Universal Taylor series for non-simply connected domains
|Title:||Universal Taylor series for non-simply connected domains||Authors:||Gardiner, Stephen J.
|Permanent link:||http://hdl.handle.net/10197/2465||Date:||May-2010||Abstract:||It is known that, for any simply connected proper subdomain Omega of the complex plane and any point zeta in Omega, there are holomorphic functions on Omega that have "universal" Taylor series expansions about zeta; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in C\Omega that have connected complement. This note shows that this phenomenon can break down for non-simply connected domains Omega, even when C\Omega is compact. This answers a question of Melas and disproves a conjecture of Müller, Vlachou and Yavrian.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Elsevier||Copyright (published version):||2010 Académie des sciences||Keywords:||Taylor series; Universal functions||Subject LCSH:||Series, Taylor's
|DOI:||10.1016/j.crma.2010.03.003||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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