# Universal functions on nonsimply connected domains

Antonios D. Melas^{[1]}

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

Annales de l’institut Fourier (2001)

- Volume: 51, Issue: 6, page 1539-1551
- ISSN: 0373-0956

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topMelas, Antonios D.. "Universal functions on nonsimply connected domains." Annales de l’institut Fourier 51.6 (2001): 1539-1551. <http://eudml.org/doc/115958>.

@article{Melas2001,

abstract = {We establish certain properties for the class $\{\mathcal \{U\}\}(\Omega ,\zeta _0)$ of universal
functions in $\Omega $ with respect to the center $\zeta _0\in \Omega $, for certain types of
connected non-simply connected domains $\Omega $. In the case where $\{\mathbb \{C\}\}/\Omega $ is discrete we prove that this class is $G_\delta $-dense in $H(\Omega )$, depends on the
center $\zeta _0$ and that the analog of Kahane’s conjecture does not hold.},

affiliation = {University of Athens, Department of Mathematics, Panepistimiopolis 157-84, Athens (Greece)},

author = {Melas, Antonios D.},

journal = {Annales de l’institut Fourier},

keywords = {power series; overconvergence; complex approximation; holomorphic function; universal function},

language = {eng},

number = {6},

pages = {1539-1551},

publisher = {Association des Annales de l'Institut Fourier},

title = {Universal functions on nonsimply connected domains},

url = {http://eudml.org/doc/115958},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Melas, Antonios D.

TI - Universal functions on nonsimply connected domains

JO - Annales de l’institut Fourier

PY - 2001

PB - Association des Annales de l'Institut Fourier

VL - 51

IS - 6

SP - 1539

EP - 1551

AB - We establish certain properties for the class ${\mathcal {U}}(\Omega ,\zeta _0)$ of universal
functions in $\Omega $ with respect to the center $\zeta _0\in \Omega $, for certain types of
connected non-simply connected domains $\Omega $. In the case where ${\mathbb {C}}/\Omega $ is discrete we prove that this class is $G_\delta $-dense in $H(\Omega )$, depends on the
center $\zeta _0$ and that the analog of Kahane’s conjecture does not hold.

LA - eng

KW - power series; overconvergence; complex approximation; holomorphic function; universal function

UR - http://eudml.org/doc/115958

ER -

## References

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- K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. of the AMS 36 (1999), 345-381 Zbl0933.47003MR1685272
- J.-P. Kahane, Baire's category Theorem and Trigonometric series, Jour. Anal. Math. 80 (2000), 143-182 Zbl0961.42001MR1771526
- W. Luh, Universal approximation properties of overconvergent power series on open sets, Analysis 6 (1986), 191-207 Zbl0589.30003MR832744
- A. Melas, V. Nestoridis, Universality of Taylor series as a generic property of holomorphic functions, Adv. in Math. 157 (2001), 138-176 Zbl0985.30023MR1813429
- V. Nestoridis, Universal Taylor series, Ann. Inst. Fourier, (Grenoble) 46 (1996), 1293-1306 Zbl0865.30001MR1427126
- V. Nestoridis, An extension of the notion of universal Taylor series, Proceedings CMFT'97, Nicosia, Cyprus, Oct. (1997) Zbl0942.30003
- V. Vlachou, A universal Taylor series in the doubly connected domain $\u2102\setminus \left\{1\right\}$ Zbl1049.30002

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