Dimension prints for continuous functions on the unit square

DOI10.1007/s10474-021-01172-4zbMath1499.26049OpenAlexW3197943168MaRDI QIDQ2236644

Mourad Ben Slimane, Maamoun Turkawi, M. Ben Abid, I. Ben Omrane

Publication date: 25 October 2021

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-021-01172-4

zbMATH Keywords

Hausdorff dimensionSierpinski carpetsFaber-Schauder systemdimension printself-affine functionsspline basisgrid of rectanglesrectangular Lipschitz regularitySchauder product functionseveral variable signals

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Fractals (28A80) Summability and bases in topological vector spaces (46A35) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Hausdorff and packing measures (28A78)

Cites Work

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• Large deviation spectra based on wavelet leaders
• Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations
• Multifractal spectrum and generic properties of functions monotone in several variables
• A higher order Faber spline basis for sampling discretization of functions
• Self-affine multifractal Sierpiński sponges in \(\mathbb{R}^d\)
• Fractional Brownian sheet
• Multifractal properties of typical convex functions
• Multiple Haar basis and \(m\)-term approximations of functions from the Besov classes. II
• The singularity spectrum for general Sierpiński carpets
• Hyperbolic wavelet analysis of classical isotropic and anisotropic Besov-Sobolev spaces
• The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields
• Dimension prints
• Multifractal formalism and anisotropic selfsimilar functions
• Dimension prints of fractal sets
• The dimensions of inhomogeneous self-affine sets

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