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

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

2011-10-25

arxiv.org/abs/1110.5478v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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