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||Journal:||Bulletin of the London Mathematical Society||Volume:||45||Issue:||1||Start page:||191||End page:||199||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Journals||Keywords:||Taylor series; Holomorphic functions||DOI:||10.1112/blms/bds078||Language:||en||Status of Item:||Not peer reviewed|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|
Show full item record
This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.