Universal Taylor series, conformal mappings and boundary behaviour

2013/01/10 by Stephen J. Gardiner, Gardiner, Stephen J. · 1 citation
Mathematics · #30B30 #30E10 #30K05 #31A05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30B30 #msc:30E10 #msc:30K05 #msc:31A05

paper · pdf · doi:10.48550/arxiv.1301.2082

12 pages. To appear in Annales de l'Institut Fourier (Grenoble)

arxiv created 2013/01/10 · arxiv updated 2013/01/11

Abstract

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.

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