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


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-12

AUTHORS

Olaf Post, Jan Simmer

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. More... »

PAGES

68

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-018-2492-0

DOI

http://dx.doi.org/10.1007/s00020-018-2492-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107412418


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