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 IR such that the regularity of f at x, measured in terms of Hölder exponent, is exactly s(x), for all x [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, as for instance conditions on the box or Tricot dimension or the multifractal spectrum of these functions. Finally we present a result on the "size" of the set of functions with prescribed local regularity.
Type de document :
Article dans une revue
Constructive Approximation, Springer Verlag, 1998, 14 (3), pp.349-385. 〈10.1007/s003659900078〉
Liste complète des métadonnées

https://hal.inria.fr/inria-00593268
Contributeur : Lisandro Fermin <>
Soumis le : vendredi 13 mai 2011 - 17:22:15
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : dimanche 14 août 2011 - 02:44:10

Fichier

Construction_of_continuous_fun...
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Khalid Daoudi, Jacques Lévy Véhel, Yves Meyer. Construction of continuous functions with prescribed local regularity. Constructive Approximation, Springer Verlag, 1998, 14 (3), pp.349-385. 〈10.1007/s003659900078〉. 〈inria-00593268〉

Partager

Métriques

Consultations de la notice

296

Téléchargements de fichiers

106