Natural Science, Mathematics, 2025
On the divergence of Fourier series in the general Haar system
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Submitted: 2024-12-06; Published: 2024-12-06
Š 2024 by author(s) and The Gufo Inc.
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(CC BY-NC 4.0).
Abstract
For any countable set Dâ[0,1]Dâ[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]âD[0,1]âD.