Universal functions on nonsimply connected domains
[Fonctions universelles dans des domaines non simplement connexes]
Melas, Antonios D.
Annales de l'Institut Fourier, Tome 51 (2001), p. 1539-1551 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 2001-01-01
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},
     volume = {51},
     year = {2001},
     pages = {1539-1551},
     doi = {10.5802/aif.1865},
     mrnumber = {1870639},
     zbl = {0989.30003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2001__51_6_1539_0}
}

Melas, Antonios D. Universal functions on nonsimply connected domains. Annales de l'Institut Fourier, Tome 51 (2001) pp. 1539-1551. doi : 10.5802/aif.1865. http://gdmltest.u-ga.fr/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 ℂ∖{1} (Submitted) | Zbl 1049.30002