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UPPER AND LOWER FREQUENTLY UNIVERSAL SERIES

Published online by Cambridge University Press:  25 February 2013

CHRISTOS PAPACHRISTODOULOS
CHRISTOS PAPACHRISTODOULOS*
Affiliation:
Department of Mathematics, University of Crete, KNOSSOS AV. 71409Heraklion, Crete, Greece e-mail: papach@math.uoc.gr
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Abstract

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We introduce the notion of upper and lower frequently universal sequences and see that ‘most’ of the universal approximations are obtained by sets of indices which have upper density 1 and lower density 0. We also show that a class of universal series related to lower density is of first category.

Keywords

30K0530E10

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 3 , September 2013, pp. 615 - 627
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Bayart, F. and Grivaux, S., Frequently hypercyclic operators, Trans. Am. Math. Soc. V. 358 (N11) (2005), 5083–5117.CrossRefGoogle Scholar
2.Bayart, F., Grosse-Erdmann, K.-G., Nestoridis, V. and Papadimitropoulos, C., Abstract theory of universal series and applications, Proc. Lond. Math. Soc. 96 (2) (2008), 417–463 doi:10.1112/plms/pdm043.Google Scholar
3.Bonilla, A. and Grosse-Erdmann, K.-G., Frequently hypercyclic operators and vectors, Ergod. Th. Dynam. Sys. 27 (2007), 383–404.CrossRefGoogle Scholar
4.Kyrezi, I. and Nestoridis, V., Examples differentiating some classes of universal series (submitted).Google Scholar
5.Kyrezi, I. and Papachristodoulos, C., On lower frequently universal series (in preparation).Google Scholar
6.Menchoff, D., Sur les series trigonometriques universelles, Dakl. Akad. Nauk. SSR (N.S.) 49 (1945), 79–82.Google Scholar
7.Nestoridis, V., Universal Taylor series, Ann. Inst. Fourier 46 (1996), 1293–1306.Google Scholar
8.Pal, J., Zweikleine bemerkungen, Tehoku Math. J. 6 (1914), 42–43.Google Scholar
9.Rudin, W., Real and complex analysis, 2nd ed. (McGraw-Hill, 1974), chapters 13 and 20.Google Scholar