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On a spectral analysis for the Sierpiński gasket. (English) Zbl 1081.31501
Summary: A complete description of the eigenvalues of the Laplacian on the finite Sierpinski gasket is presented. We then demonstrate highly oscillatory behaviours of the distribution function of the eigenvalues, the integrated density of states (for the infinite gasket) and the spectrum of the Laplacian on the infinite gasket. The method has two ingredients: the decimation method in calculating eigenvalues due to Rammal and Toulouse and a simple description of the Dirichlet form associated with the Laplacian.

MSC:
31C25 Dirichlet forms
47B99 Special classes of linear operators
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