prevalence; generic proper-ties of functions; multifractal formalism; sequence spaces
Abstract :
[en] Spaces called S-v were introduced by Jaffard [16] as spaces of functions characterized by the number similar or equal to 2(v(alpha)j) of their wavelet coefficients having a size greater than or similar to 2(-alpha j) at scale j. They are Polish vector spaces for a natural distance. In those spaces we show that multifractal functions are prevalent (an infinite-dimensional "almost-every"). Their spectrum of singularities can be computed from v, which justifies a new multifractal formalism, not limited to concave spectra.
Disciplines :
Mathematics
Author, co-author :
Aubry, Jean-Marie ; Université de Liège - ULiège > Département de mathématique > Analyse
Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes
Dispa, S.
Language :
English
Title :
Prevalenee of multifractal functions in S-nu spaces