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An Improved Multifractal Formalism and Self Similar Measures

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Title: An Improved Multifractal Formalism and Self Similar Measures
Author: Riedi, Rudolf H.
Type: Journal Paper
Keywords: Temporary
Citation: R. H. Riedi, "An Improved Multifractal Formalism and Self Similar Measures," Journal of Math Analysis and Application, 1995.
Abstract: To characterize the geometry of a measure, its so-called generalized dimensions D(q) have been introduced recently. The mathematically precise definition given by Falconer turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range. A new definition is introduced, which is based on box-counting too, but which carries relevant information also for negative q. In particular, rigorous proofs are provided for the Legendre connection between generalized dimensions and the so-called multifractal spectrum and for the implicit formula giving the generalized dimensions of self-similar measures, which was until now known only for positive q.
Date Published: 1995-01-01

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  • ECE Publications [1046 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.