Natural Sciences, Mathematics, 2026
On the divergence of Fourier series in the general Haar system
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Submitted: 2024-12-06
© 2026 by author(s) and The Gufo Inc.
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Abstract
For any countable set D⊂[0,1]D⊂[0,1], we construct a bounded measurable function ff such that the Fourier series of ff with respect to the regular general Haar system is divergent on DD and convergent on [0,1]∖D[0,1]∖D.