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Good measures on locally compact Cantor sets
Good measures locally compact Cantor sets Dynamical Systems
2012/4/17
We study the set M(X) of full non-atomic Borel (finite or infinite) measures on a non-compact locally compact Cantor set X. For an infinite measure $\mu$ in M(X), the set $\mathfrak{M}_\mu = \{x \in X...
$L^2$-norm and estimates from below for Riesz transforms on Cantor sets
$L^2$-norm estimates from below Riesz transforms Cantor sets
2011/1/18
The aim of this paper is to estimate the L2-norms of vector-valued Riesz trans-forms Rs
and the norms of Riesz operators on Cantor sets in Rd, as well as to study the distribution of values of Rs ...
Spectral triples and Gibbs measures for expanding maps on Cantor sets
spectral triple Dixmier trace expanding map Gibbs measure
2010/12/14
Let T : ! be an expanding map on a Cantor set. For each suitably normalized H¨older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as ...