Universal functions on nonsimply connected domains
Annales de l'Institut Fourier, Volume 51 (2001) no. 6, p. 1539-1551

We establish certain properties for the class $𝒰\left(\Omega ,{\zeta }_{0}\right)$ 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 $ℂ/\Omega$ is discrete we prove that this class is ${G}_{\delta }$-dense in $H\left(\Omega \right)$, depends on the center ${\zeta }_{0}$ and that the analog of Kahane’s conjecture does not hold.

Dans le cas de certains domaines non simplement connexes, nous établissons l'existence et la résidualité de fonctions universelles par rapport à un centre. Nous examinons aussi l'analogue de la conjecture de Kahane.

DOI : https://doi.org/10.5802/aif.1865
Classification:  30B30,  30B10
Keywords: power series, overconvergence, complex approximation
@article{AIF_2001__51_6_1539_0,
author = {Melas, Antonios D.},
title = {Universal functions on nonsimply connected domains},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {51},
number = {6},
year = {2001},
pages = {1539-1551},
doi = {10.5802/aif.1865},
zbl = {0989.30003},
mrnumber = {1870639},
language = {en},
url = {http://www.numdam.org/item/AIF_2001__51_6_1539_0}
}

Melas, Antonios D. Universal functions on nonsimply connected domains. Annales de l'Institut Fourier, Volume 51 (2001) no. 6, pp. 1539-1551. doi : 10.5802/aif.1865. http://www.numdam.org/item/AIF_2001__51_6_1539_0/

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