A Dichotomy Principle for Universal Series

• Autorzy: V. Farmaki , V. Nestoridis
• Języki publikacji: EN

Abstrakty

EN

Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence $(α_{j})_{j=1}^{∞}$ of scalars, there exists a subsequence $(α_{k_j})_{j=1}^{∞}$ such that either every subsequence of $(α_{k_j})_{j=1}^{∞}$ defines a universal series, or no subsequence of $(α_{k_j})_{j=1}^{∞}$ defines a universal series. In particular examples we decide which of the two cases holds.

Kategorie tematyczne

• 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
• 05D10: Ramsey theory
• 30B30: Boundary behavior of power series, over-convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 2
• Strony: 93-104

Daty

wydano

2008

Twórcy

autor

V. Farmaki

• Department of Mathematics, Athens University, Panepistemiopolis, 15784 Athens, Greece

autor

V. Nestoridis

• Department of Mathematics, Athens University, Panepistemiopolis, 15784 Athens, Greece
• Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus

Identyfikatory

DOI

10.4064/ba56-2-1