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Singularity spectrum of multifractal functions involving oscillating singularities

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Abstract

We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating singularities. These functions are defined by explicit coefficients on an orthonormal wavelet basis. We compute their Hölder regularity and oscillation at every point and we deduce their spectrum of oscillating singularities.

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Authors and Affiliations

  1. Centre de Recherche Paul Pascal, Avenue Schweitzer, 33600, Pessac, France

    A. Arneodo & J. F. Muzy

  2. Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128, Palaiseau, France

    E. Bacry

  3. Départment de Mathématiques Université Paris XII, 61 Avenue du Général de Gaulle, 94010, Créteil, France

    A. Arneodo, E. Bacry, S. Jaffard & J. F. Muzy

  4. CMLA, ENS Cachan, 61 Avenue du Président Wilson, 94235, Cachan, France

    S. Jaffard

Authors
  1. A. Arneodo
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  2. E. Bacry
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  3. S. Jaffard
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  4. J. F. Muzy
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Communicated by John J. Benedetto

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Arneodo, A., Bacry, E., Jaffard, S. et al. Singularity spectrum of multifractal functions involving oscillating singularities. The Journal of Fourier Analysis and Applications 4, 159–174 (1998). https://doi.org/10.1007/BF02475987

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  • DOI: https://doi.org/10.1007/BF02475987

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