Approximation of Fractals by Discrete Graphs: Norm Resolvent and Spectral Convergence

  • Olaf PostEmail author
  • Jan Simmer


We show a norm convergence result for the Laplacian on a class of pcf self-similar fractals with arbitrary Borel regular probability measure which can be approximated by a sequence of finite-dimensional weighted graph Laplacians. As a consequence other functions of the Laplacians (heat operator, spectral projections etc.) converge as well in operator norm. One also deduces convergence of the spectrum and the eigenfunctions in energy norm.


Post-critically finite fractals Spectral convergence Convergence of operators Discrete approximation 


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Authors and Affiliations

  1. 1.Fachbereich 4 – MathematikUniversität TrierTrierGermany

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