Construction of Continuous Functions with Prescribed Local Regularity

Abstract : In this work we investigate both from a theoretical and a practical point of view the following problem¸: Let $s$ be a function from $[0¸;1]$ to $[0¸;1]$. Under which conditions does there exist a continuous function $f$ from $[0¸;1]$ to $\RR$ such that the regularity of $f$ at $x$, measured in terms of Hölder exponent, is exactly $s(x)$, for all $x \in [0¸;1]$¸? \\ We obtain a necessary and sufficient condition on $s$ and give three constructions of the associated function $f$. We also examine some extensions regarding, for instance, the box or Tricot dimension or the multifractal spectrum. Finally we present a result on the «size» of the set of functions with prescribed local regularity.
Type de document :
[Research Report] RR-2763, INRIA. 1995
Liste complète des métadonnées
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 14:06:27
Dernière modification le : jeudi 11 janvier 2018 - 06:12:21
Document(s) archivé(s) le : lundi 5 avril 2010 - 00:01:57



  • HAL Id : inria-00073928, version 1



Khalid Daoudi, Jacques Lévy Véhel, Yves Meyer. Construction of Continuous Functions with Prescribed Local Regularity. [Research Report] RR-2763, INRIA. 1995. 〈inria-00073928〉



Consultations de la notice


Téléchargements de fichiers