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- W4375948482 abstract "In this work and its companion [1], we construct Baire function spaces in which typical elements share the same prescribed multifractal behavior and obey a multifractal formalism, providing a solution to the so-called Frisch-Parisi conjecture for functions, an inverse problem raised by S. Jaffard. In this first part, a family Ed of almost-doubling fully supported capacities on Rd with prescribed singularity spectra is constructed. With each μ∈Ed we associate a Baire function space Bμ(Rd) (a generalisation of Hölder-Zygmund spaces) in which typical functions share the same singularity spectrum as μ. This yields a partial solution to the conjecture. In [1], we introduce and study a family B={Bqμ,p(Rd)}μ∈Ed,(p,q)∈[1,+∞]2 of heterogeneous Besov spaces that contains {Bμ(Rd)}μ∈Ed and generalises in a natural direction the family of standard Besov spaces, and we solve the inverse problem exhaustively inside B. Dans ce travail et le précédent [1], nous construisons des espaces fonctionnels de Baire dans lesquels les éléments génériques partagent le même comportement multifractal prescrit et satisfont un formalisme multifractal. Ceci répond positivement à la conjecture dite de Frisch-Parisi pour les fonctions, problème inverse posé par S. Jaffard. Dans cette première partie, nous construisons une famille Ed de capacités quasi-doublantes, de support égal à Rd, et ayant des spectres de singularité prescrits. A chaque μ dans Ed est associé un espace fonctionnel de Baire Bμ(Rd) (généralisation des espaces de Hölder-Zygmund) dans lequel les fonctions génériques partagent le même spectre de singularité que μ. Ceci résout partiellement la conjecture. Dans [1], nous introduisons et étudions une famille B={Bqμ,p(Rd)}μ∈Ed,(p,q)∈[1,+∞]2 d'espaces de Besov hétérogènes qui contient {Bμ(Rd)}μ∈Ed et généralise dans une direction naturelle la famille des espaces de Besov standard, puis nous résolvons le problème inverse de manière exhaustive dans B." @default.
- W4375948482 created "2023-05-10" @default.
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- W4375948482 date "2023-07-01" @default.
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- W4375948482 title "The Frisch-Parisi conjecture I: Prescribed multifractal behavior, and a partial solution" @default.
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- W4375948482 doi "https://doi.org/10.1016/j.matpur.2023.05.003" @default.
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