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 HausdorffBesicovitch 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 HausdorffBesicovitch functionals do not depend on the generalized limit procedure.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404295
 Bibcode:
 2004math......4295G
 Keywords:

 Mathematics  Operator Algebras;
 46Lxx;
 28A80
 EPrint:
 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