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Wavelet transforms and order-two densities of fractals

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Abstract

We highlight a correspondence between order-two densities and wavelet-like transforms of certain fractal measures. We use a variant of the ergodic theorem to demonstrate that these densities and transforms are well-behaved for a large class of quasi-self-similar fractals. We show that parallel ideas can be used to study the local behavior of certain fractal functions.

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Authors and Affiliations

  1. School of Mathematics, University Walk, BS8 1TW, Bristol, UK

    K. J. Falconer

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  1. K. J. Falconer
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Falconer, K.J. Wavelet transforms and order-two densities of fractals. J Stat Phys 67, 781–793 (1992). https://doi.org/10.1007/BF01049726

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  • DOI: https://doi.org/10.1007/BF01049726

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