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

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Abstract

We study the size, in terms of the Hausdorff dimension, of the subsets of T such that the Fourier series of a generic function in L 1(T), L p(T), or C(T) may behave badly. Genericity is related to the Baire Category Theorem or the notion of prevalence. This paper is a continuation of [3].

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Authors and Affiliations

  1. Clermont Université, Université Blaise Pascal, BP 10448, F-63000, Clerment-Ferrand, France

    Frédéric Bayart & Yanick Heurteaux

  2. Laboratoire de Mathématiques, CNRS, UMR 6620, F-63177, Aubière Cedex, France

    Frédéric Bayart & Yanick Heurteaux

Authors
  1. Frédéric Bayart
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  2. Yanick Heurteaux
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Correspondence to Frédéric Bayart.

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Bayart, F., Heurteaux, Y. Multifractal analysis of the divergence of Fourier series: The extreme cases. JAMA 124, 387–408 (2014). https://doi.org/10.1007/s11854-014-0036-3

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  • DOI: https://doi.org/10.1007/s11854-014-0036-3

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