Universal functions on nonsimply connected domains

Antonios D. Melas[1]

  • [1] University of Athens, Department of Mathematics, Panepistimiopolis 157-84, Athens (Greece)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 6, page 1539-1551
  • ISSN: 0373-0956

Abstract

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We establish certain properties for the class 𝒰 ( Ω , ζ 0 ) of universal functions in Ω with respect to the center ζ 0 ∈ Ω , for certain types of connected non-simply connected domains Ω . In the case where ℂ / Ω is discrete we prove that this class is G δ -dense in H ( Ω ) , depends on the center ζ 0 and that the analog of Kahane’s conjecture does not hold.

How to cite

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Melas, Antonios D.. "Universal functions on nonsimply connected domains." Annales de l’institut Fourier 51.6 (2001): 1539-1551. <http://eudml.org/doc/115958>.

@article{Melas2001,
abstract = {We establish certain properties for the class $\{\mathcal \{U\}\}(\Omega ,\zeta _0)$ of universal functions in $\Omega $ with respect to the center $\zeta _0\in \Omega $, for certain types of connected non-simply connected domains $\Omega $. In the case where $\{\mathbb \{C\}\}/\Omega $ is discrete we prove that this class is $G_\delta $-dense in $H(\Omega )$, depends on the center $\zeta _0$ and that the analog of Kahane’s conjecture does not hold.},
affiliation = {University of Athens, Department of Mathematics, Panepistimiopolis 157-84, Athens (Greece)},
author = {Melas, Antonios D.},
journal = {Annales de l’institut Fourier},
keywords = {power series; overconvergence; complex approximation; holomorphic function; universal function},
language = {eng},
number = {6},
pages = {1539-1551},
publisher = {Association des Annales de l'Institut Fourier},
title = {Universal functions on nonsimply connected domains},
url = {http://eudml.org/doc/115958},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Melas, Antonios D.
TI - Universal functions on nonsimply connected domains
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 6
SP - 1539
EP - 1551
AB - We establish certain properties for the class ${\mathcal {U}}(\Omega ,\zeta _0)$ of universal functions in $\Omega $ with respect to the center $\zeta _0\in \Omega $, for certain types of connected non-simply connected domains $\Omega $. In the case where ${\mathbb {C}}/\Omega $ is discrete we prove that this class is $G_\delta $-dense in $H(\Omega )$, depends on the center $\zeta _0$ and that the analog of Kahane’s conjecture does not hold.
LA - eng
KW - power series; overconvergence; complex approximation; holomorphic function; universal function
UR - http://eudml.org/doc/115958
ER -

References

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  1. G. Costakis, Some remarks on universal functions and Taylor series, Math. Proc. of the Cambr. Phil. Soc. 128 (2000), 157-175 Zbl0956.30003MR1724436
  2. K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. of the AMS 36 (1999), 345-381 Zbl0933.47003MR1685272
  3. J.-P. Kahane, Baire's category Theorem and Trigonometric series, Jour. Anal. Math. 80 (2000), 143-182 Zbl0961.42001MR1771526
  4. W. Luh, Universal approximation properties of overconvergent power series on open sets, Analysis 6 (1986), 191-207 Zbl0589.30003MR832744
  5. A. Melas, V. Nestoridis, Universality of Taylor series as a generic property of holomorphic functions, Adv. in Math. 157 (2001), 138-176 Zbl0985.30023MR1813429
  6. V. Nestoridis, Universal Taylor series, Ann. Inst. Fourier, (Grenoble) 46 (1996), 1293-1306 Zbl0865.30001MR1427126
  7. V. Nestoridis, An extension of the notion of universal Taylor series, Proceedings CMFT'97, Nicosia, Cyprus, Oct. (1997) Zbl0942.30003
  8. V. Vlachou, A universal Taylor series in the doubly connected domain ℂ ∖ { 1 }  Zbl1049.30002

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