A generalization of universal Taylor series in simply connected domains
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|Title:||A generalization of universal Taylor series in simply connected domains||Authors:||Tsirivas, Nikolaos||Permanent link:||http://hdl.handle.net/10197/3893||Date:||Apr-2012||Abstract:||Let Ω be a simply connected proper subdomain of the complex plane and z0 be a point in Ω. It is known that there are holomorphic functions f on Ω for which the partial sums (Sn(f,z0)) of the Taylor series about z0 have universal approximation properties outside Ω. In this paper we investigate what can be said for the sequence (βnSn(f,z0)) when (βn) is a sequence of complex numbers. We also study a related analogue of a classical theorem of Seleznev concerning the case where the radius of convergence of the universal power series is zero.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Elsevier||Journal:||Journal of Mathematical Analysis and Applications||Volume:||388||Issue:||1||Start page:||261||End page:||369||Copyright (published version):||2011 Elsevier Inc||Keywords:||Universal series; Cesàro hypercyclicity; Universality; Hypercyclicity; Bernstein–Walsh Theorem; Seleznev Theorem||Subject LCSH:||Series, Taylor's||DOI:||10.1016/j.jmaa.2011.11.038||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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