Repository logo
  • Log In
    New user? Click here to register.Have you forgotten your password?
University College Dublin
    Colleges & Schools
    Statistics
    All of DSpace
  • Log In
    New user? Click here to register.Have you forgotten your password?
  1. Home
  2. College of Science
  3. School of Mathematics and Statistics
  4. Mathematics and Statistics Research Collection
  5. Universal Taylor series for non-simply connected domains
 
  • Details
Options

Universal Taylor series for non-simply connected domains

Alternative Title
Séries universelles de Taylor pour les domaines non-simplement connexes
Author(s)
Gardiner, Stephen J.  
Tsirivas, Nikolaos  
Uri
http://hdl.handle.net/10197/2465
Date Issued
2010-05
Date Available
2010-09-28T14:19:19Z
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.
Sponsorship
Science Foundation Ireland
Type of Material
Journal Article
Publisher
Elsevier
Journal
Comptes Rendus Mathématique
Volume
348
Issue
9-10
Start Page
521
End Page
524
Copyright (Published Version)
2010 Académie des sciences
Subjects

Taylor series

Universal functions

Subject – LCSH
Series, Taylor's
Analytic functions
DOI
10.1016/j.crma.2010.03.003
Web versions
http://dx.doi.org/10.1016/j.crma.2010.03.003
Language
English
Status of Item
Peer reviewed
ISSN
1631-073X
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-sa/1.0/
File(s)
Loading...
Thumbnail Image
Name

universalnscf.pdf

Size

96.43 KB

Format

Adobe PDF

Checksum (MD5)

20838e1e1472d330a545e2be8e83e619

Owning collection
Mathematics and Statistics Research Collection

Item descriptive metadata is released under a CC-0 (public domain) license: https://creativecommons.org/public-domain/cc0/.
All other content is subject to copyright.

For all queries please contact research.repository@ucd.ie.

Built with DSpace-CRIS software - Extension maintained and optimized by 4Science

  • Cookie settings
  • Privacy policy
  • End User Agreement