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1 results

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

  • Sze-Man Ngai
  • Journal:
    Canadian Journal of Mathematics / Volume 63 / Issue 3 / 01 June 2011
    Published online by Cambridge University Press:
    20 November 2018, pp. 648-688
    Print publication:
    01 June 2011
    • Article
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  • 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.