Boundary behaviour of functions which possess universal Taylor series
|Title:||Boundary behaviour of functions which possess universal Taylor series||Authors:||Gardiner, Stephen J.||Permanent link:||http://hdl.handle.net/10197/4220||Date:||Feb-2013||Abstract:||It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\ Ω that have connected complement. This paper establishes a strong unboundedness property for such functions near every boundary point. The result is new even in the case of the disc, where it strengthens work of several authors.||Type of material:||Journal Article||Publisher:||Oxford Journals||Copyright (published version):||2013, Oxford Journals||Keywords:||Taylor series;Holomorphic functions||DOI:||10.1112/blms/bds078||Language:||en||Status of Item:||Not peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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