Search: MSC category 35J05
( Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] )
1. CJM 2011 (vol 63 pp. 648)
||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 identities
Categories:28A80, , , , 35P20, 35J05, 43A05, 47A75