Cantor's Bijection; Hölder Regularity; Multifractal function
Abstract :
[en] Multifractal analysis has been introduced in the context of turbulence. Some tools have
been developed to study the solutions of some PDEs. In this talk, we will examine
the regularity of Cantor's bijection between the irrational numbers of the unit interval
[0,1] and the irrational numbers of the unit square [0,1]^2. We will particularly show
that its H older exponent is equal to 1/2 almost everywhere (with respect to the Lebesgue
measure).
Disciplines :
Mathematics
Author, co-author :
Simons, Laurent ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
About the Regularity of Cantor's Bijection
Alternative titles :
[en] A propos de la régularité de la bijection de Cantor
Publication date :
07 May 2012
Event name :
Functional Analysis : Applications to Complex Analysis and Partial Differential Equations