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# Universal Power Series in $\mathbb{C}^N$

Published:2011-02-10
Printed: Jun 2011
• Raphaël Clouâtre,
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
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## Abstract

We establish the existence of power series in $\mathbb{C}^N$ with the property that the subsequences of the sequence of partial sums uniformly approach any holomorphic function on any well chosen compact subset outside the set of convergence of the series. We also show that, in a certain sense, most series enjoy this property.
 MSC Classifications: 32A05 - Power series, series of functions 32E30 - Holomorphic and polynomial approximation, Runge pairs, interpolation

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