Wavelet transforms and order-two densities of fractals

DOI10.1007/BF01049726zbMath0893.28006MaRDI QIDQ1203224

Kenneth J. Falconer

Publication date: 26 September 1994

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

wavelet transformmixing repellororder-two averagesquasi-self-similar fractals

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80)

Related Items (16)

Average densities of the image and zero set of stable processes ⋮ On Bandt's tangential distribution for self-similar measures ⋮ Random cutout sets with spatially inhomogeneous intensities ⋮ Order‐two density of sets and measures with non‐integral dimension ⋮ Fractional differentiation in the self-affine case. IV — random measures ⋮ Fractional Differentiation in the Self‐Affine Case. V ‐ The Local Degree of Differentiability ⋮ Densities of Self-Similar Measures on the Line ⋮ Order‐two density and the strong law of large numbers ⋮ Riesz s-equilibrium measures on \(d\)-dimensional fractal sets as \(s\) approaches \(d\) ⋮ Fractional derivatives of Weierstrass-type functions ⋮ Dynamical integral transform on fractal sets and the computation of entropy ⋮ The average density of the path of planar Brownian motion ⋮ Some Random sequences related to average density of self-similar measures ⋮ Symmetry properties of average densities and tangent measure distributions of measures on the line ⋮ Measures and their dimension spectrums for cookie-cutter sets in \(\mathbb{R}^d\) ⋮ The pointwise densities of the Cantor measure

Cites Work

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• On the wavelet analysis for multifractal sets
• On the wavelet transformation of fractal objects.
• Analogues of the Lebesgue Density Theorem for Fractal Sets of Reals and Integers
• Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
• The singularity spectrumf(α) for cookie-cutters
• On the Weierstrass-Mandelbrot fractal function
• Fractional Differentiation in the Self-Affine Case III. The Density of the Cantor Set
• Some properties of mixing repellers
• Continuous and Discrete Wavelet Transforms
• Repellers for real analytic maps
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions
• On the fundamental geometrical properties of linearly measurable plane sets of points. II

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