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arXiv · 1110.5478

Multifractal analysis of the divergence of Fourier series: the extreme cases

Frédéric Bayart·Yanick Heurteaux
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Abstract

We study the size, in terms of the Hausdorff dimension, of the subsets of $\mathbb T$ such that the Fourier series of a generic function in $L^1(\TT)$, $L^p(\TT)$ or in $\mathcal C(\mathbb T)$ may behave badly. Genericity is related to the Baire category theorem or to the notion of prevalence.

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Frédéric Bayart, Yanick Heurteaux. 2011-10-25. Multifractal analysis of the divergence of Fourier series: the extreme cases. https://arxiv.org/abs/1110.5478

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