Universal functions on nonsimply connected domains
- [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
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topMelas, 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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- A. Melas, V. Nestoridis, Universality of Taylor series as a generic property of holomorphic functions, Adv. in Math. 157 (2001), 138-176 Zbl0985.30023MR1813429
- V. Nestoridis, Universal Taylor series, Ann. Inst. Fourier, (Grenoble) 46 (1996), 1293-1306 Zbl0865.30001MR1427126
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