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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 165-168 (2004)
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Statistical convergence of Walsh-Fourier series

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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:**

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© 2004 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
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