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dc.contributor.authorRiedi, Rudolf H.
Mandelbrot, Benoit
dc.creatorRiedi, Rudolf H.
Mandelbrot, Benoit 2007-10-31T01:01:09Z 2007-10-31T01:01:09Z 1997-01-20 2004-01-14
dc.identifier.citation R. H. Riedi and B. Mandelbrot, "Inversion Formula for Continuous Multifractals," Advances in Applied Mathematics, 1997.
dc.description Journal Paper
dc.description.abstract In a previous paper the authors introduced the inverse measure Âµâ   of a probability measure µ on [0,1]. It was argued that the respective multifractal spectra are linked by the 'inversion formula' fâ  (a) = af(1/a). Here, the statements of Part I are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures. Thereby, f may stand for the Hausdorff spectrum, the pacing spectrum, or the coarse grained spectrum. With a closer look at the special case of self-similar measures we offer a motivation of the inversion formula as well as a discussion of possible generalizations. Doing so we find a natural extension of the scope of the notion 'self-similar' and a failure of the usual multifractal formalism.
dc.language.iso eng
dc.title Inversion Formula for Continuous Multifractals
dc.type Journal article
dc.citation.bibtexName article
dc.citation.journalTitle Advances in Applied Mathematics 2004-01-22
dc.contributor.orgDigital Signal Processing (
dc.type.dcmi Text
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  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
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    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

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