Statistical convergence of Walsh-Fourier series

Móricz, Ferenc (2004) Statistical convergence of Walsh-Fourier series. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 20 (2). pp. 165-168. ISSN 0866-0174

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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.

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