no. 6
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.

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 ∈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.

DOI : 10.5802/aif.1865
Classification : 30B30, 30B10
Keywords: power series, overconvergence, complex approximation
Mot clés : séries de puissance, approximation complexe, propriété générique

Melas, Antonios D. 1

1 University of Athens, Department of Mathematics, Panepistimiopolis 157-84, Athens (Greece) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1865/

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