Dixmier traces and coarse multifractal analysis
نویسندگان
چکیده
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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