Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 165-168 (2004)

Statistical convergence of Walsh-Fourier series

F. Móricz

University of Szeged

Abstract: This is a brief and concise account of the basic concepts and results on statistical convergence, strong Cesáro summability and Walsh-Fourier series. To emphasize the significance of statistical convergence, for example we mention the fact that the one-dimensional Walsh-Fourier series of an integrable (in Lebesgue's sense) function may be divergent almost everywhere, but it is statistically convergent almost everywhere. The case of multi-dimensional Walsh-Fourier series is also considered. For future research, we raise two open problems and formulate two conjectures.

Keywords: Statistical convergence, almost convergence, natural density, strong Cesáro summability, Walsh-Fourier series, W-continuity.

Classification (MSC2000): 42C10

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2004 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition