Geodesic
UPPER AND LOWER FREQUENTLY UNIVERSAL SERIES
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 615-627

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S001708951200078X
Mots-clés : 30K05, 30E10 
PAPACHRISTODOULOS, CHRISTOS. UPPER AND LOWER FREQUENTLY UNIVERSAL SERIES. Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 615-627. doi: 10.1017/S001708951200078X
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[1] 1.Bayart, F. and Grivaux, S., Frequently hypercyclic operators, Trans. Am. Math. Soc. V. 358 (N11) (2005), 5083–5117. Google Scholar | DOI

[2] 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] 3.Bonilla, A. and Grosse-Erdmann, K.-G., Frequently hypercyclic operators and vectors, Ergod. Th. Dynam. Sys. 27 (2007), 383–404. Google Scholar | DOI

[4] 4.Kyrezi, I. and Nestoridis, V., Examples differentiating some classes of universal series (submitted). Google Scholar

[5] 5.Kyrezi, I. and Papachristodoulos, C., On lower frequently universal series (in preparation). Google Scholar

[6] 6.Menchoff, D., Sur les series trigonometriques universelles, Dakl. Akad. Nauk. SSR (N.S.) 49 (1945), 79–82. Google Scholar

[7] 7.Nestoridis, V., Universal Taylor series, Ann. Inst. Fourier 46 (1996), 1293–1306. Google Scholar

[8] 8.Pal, J., Zweikleine bemerkungen, Tehoku Math. J. 6 (1914), 42–43. Google Scholar

[9] 9.Rudin, W., Real and complex analysis, 2nd ed. (McGraw-Hill, 1974), chapters 13 and 20. Google Scholar

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