Inversion formula for continuous multifractals
type: Item
instance of: scholarly article
title: Inversion formula for continuous multifractals
zbMATH Open document ID: 0892.28007
author: Rudolf H. Riedi
author: Benoît B. Mandelbrot
published in: Advances in Applied Mathematics
publication date: 1998-07-14T00:00:00Z
review text: In their previous paper [Adv. Appl. Math. 18, No. 1, 50-58 (1977; Zbl 0870.28004)] the authors introduced the inverse measure of a multifractal \(\mu\) and argued heuristically that their multifractal spectra are linked by the ``inversion formula''. In this paper, they establish rigorously the inversion formula for the Hausdorff, packing and coarse grained spectra under the assumption that both \(\mu\) and its inverse measure are continuous. In the discontinuous case, the authors consider especially discontinuous self-similar measures and show that the inversion formula still holds for the Hausdorff and packing spectra, but it does not hold for the coarse grained spectrum. The details of these and further related results are presented in their paper in Math. Proc. Camb. Philos. Soc. 123, No. 1, 133-157 (1998; following review).
reviewed by: Y. Xiao
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 1089805
zbMATH Keywords: coarse grained spectrum
zbMATH Keywords: multifractal
zbMATH Keywords: inverse measure
zbMATH Keywords: Hausdorff spectrum
zbMATH Keywords: packing spectrum
MaRDI profile type: Publication
OpenAlex ID: W2041286557
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DOI: 10.1006/AAMA.1997.0550
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description: scientific article; zbMATH DE number 1089805