Melas, Antonios D.
Universal functions on nonsimply connected domains  [ Fonctions universelles dans des domaines non simplement connexes ]
Annales de l'institut Fourier, Tome 51 (2001) no. 6 , p. 1539-1551
Zbl 0989.30003 | MR 1870639
doi : 10.5802/aif.1865
URL stable : http://www.numdam.org/item?id=AIF_2001__51_6_1539_0

Classification:  30B30,  30B10
Mots clés: séries de puissance, approximation complexe, propriété générique
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 /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.

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