TY - JOUR
T1 - Dixmier traces and coarse multifractal analysis
AU - Falconer, Kenneth John
AU - Samuel, A
PY - 2011/3
Y1 - 2011/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80053065631&partnerID=8YFLogxK
UR - http://journals.cambridge.org/action/displayFulltext?type=1&fid=7191580&jid=&volumeId=&issueId=-1&aid=7191572&bodyId=&membershipNumber=&societyETOCSession=
U2 - 10.1017/S0143385709001102
DO - 10.1017/S0143385709001102
M3 - Article
SN - 0143-3857
VL - 31
SP - 369
EP - 381
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -