Universal Taylor series, conformal mappings and boundary behaviour
|Title:||Universal Taylor series, conformal mappings and boundary behaviour||Authors:||Gardiner, Stephen J.||Permanent link:||http://hdl.handle.net/10197/5645||Date:||Dec-2013||Online since:||2014-06-18T14:08:50Z||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.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Annales De L'Institit Fourier||Journal:||Annales De L'Institit Fourier(Grenoble)||Volume:||63||Issue:||6||Start page:||327||End page:||339||Copyright (published version):||2013 the authors||Keywords:||Complex variables||Other versions:||http://arxiv.org/abs/1301.2082||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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