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.
arXiv Mathematics e-prints
- Pub Date:
- April 2004
- Mathematics - Operator Algebras;
- 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