Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T05:57:47.779Z Has data issue: false hasContentIssue false
  • English
  • Français

RESTRICTED UNIVERSALITY OF POWER SERIES

Published online by Cambridge University Press:  23 October 2001

JEAN-PIERRE KAHANE  and
ANTONIOS D. MELAS
JEAN-PIERRE KAHANE
Affiliation:
Batiment 425 (Mathematique), Université de Paris-Sud, 91405 Orsay Cedex, France; jean-pierre.kahane@math.u-psud.fr
ANTONIOS D. MELAS
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157-84, Greece; amelas@math.uoa.gr
Get access

Abstract

We prove the existence of a power series having radius of convergence 0, whose partial sums have universal approximation properties on any compact set with connected complement that is contained in a finite union of circles centred at 0 and having rational radii, but do not have such properties on any compact set with nonempty interior. This relates to a theorem of A. I. Seleznev.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 5 , September 2001 , pp. 543 - 552
Copyright
© The London Mathematical Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)