Dixmier traces and coarse multifractal analysis
/ Authors
/ Abstract
Abstract We show how multifractal properties of a measure supported by a fractal Fâ[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.
Journal: Ergodic Theory and Dynamical Systems