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.
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Aubry, JM., Bastin, F. & Dispa, S. Prevalence of Multifractal Functions in Sv Spaces. J Fourier Anal Appl 13, 175–185 (2007). https://doi.org/10.1007/s00041-006-6019-8
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DOI: https://doi.org/10.1007/s00041-006-6019-8