ON DIVERGENCE OF FOURIER–WALSH SERIES OF CONTINUOUS FUNCTION

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Submitted: 2025-02-11; Published: 2025-02-11

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Abstract

We prove that for any perfect set P of positive measure, for which 0 is a density point, one can construct a function f (x) continuous on [0, 1) such that each measurable and bounded function, which coincides with f (x) on the set P has diverging Fourier–Walsh series at 0.