Eigenmodes of the Laplacian on some Laakso spaces
2009; Taylor & Francis; Volume: 54; Issue: 6 Linguagem: Inglês
10.1080/17476930903009584
ISSN1747-6941
AutoresKevin Romeo, Benjamin Steinhurst,
Tópico(s)Random Matrices and Applications
ResumoAbstract We analyse the spectrum of a self-adjoint operator on a Laakso space using the projective limit construction originally given by Barlow and Evans. We will use the hierarchical cell structure induced by the choice of approximating quantum graphs to calculate the spectrum with multiplicities. We also extend the method for using the hierarchical cell structure to more general projective limits beyond Laakso spaces. Keywords: fractalLaplacianprojective limiteigenvalueseigenfunctionsAMS Subject Classifications:: 34L40 (primary)34L1654B30 Acknowledgements The authors thank Alexander Teplyaev, Daniel Ford, and Robert Strichartz for their support and feedback throughout the production of this article.
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