Dixmier traces and coarse multifractal analysis
Classical Analysis and ODEs
2009-05-20 v1
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 equivalent to integration with respect to an auxilary multifractal measure.
Keywords
Cite
@article{arxiv.0905.3052,
title = {Dixmier traces and coarse multifractal analysis},
author = {K. J. Falconer and A. Samuel},
journal= {arXiv preprint arXiv:0905.3052},
year = {2009}
}