It is shown that every at most countable set F in an n-dimensional unit cube [0, 1]n is a set of divergence for the n-fold Fourier–Haar series of a certain bounded measurable function, i.e., there exists a bounded measurable function defined on [0, 1]n whose n-fold Fourier–Haar series is convergent in Pringsheim’s sense on [0, 1]n\F and divergent on the cubes in F.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 12, pp. 1625–1639, December, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i12.6886.
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Bitsadze, K.R. On the Sets of Divergence of Multiple Fourier–Haar Series. Ukr Math J 74, 1854–1871 (2023). https://doi.org/10.1007/s11253-023-02174-x
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DOI: https://doi.org/10.1007/s11253-023-02174-x