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Stephen J. Gardiner
Universal Taylor series, conformal mappings and boundary behaviour
(Séries de Taylor universelles, transformations conformes et comportement à la frontière)
Annales de l'institut Fourier, 64 no. 1 (2014), p. 327-339, doi: 10.5802/aif.2849
Article PDF | Reviews MR 3330551 | Zbl 06387276
Class. Math.: 30K05, 30B30, 30E10, 31A05
Keywords: Universal Taylor series, conformal mappings, angular boundary behaviour.

Résumé - Abstract

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

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