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June, 2009 Universal Taylor series with maximal cluster sets
Luis Bernal-González , Antonio Bonilla , María C. Calderón-Moreno , José A. Prado-Bassas
Rev. Mat. Iberoamericana 25(2): 757-780 (June, 2009).

Abstract

We link the overconvergence properties of certain Taylor series in the unit disk to the maximality of their cluster sets, so connecting outer wild behavior to inner wild behavior. Specifically, it is proved the existence of a dense linear manifold of holomorphic functions in the disk that are, except for zero, universal Taylor series in the sense of Nestoridis and, simultaneously, have maximal cluster sets along many curves tending to the boundary. Moreover, it is constructed a dense linear manifold of universal Taylor series having, for each boundary point, limit zero along some path which is tangent to the corresponding radius. Finally, it is proved the existence of a closed infinite dimensional manifold of holomorphic functions enjoying the two-fold wild behavior specified at the beginning.

Citation

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Luis Bernal-González . Antonio Bonilla . María C. Calderón-Moreno . José A. Prado-Bassas . "Universal Taylor series with maximal cluster sets." Rev. Mat. Iberoamericana 25 (2) 757 - 780, June, 2009.

Information

Published: June, 2009
First available in Project Euclid: 13 October 2009

zbMATH: 1186.30003
MathSciNet: MR2569553

Subjects:
Primary: 30B30
Secondary: 30D40 , 30E10 , 47B38

Keywords: closed linear submanifold , curve with non-total oscillation , dense linear submanifold , differential operator , maximal cluster set , universal Taylor series

Rights: Copyright © 2009 Departamento de Matemáticas, Universidad Autónoma de Madrid

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