Inversion Formula for Continuous Multifractals
| dc.citation.bibtexName | article | en_US |
| dc.citation.journalTitle | Advances in Applied Mathematics | en_US |
| dc.contributor.author | Riedi, Rudolf H. | en_US |
| dc.contributor.author | Mandelbrot, Benoit | en_US |
| dc.contributor.org | Digital Signal Processing (http://dsp.rice.edu/) | en_US |
| dc.date.accessioned | 2007-10-31T01:01:09Z | en_US |
| dc.date.available | 2007-10-31T01:01:09Z | en_US |
| dc.date.issued | 1997-01-20 | en_US |
| dc.date.modified | 2004-01-22 | en_US |
| dc.date.submitted | 2004-01-14 | en_US |
| dc.description | Journal Paper | en_US |
| dc.description.abstract | In a previous paper the authors introduced the inverse measure <i>µ</i><sup>â </sup> of a probability measure <i>µ</i> on [0,1]. It was argued that the respective multifractal spectra are linked by the 'inversion formula' <i>f</i><sup>â </sup>(<i>a</i>) = <i>a</i><i>f</i>(1/<i>a</i>). 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, <i>f</i> 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. | en_US |
| dc.identifier.citation | R. H. Riedi and B. Mandelbrot, "Inversion Formula for Continuous Multifractals," <i>Advances in Applied Mathematics,</i> 1997. | en_US |
| dc.identifier.doi | http://dx.doi.org/10.1006/aama.1997.0550 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/20267 | en_US |
| dc.language.iso | eng | en_US |
| dc.subject | Temporary | en_US |
| dc.subject.keyword | Temporary | en_US |
| dc.subject.other | Multifractals | en_US |
| dc.title | Inversion Formula for Continuous Multifractals | en_US |
| dc.type | Journal article | en_US |
| dc.type.dcmi | Text | en_US |
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