Spectral Asymptotics of Laplacians Associated with One-dimensional Iterated Function Systems with Overlaps

Ngai, Sze-Man

Canadian journal of mathematics, Tome 63 (2011) no. 3, pp. 648-688

Résumé

We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition.

Détail

DOI : 10.4153/CJM-2011-011-3

Mots-clés : 28A80, 35P20, 35J05, 43A05, 47A75, spectral dimension, fractal, Laplacian, self-similar measure, iterated function system with overlaps, second-order self-similar identities

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