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arXiv · 2206.01124

The divergence of Mock Fourier series for spectral measures

Wu-Yi Pan·Wen-Hui Ai
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Abstract

In this paper, we study divergence properties of Fourier series on Cantor-type fractal measure, also called Mock Fourier series. We give a sufficient condition under which the Mock Fourier series for doubling spectral measure is divergent on non-zero set. In particularly, there exists an example of the quarter Cantor measure whose Mock Fourier sums is not almost everywhere convergent.

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Wu-Yi Pan, Wen-Hui Ai. 2022-06-02. The divergence of Mock Fourier series for spectral measures. https://doi.org/10.1017/prm.2022.68

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