An application of Kronecker's theorem to rational functions
type: Item
instance of: scholarly article
title: An application of Kronecker's theorem to rational functions
zbMATH Open document ID: 0787.30001
DOI: 10.1007/BF01459731
published in: Mathematische Annalen
publication date: 1994-05-15T00:00:00Z
full work available at URL: https://eudml.org/doc/165167
review text: Let \(\sum^ \infty_{n=0} a_ n z^ n\) be the Taylor series of a rational function regular at zero. Suppose that the limit set \(L(z)\) of the sequence of the partial sums \(\sum^ N_{n=0} a_ n z^ n\), \(N=0,1,\dots,\) is contained in a finite union of circles, for any \(z\) belonging in a ``large'' subset \(E\) of the unit circle. Using Kronecker's theorem in diophantine approximation it is proven here that \(\sum^ \infty_{n=0} a_ n z^ n\) can be decomposed as a sum of two power series; one of them converges on \(E\) and the partial sums of the other lie on a finite union of circles.
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 42A99
zbMATH DE Number: 537313
author: Emmanuel S. Katsoprinakis
author: V. Nestoridis
MaRDI profile type: Publication
cites work: Q3856819
cites work: Q3310104
cites work: On a theorem of Marcinkiewicz and Zygmund for Taylor series
cites work: Partial sums of Taylor series on a circle
cites work: Limit points of partial sums of Taylor series
cites work: Distribution of Partial Sums of the Taylor Development of Rational Functions
description: scientific article; zbMATH DE number 537313