Universal Taylor series

Vassili Nestoridis

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 5, page 1293-1306
  • ISSN: 0373-0956

Abstract

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We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a G δ -dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.

How to cite

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Nestoridis, Vassili. "Universal Taylor series." Annales de l'institut Fourier 46.5 (1996): 1293-1306. <http://eudml.org/doc/75213>.

@article{Nestoridis1996,
abstract = {We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a $G_\delta $-dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.},
author = {Nestoridis, Vassili},
journal = {Annales de l'institut Fourier},
keywords = {generic property; overconvergence; power series; limit set; rational functions},
language = {eng},
number = {5},
pages = {1293-1306},
publisher = {Association des Annales de l'Institut Fourier},
title = {Universal Taylor series},
url = {http://eudml.org/doc/75213},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Nestoridis, Vassili
TI - Universal Taylor series
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 5
SP - 1293
EP - 1306
AB - We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a $G_\delta $-dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.
LA - eng
KW - generic property; overconvergence; power series; limit set; rational functions
UR - http://eudml.org/doc/75213
ER -

References

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  14. [14] V. NESTORIDIS, Limit points of partial sums of Taylor series, Matematika, 38 (1991), 239-249. Zbl0759.30003MR93f:30004
  15. [15] V. NESTORIDIS, Distribution of partial sums of the Taylor development of rational functions, Transactions of A.M.S., 346, n° 1 (1994), 283-295. Zbl0818.30001MR95i:30003
  16. [16] V. NESTORIDIS, S. K. PICHORIDES, The circular structure of the set of limit points of partial sums of Taylor series, Séminaire d'Analyse Harmonique, Université de Paris-Sud, Mathématiques, Orsay, France (1989-1990), 71-77. Zbl0724.41025MR92h:30005
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  18. [18] A. ZYGMUND, Trigonometric Series, second edition reprinted, Vol. I, II, Cambridge University Press, 1979. 

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