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A Family of Functions with Two Different Spectra of Singularities
Authors:Claire Coiffard  Clothilde Mélot  Thomas Willer
Institution:1. CNRS, Centrale Marseille, I2M, UMR 7373, Aix-Marseille Université, 13453?, Marseille, France
Abstract:Our goal is to study the multifractal properties of functions of a given family which have few non vanishing wavelet coefficients. We compute at each point the pointwise Hölder exponent of these functions and also their local \(L^p\) regularity, computing the so-called \(p\) -exponent. We prove that in the general case the Hölder and \(p\) -exponent are different at each point. We also compute the dimension of the sets where the functions have a given pointwise regularity and prove that these functions are multifractal both from the point of view of Hölder and \(L^p\) local regularity with different spectra of singularities. Furthermore, we check that multifractal formalism type formulas hold for functions in that family.
Keywords:
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