe Ω, possède une série universelle de Taylor autour d’un point de Ω si tout polynôme sur tout compact K en-dehors de Ω peut être approximé par des sommes partielles de cette série (pourvu que le complémentaire de K soit connexe). Cet article montre que cette propriété n’est pas invariante par transformation conforme et, dans le cas où Ω est le disque unité, que ces fonctions ont un comportement extrême dans le sens des limites angulaires.

A holomorphic function f on a simply connected domain Ω is said to possess a universal Taylor series about a point in Ω if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside Ω (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where Ω is the unit disc, that such functions have extreme angular boundary behaviour.

DOI : 10.5802/aif.2849
Classification : 30K05, 30B30, 30E10, 31A05
Keywords: Universal Taylor series, conformal mappings, angular boundary behaviour.
Mot clés : Séries de Taylor universelles, transformations conformes, comportement angulaire à la frontière.

Gardiner, Stephen J. 1

1 School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland. 
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Gardiner, Stephen J. Universal Taylor series, conformal mappings and boundary behaviour. Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 327-339. doi : 10.5802/aif.2849. https://aif.centre-mersenne.org/articles/10.5802/aif.2849/

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