Dixmier traces and coarse multifractal analysis

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12 Citations (Scopus)

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 languageEnglish
Pages (from-to)369-381
Number of pages13
JournalErgodic Theory and Dynamical Systems
Volume31
Issue number2
Early online date2 Feb 2010
DOIs
Publication statusPublished - Mar 2011

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