A family of functions with two different spectra of singularities - Archive ouverte HAL Accéder directement au contenu
Rapport Année : 2013

A family of functions with two different spectra of singularities

Clothilde Melot
  • Fonction : Auteur
  • PersonId : 953550
Thomas Willer
  • Fonction : Auteur
  • PersonId : 953551

Résumé

Our goal is to study the multifractal properties of functions of a given family which have few non vanishing wavelet coeffi cients. We compute at each point the pointwise Holder exponent of these functions and also their local Lp regularity, computing the so-called p-exponent. We prove that in the general case the Holder and p exponent are di fferent 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 Holder and Lp local regularity with different spectra of singularities. Furthermore, we check that multifractal formalism type formulas hold for the functions in that family.
Fichier principal
Vignette du fichier
sparse_multifractal_signal.pdf (194.67 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00831404 , version 1 (06-06-2013)
hal-00831404 , version 2 (04-03-2014)
hal-00831404 , version 3 (08-09-2014)
hal-00831404 , version 4 (10-07-2015)
hal-00831404 , version 5 (30-07-2015)

Identifiants

  • HAL Id : hal-00831404 , version 1

Citer

Claire Coiffard, Clothilde Melot, Thomas Willer. A family of functions with two different spectra of singularities. 2013. ⟨hal-00831404v1⟩
351 Consultations
311 Téléchargements

Partager

Gmail Facebook X LinkedIn More