Prevalenee of multifractal functions in S-nu spaces

peer reviewedSpaces 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

The S\nu spaces: new spaces defined with wavelet coefficients and related to multifractal analysis

In the context of multifractal analysis, more precisely in the context of the study of H\"older regularity, Stéphane Jaffard introduced new spaces of functions related to the distributionof wavelet coefficients, the ${\cal S}^{\nu}$ spaces. From a functional analysis point of view, one can define the corresponding sequence spaces, endow them with natural topologies and study their properties. The results lead to construct probability Borel measures with applications in the context of multifractal analysis