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.
Keywords
Cite
@article{arxiv.math/0404295,
title = {Dimensions and spectral triples for fractals in R^N},
author = {Daniele Guido and Tommaso Isola},
journal= {arXiv preprint arXiv:math/0404295},
year = {2009}
}
Comments
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