Some Functional Equations Revisited: The Multifractal Properties

DOI10.1080/1065246031000074335zbMath1068.28006OpenAlexW2022140185MaRDI QIDQ4440688

Mourad Ben Slimane

Publication date: 2003

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1065246031000074335

zbMATH Keywords

Sobolev spacesHausdorff dimensionHölder regularityfractal setmultifractal formalism

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) Singular functions, Cantor functions, functions with other special properties (26A30) Functional equations for real functions (39B22) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (7)

Baire typical results for mixed Hölder spectra on product of continuous Besov or oscillation spaces ⋮ Mixed wavelet leaders multifractal formalism for Baire generic functions in a product of intersections of Hölder spaces with non-continuous Besov spaces ⋮ Pointwise regularity of parameterized affine zipper fractal curves ⋮ Mixed wavelet leaders multifractal formalism in a product of critical Besov spaces ⋮ On wavelet and leader wavelet based large deviation multifractal formalisms for non-uniform Hölder functions ⋮ On the Baire generic validity of the \(t\)-multifractal formalism in Besov and Sobolev spaces ⋮ Baire generic results for the anisotropic multifractal formalism

Cites Work

• Unnamed Item
• Old friends revisited: The multifractal nature of some classical functions
• Pointwise smoothness, two-microlocalization and wavelet coefficients
• Singularity spectrum of fractal signals from wavelet analysis: Exact results
• Multifractal formalism for self-similar functions under the action of nonlinear dynamical systems
• Multi-fractal formalism for quasi-self-similar functions
• Local regularity of nonsmooth wavelet expansions and application to the Polya function
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
• Multifractal formalism and anisotropic selfsimilar functions
• Multifractal Formalism for Functions Part I: Results Valid For All Functions
• The Structure of Monotone Functions

This page was built for publication: Some Functional Equations Revisited: The Multifractal Properties