On the uniform convergence of double sine series

• Autorzy: Péter Kórus , Ferenc Móricz
• Języki publikacji: EN

Abstrakty

EN

Let a single sine series (*) $∑^{∞}_{k=1} a_{k} sin kx$ be given with nonnegative coefficients ${a_{k}}$. If ${a_{k}}$ is a "mean value bounded variation sequence" (briefly, MVBVS), then a necessary and sufficient condition for the uniform convergence of series (*) is that $ka_{k} → 0$ as k → ∞. The class MVBVS includes all sequences monotonically decreasing to zero. These results are due to S. P. Zhou, P. Zhou and D. S. Yu. In this paper we extend them from single to double sine series (**) $∑^{∞}_{k=1} ∑^{∞}_{l=1} c_{kl} sin kx sin ly$, even with complex coefficients ${c_{kl}}$. We also give a uniform boundedness test for the rectangular partial sums of series (**), and slightly improve the results on single sine series.

Kategorie tematyczne

• 42B99: None of the above, but in this section
• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 1
• Strony: 79-97

Daty

wydano

2009

Twórcy

autor

Péter Kórus

• University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, 6720 Szeged, Hungary

autor

Ferenc Móricz

• University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Identyfikatory

DOI

10.4064/sm193-1-4