Universal functions on nonsimply connected domains

Melas, Antonios D.

doi:10.5802/aif.1865

Universal functions on nonsimply connected domains
[Fonctions universelles dans des domaines non simplement connexes]

Melas, Antonios D.¹

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

Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1539-1551.

Résumé
Abstract

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.

We establish certain properties for the class $𝒰 (Ω, ζ_{0})$ of universal functions in $Ω$ with respect to the center $ζ_{0} \in Ω$ , 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.

MR Zbl

DOI : 10.5802/aif.1865

Classification : 30B30, 30B10
Keywords: power series, overconvergence, complex approximation
Mot clés : séries de puissance, approximation complexe, propriété générique

Affiliations des auteurs :

Melas, Antonios D. ¹

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

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     title = {Universal functions on nonsimply connected domains},
     journal = {Annales de l'Institut Fourier},
     pages = {1539--1551},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
     number = {6},
     year = {2001},
     doi = {10.5802/aif.1865},
     mrnumber = {1870639},
     zbl = {0989.30003},
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Melas, Antonios D. Universal functions on nonsimply connected domains. Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1539-1551. doi : 10.5802/aif.1865. http://www.numdam.org/articles/10.5802/aif.1865/

Bibliographie
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