Multifractal analysis of the divergence of Fourier series
Frédéric Bayart, Yanick Heurteaux (2012)
Annales scientifiques de l'École Normale Supérieure
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A famous theorem of Carleson says that, given any function , , its Fourier series converges for almost every . Beside this property, the series may diverge at some point, without exceeding . We define the divergence index at as the infimum of the positive real numbers such that and we are interested in the size of the exceptional sets , namely the sets of with divergence index equal to . We show that quasi-all functions in have a multifractal behavior with respect to...