HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

2-microlocal Formalism

Abstract : This paper is devoted to the study of a fine way to measure the local regularity of distributions. Starting from the 2-microlocal analysis introduce- d by J.M. Bony, we develop a 2-microlocal formalism, much in the spirit of the multifractal formalism. This allows to define a new regularity function, that we call the 2-microlocal spectrum. The 2-microlocal spectrum proves to be a powerful tool that we apply in three directions. First, it allows to recover all previously known results on local regularity exponents, as well as to discover new properties about them. Second, the 2-microlocal spectrum provides a deeper understanding of the 2-microlocal frontiers. It yields in particular a natural way of prescribing these frontiers on a countable dense set of points. Finally, we explore the close parallel between the multifractal and 2-microlocal formalisms. These applications are illustrated on examples such as the Weierstrass and the Riemann functions, as well as lacunary wavelet series.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00071846
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Tuesday, May 23, 2006 - 6:56:52 PM
Last modification on : Friday, March 11, 2022 - 4:20:02 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:40:59 PM

Identifiers

  • HAL Id : inria-00071846, version 1

Collections

Citation

Jacques Lévy Véhel, Stéphane Seuret. 2-microlocal Formalism. [Research Report] RR-4741, INRIA. 2003. ⟨inria-00071846⟩

Share

Metrics

Record views

90

Files downloads

112