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

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Abstract

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.

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  1. Fachbereich 4 – Mathematik, Universität Trier, 54286, Trier, Germany

    Olaf Post & Jan Simmer

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  1. Olaf Post
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  2. Jan Simmer
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Correspondence to Olaf Post.

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Post, O., Simmer, J. Approximation of Fractals by Discrete Graphs: Norm Resolvent and Spectral Convergence. Integr. Equ. Oper. Theory 90, 68 (2018). https://doi.org/10.1007/s00020-018-2492-0

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