Dimensions and spectral triples for fractals in R^N

Details Dimensions and spectral triples for fractals in R^N Dimensions and spectral triples for fractals in R^N

2004-04-16

arxiv.org/abs/math/0404295v2

In "Advances in Operator Algebras and Mathematical Physics", Proceedings of the Conference held in Sinaia, Romania, June 2003,

Mathematics

Operator Algebras

24 pages, 4 figures. To appear in Proceedings of the Conference "Operator Algebras and Mathematical Physics" held in Sinaia, R

Scientific paper

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.

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