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arXiv · 0905.3052

Dixmier traces and coarse multifractal analysis

K. J. Falconer·A. Samuel
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Abstract

We show how multifractal properties of a measure supported by a fractal F contained in [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 noncommutative integral over $F$ equivalent to integration with respect to an auxilary multifractal measure.

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K. J. Falconer, A. Samuel. 2009-05-19. Dixmier traces and coarse multifractal analysis. https://arxiv.org/abs/0905.3052

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