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

Frédéric Bayart (1) , Yanick Heurteaux (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Fourier series; Hausdorff dimension; prevalence

Domaines: Analyse classique [math.CA]

Frédéric Bayart, Yanick Heurteaux. Multifractal analysis of the divergence of Fourier series: the extreme cases. Journal d'analyse mathématique, 2014, 124 (1), pp 387-408. ⟨hal-00635447⟩