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
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.
DOI : https://doi.org/10.5802/aif.1865
Classification:  30B30,  30B10
Mots clés: séries de puissance, approximation complexe, propriété générique
@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, Tome 51 (2001) no. 6, pp. 1539-1551. doi : 10.5802/aif.1865. https://www.numdam.org/item/AIF_2001__51_6_1539_0/

[1] G. Costakis Some remarks on universal functions and Taylor series, Math. Proc. of the Cambr. Phil. Soc., Tome 128 (2000), pp. 157-175 | Article | MR 1724436 | Zbl 0956.30003

[2] K.-G. Grosse-Erdmann Universal families and hypercyclic operators, Bull. of the AMS, Tome 36 (1999) no. 3, pp. 345-381 | Article | MR 1685272 | Zbl 0933.47003

[3] J.-P. Kahane Baire's category Theorem and Trigonometric series, Jour. Anal. Math., Tome 80 (2000), pp. 143-182 | Article | MR 1771526 | Zbl 0961.42001

[4] W. Luh Universal approximation properties of overconvergent power series on open sets, Analysis, Tome 6 (1986), pp. 191-207 | MR 832744 | Zbl 0589.30003

[5] A. Melas; V. Nestoridis Universality of Taylor series as a generic property of holomorphic functions, Adv. in Math., Tome 157 (2001) no. 2, pp. 138-176 | Article | MR 1813429 | Zbl 0985.30023

[6] V. Nestoridis Universal Taylor series, Ann. Inst. Fourier, (Grenoble), Tome 46 (1996) no. 5, pp. 1293-1306 | Article | Numdam | MR 1427126 | Zbl 0865.30001

[7] V. Nestoridis An extension of the notion of universal Taylor series, Proceedings CMFT'97, Nicosia, Cyprus, Oct. (1997) | Zbl 0942.30003

[8] V. Vlachou A universal Taylor series in the doubly connected domain {1} (Submitted) | Zbl 1049.30002