The divergence of Mock Fourier series for spectral measures

2022/06/02 by Wuyi Pan, Pan, Wu-Yi, Wen‐Hui Ai +1 · 1 citation
Mathematics · #28A80 #42A20 #42B05 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · doi:10.48550/arxiv.2206.01124

openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On infinite scalings of the canonical spectrum for self-similar spectral measures

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• Fractal Subseries of the Harmonic Series
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• Scaling of spectra of Cantor-type measures and some number theoretic considerations