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: | |
本文献已被 SpringerLink 等数据库收录! |
|