Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 35J05 ( Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] )

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2011 (vol 63 pp. 648)

Ngai, Sze-Man
 Spectral Asymptotics of Laplacians Associated with One-dimensional Iterated Function Systems with Overlaps 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. Keywords:spectral dimension, fractal, Laplacian, self-similar measure, iterated function system with overlaps, second-order self-similar identitiesCategories:28A80, , , , 35P20, 35J05, 43A05, 47A75

© Canadian Mathematical Society, 2015 : https://cms.math.ca/