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Besov spaces in multifractal environment and the Frisch-Parisi conjecture

Abstract : We give a solution to the so-called Frisch-Parisi conjecture by constructing a Baire functional space in which typical functions satisfy a multifractal formalism, with a prescribed singularity spectrum. This achievement combines three ingredients developed in this paper. First we prove the existence of almost-doubling fully supported Radon measure on $\R^d$ with a prescribed multifractal spectrum. Second we define new \textit{heterogeneous} Besov like spaces possessing a wavelet characterization; this uses the previous doubling measures. Finally, we fully describe the multifractal nature of typical functions in these functional spaces.
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Submitted on : Wednesday, July 15, 2020 - 4:54:59 PM
Last modification on : Friday, March 11, 2022 - 4:20:02 PM
Long-term archiving on: : Monday, November 30, 2020 - 10:51:03 PM

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arxiv.2007.00971.pdf
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  • HAL Id : hal-02899957, version 1
  • ARXIV : 2007.00971

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Julien Barral, Stephane Seuret. Besov spaces in multifractal environment and the Frisch-Parisi conjecture. 2020. ⟨hal-02899957⟩

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