Dimensions and spectral triples for fractals in R^N

Abstract

Two spectral triples are introduced for a class of fractals in R^n. The definitions of noncommutative Hausdorff dimension and noncommutative tangential dimensions, as well as the corresponding Hausdorff and Hausdorff-Besicovitch functionals considered in math.OA/0202108, are studied for the mentioned fractals endowed with these spectral triples, showing in many cases their correspondence with classical objects. In particular, for any limit fractal, the Hausdorff-Besicovitch functionals do not depend on the generalized limit procedure.

24 pages, 4 figures. To appear in Proceedings of the Conference "Operator Algebras and Mathematical Physics" held in Sinaia, Romania, June 2003, O. Bratteli, R. Longo H. Siedentop Eds., Theta Foundation, Bucarest

References in corpus (3)

• Dimensions and singular traces for spectral triples, with applications to fractals
• Tangential dimensions II. Measures
• Tangential dimensions I. Metric spaces

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