Prevalence of Multifractal Functions in Sv Spaces

Abstract

Spaces called Sv were introduced by Jaffard [16] as spaces of functions characterized by the number ≃ 2ν(α)j of their wavelet coefficients having a size ≳ 2−αj 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 ν, which justifies a new multifractal formalism, not limited to concave spectra.