On the Frisch-Parisi conjecture

DOI10.1016/S0021-7824(00)00161-6zbMath0963.28009WikidataQ123218728 ScholiaQ123218728MaRDI QIDQ1583577

Stéphane Jaffard

Publication date: 29 October 2000

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

waveletsSobolev spaceBesov spaceHausdorff dimensionHölder exponentmultifractal functionsFrisch-Parisi conjecture

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (52)

Multivariate multifractal formalism for simultaneous pointwise (Tuipi)i regularities ⋮ Baire typical results for mixed Hölder spectra on product of continuous Besov or oscillation spaces ⋮ Nonparametric reconstruction of a multifractal function from noisy data ⋮ Confidence bands in density estimation ⋮ Detecting multifractal stochastic processes under heavy-tailed effects ⋮ The Hausdorff dimension of graphs of prevalent continuous functions ⋮ Mixed wavelet leaders multifractal formalism for Baire generic functions in a product of intersections of Hölder spaces with non-continuous Besov spaces ⋮ Multivariate wavelet leaders Rényi dimension and multifractal formalism in mixed Besov spaces ⋮ Spatially adaptive density estimation by localised Haar projections ⋮ How smooth is almost every function in a Sobolev space? ⋮ Mixed wavelet leaders multifractal formalism in a product of critical Besov spaces ⋮ Prevalent mixed Hölder spectra and mixed multifractal formalism in a product of continuous Besov spaces ⋮ Mixing for Generic Rough Shear Flows ⋮ Multifractal analysis of sums of random pulses ⋮ The Frisch-Parisi conjecture. I: Prescribed multifractal behavior, and a partial solution ⋮ Three examples of residual pathologies ⋮ The Frisch-Parisi conjecture. II: Besov spaces in multifractal environment, and a full solution ⋮ Divergence of wavelet series: a multifractal analysis ⋮ An algorithm for computing non-concave multifractal spectra using the \(S^\nu\) spaces ⋮ Honest adaptive confidence bands and self-similar functions ⋮ Concentration inequalities and confidence bands for needlet density estimators on compact homogeneous manifolds ⋮ New Exponents for Pointwise Singularity Classification ⋮ Spatially-adaptive sensing in nonparametric regression ⋮ Volumetric theory of intermittency in fully developed turbulence ⋮ MULTIFRACTAL ANALYSIS OF FUNCTIONS ON HEISENBERG AND CARNOT GROUPS ⋮ Multifractal analysis in a mixed asymptotic framework ⋮ On the estimation of the large deviations spectrum ⋮ Oscillating singularities in Besov spaces. ⋮ On wavelet and leader wavelet based large deviation multifractal formalisms for non-uniform Hölder functions ⋮ Typical upper \(L^q\)-dimensions of measures for \(q\in [0,1\)] ⋮ Baire generic histograms of wavelet coefficients and large deviation formalism in Besov and Sobolev spaces ⋮ Multifractal spectrum and generic properties of functions monotone in several variables ⋮ Some generic properties in analysis, ⋮ Convergence of the Structure Function of a Multifractal Random Walk in a Mixed Asymptotic Setting ⋮ Regularity criteria for almost every function in Sobolev spaces ⋮ Multifractal analysis of complex random cascades ⋮ A survey on prescription of multifractal behavior ⋮ Topological properties of the sequence spaces \(S^{\nu }\) ⋮ Singularity spectrum of generic \(\alpha \)-Hölder regular functions after time subordination ⋮ PrevalentL^q-dimensions of measures ⋮ \(T^{[p}\)-formalism in Besov spaces] ⋮ BOUNDS ON THE SUPPORT OF THE MULTIFRACTAL SPECTRUM OF STOCHASTIC PROCESSES ⋮ On multifractality and time subordination for continuous functions ⋮ Inverse Problems in Multifractal Analysis ⋮ Multifractal phenomena and packing dimension ⋮ On the average L^q-dimensions of typical measures ⋮ On the Baire generic validity of the \(t\)-multifractal formalism in Besov and Sobolev spaces ⋮ On the pointwise regularity of functions in critical Besov spaces ⋮ Topology on new sequence spaces defined with wavelet leaders ⋮ Some results of multifractale analysis in analysis ⋮ Typical \(L^q\)-dimensions of measures ⋮ Baire generic results for the anisotropic multifractal formalism

This page was built for publication: On the Frisch-Parisi conjecture