Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T14:19:58.827Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE FREQUENT UNIVERSALITY OF UNIVERSAL TAYLOR SERIES IN THE COMPLEX PLANE

Part of: General theory of linear operators Universal holomorphic functions

Published online by Cambridge University Press:  10 June 2016

A. MOUZE  and
V. MUNNIER
A. MOUZE
Affiliation:
Laboratoire Paul Painlevé, UMR 8524, Université Lille 1, Cité Scientifique, 59650 Villeneuve d'Ascq, France e-mail: [email protected]
V. MUNNIER
Affiliation:
École Centrale de Lille, Cité Scientifique, CS20048, 59651 Villeneuve d'Ascq cedex, France e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that the classical universal Taylor series in the complex plane are never frequently universal. On the other hand, we prove the 1-upper frequent universality of all these universal Taylor series.

MSC classification

Primary: 30K05: Universal Taylor series
Secondary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 1 , January 2017 , pp. 109 - 117
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

REFERENCES

1. Bayart, F. and Grivaux, S., Hypercyclicité, le rôle du spectre ponctuel unimodulaire, C. R. Math. Acad. Sci. Paris 338 (9) (2004), 703–708.Google Scholar
2. Bayart, F. and Grivaux, S., Frequently hypercyclic operators, Trans. Amer. Math. Soc. 358 (2006), 5083–5117.Google Scholar
3. Bayart, F., Grosse-Erdmann, K.-G., Nestoridis, V. and Papadimitropoulos, C., Abstract theory of universal series and applications, Proc. London Math. Soc. 96 (2008), 417–463.CrossRefGoogle Scholar
4. Binmore, K. G., On Turán's lemma, Bull. London Math. Soc. 3 (1971), 313–317.CrossRefGoogle Scholar
5. Birkhoff, G. D., Démonstration d'un théorème élémentaire sur les fonctions entières, C. R. Math. Acad. Sci. Paris 189 (1929), 473–475.Google Scholar
6. Bonilla, A., Grosse-Erdmann, K.-G., Frequently hypercyclic operators and vectors, Ergodic Theory Dynam. Syst. 27 (2) (2007), 383–404.Google Scholar
7. Chui, C. K. and Parnes, M.N., Approximation by overconvergence of power series, J. Math. Anal. Appl. 36 (1971), 693–696.Google Scholar
8. Erdmann, K-G. Grosse, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giersen 176 (1987), 1–84.Google Scholar
9. Grosse Erdmann, K.-G., Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (3) (1999), 345–381.CrossRefGoogle Scholar
10. Kyrezi, I., Nestoridis, V. and Papachristodoulos, C., Some remarks on abstract universal series, J. Math. Anal. Appl. 387 (2012), 878–884.Google Scholar
11. MacLane, G. R., Sequences of derivatives and normal families, J. Analyse Math. 2 (1952) 72–87.Google Scholar
12. Nestoridis, V., Universal Taylor series, Ann. Inst. Fourier (Grenoble) 46 (5) (1996), 1293–1306.CrossRefGoogle Scholar
13. Papachristodoulos, C., Upper and lower frequently universal series, Glasg. Math. J. 55 (3) (2013), 615–627.Google Scholar
14. Luh, W., Approximation analytischer Funktionen durch uberkonvergente Potenzreihen und deren Matrix-Transformierten, Mitt. Math. Sem. Giessen 88 (1970), 1–56.Google Scholar
15. Seleznev, A. I., On universal power series, Math. Sbornik N.S. 28 (1951), 453–460.Google Scholar
16. Turán, P., Eine neue Methode in der Analysis und deren Anwendungen (Akadémiai Kiadó, Budapest, 1953).Google Scholar