Dixmier traces and coarse multifractal analysis

Kenneth John Falconer; Tony Samuel

doi:10.1017/S0143385709001102

Dixmier traces and coarse multifractal analysis

Kenneth John Falconer, Tony Samuel

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show how multifractal properties of a measure supported by a fractal F⊆[0,1] may be expressed in terms of complementary intervals of F and thus in terms of spectral triples and the Dixmier trace of certain operators. For self-similar measures this leads to a non-commutative integral over F equivalent to integration with respect to an auxiliary multifractal measure.

Original language	English
Pages (from-to)	369-381
Number of pages	13
Journal	Ergodic Theory and Dynamical Systems
Volume	31
Issue number	2
Early online date	2 Feb 2010
DOIs	https://doi.org/10.1017/S0143385709001102
Publication status	Published - Mar 2011

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10.1017/S0143385709001102

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abstract = "We show how multifractal properties of a measure supported by a fractal F⊆[0,1] may be expressed in terms of complementary intervals of F and thus in terms of spectral triples and the Dixmier trace of certain operators. For self-similar measures this leads to a non-commutative integral over F equivalent to integration with respect to an auxiliary multifractal measure.",

author = "Falconer, {Kenneth John} and Tony Samuel",

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AB - We show how multifractal properties of a measure supported by a fractal F⊆[0,1] may be expressed in terms of complementary intervals of F and thus in terms of spectral triples and the Dixmier trace of certain operators. For self-similar measures this leads to a non-commutative integral over F equivalent to integration with respect to an auxiliary multifractal measure.

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Dixmier traces and coarse multifractal analysis

Abstract

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A commutative noncommutative fractal geometry

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Dixmier traces and coarse multifractal analysis

Abstract

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Student theses

A commutative noncommutative fractal geometry

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