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The spectra of the Laplacians of fractal graphs not satisfying spectral decimation

Part of: Classical measure theory

Published online by Cambridge University Press:  12 August 2010

Jonathan Jordan
Jonathan Jordan
Affiliation:
Department of Probability and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK (jonathan.jordan@shef.ac.uk)
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Abstract

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We consider the spectra of the Laplacians of two sequences of fractal graphs in the context of the general theory introduced by Sabot in 2003. For the sequence of graphs associated with the pentagasket, we give a description of the eigenvalues in terms of the iteration of a map from (ℂ2)3 to itself. For the sequence of graphs introduced in a previous paper by the author, we show that the results found therein can be related to Sabot's theory.

Keywords

fractal graphsLaplacianspectral decimationpentagasket

MSC classification

Secondary: 28A80: Fractals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 731 - 746
Copyright
Copyright © Edinburgh Mathematical Society 2010

References

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