Article contents
ON THE FREQUENT UNIVERSALITY OF UNIVERSAL TAYLOR SERIES IN THE COMPLEX PLANE
Published online by Cambridge University Press: 10 June 2016
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
- Type
- Research Article
- Information
- 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
You have
Access
- 6
- Cited by