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Article contents
Divergence of mock Fourier series for spectral measures
Part of:
Classical measure theory
Harmonic analysis in several variables
Harmonic analysis in one variable
Published online by Cambridge University Press: 17 October 2022
Abstract
In this paper, we study divergence properties of the Fourier series on Cantor-type fractal measure, also called the mock Fourier series. We give a sufficient condition under which the mock Fourier series for doubling spectral measure is divergent on a set of strictly positive measure. In particular, there exists an example of the quarter Cantor measure whose mock Fourier sums are not almost everywhere convergent.
MSC classification
Primary:
28A80: Fractals
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 6 , December 2023 , pp. 1818 - 1832
- Copyright
- Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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