Mathematics – Operator Algebras
Scientific paper
2009-08-07
Mathematics
Operator Algebras
29 pages, 4 figures
Scientific paper
Pearson and Bellissard recently built a spectral triple - the data of Riemanian noncommutative geometry - for ultrametric Cantor sets. They derived a family of Laplace-Beltrami like operators on those sets. Motivated by the applications to specific examples, we revisit their work for the transversals of tiling spaces, which are particular self-similar Cantor sets. We use Bratteli diagrams to encode the self-similarity, and Cuntz-Krieger algebras to implement it. We show that the abscissa of convergence of the zeta-function of the spectral triple gives indications on the exponent of complexity of the tiling. We determine completely the spectrum of the Laplace-Beltrami operators, give an explicit method of calculation for their eigenvalues, compute their Weyl asymptotics, and a Seeley equivalent for their heat kernels.
Julien Antoine
Savinien Jean
No associations
LandOfFree
Transverse Laplacians for Substitution Tilings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Transverse Laplacians for Substitution Tilings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transverse Laplacians for Substitution Tilings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-153681