Revista Matemática Iberoamericana


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Volume 31, Issue 1, 2015, pp. 313–348
DOI: 10.4171/RMI/836

Published online: 2015-03-05

The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields

Patrice Abry[1], Marianne Clausel[2], Stéphane Jaffard[3], Stéphane G. Roux[4] and Béatrice Vedel[5]

(1) École Normale Supérieure de Lyon, France
(2) Université de Grenoble, Saint-Martin-d'Hères, France
(3) Université Paris Est, Créteil, France
(4) École Normale Supérieure de Lyon, France
(5) Université de Bretagne-Sud, Vannes, France

Global and local regularity of functions in anisotropic function spaces is analyzed in the common framework provided by hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities derived from the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy, and its properties are investigated.

Keywords: Hyperbolic wavelet analysis, anisotropic Besov spaces, pointwise Hölder regularity, anisotropic multifractal analysis

Abry Patrice, Clausel Marianne, Jaffard Stéphane, Roux Stéphane, Vedel Béatrice: The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields. Rev. Mat. Iberoamericana 31 (2015), 313-348. doi: 10.4171/RMI/836