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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; [email protected]
ANTONIOS D. MELAS
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157-84, Greece; [email protected]
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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

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