Universal Taylor series, conformal mappings and boundary behaviour
[Séries de Taylor universelles, transformations conformes et comportement à la frontière]
Gardiner, Stephen J.
Annales de l'Institut Fourier, Tome 64 (2014), p. 327-339 / Harvested from Numdam
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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.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2849
Classification:  30K05,  30B30,  30E10,  31A05
Mots clés: Séries de Taylor universelles, transformations conformes, comportement angulaire à la frontière. 
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     author = {Gardiner, Stephen J.},
     title = {Universal Taylor series, conformal mappings and boundary behaviour},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {327-339},
     doi = {10.5802/aif.2849},
     zbl = {06387276},
     mrnumber = {3330551},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_1_327_0}
}

Gardiner, Stephen J. Universal Taylor series, conformal mappings and boundary behaviour. Annales de l'Institut Fourier, Tome 64 (2014) pp. 327-339. doi : 10.5802/aif.2849. http://gdmltest.u-ga.fr/item/AIF_2014__64_1_327_0/

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