GAPS IN THE RATIOS OF THE SPECTRA OF LAPLACIANS ON FRACTALS

DOI10.1142/S0218348X0900451XzbMath1187.35143OpenAlexW2035677629MaRDI QIDQ5190004

Kathryn E. Hare, Denglin Zhou

Publication date: 11 March 2010

Published in: Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218348x0900451x

zbMATH Keywords

eigenvaluesspectrumLaplaciangapsSierpiński gasketspectral decimationfractal treeVicsek set

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractals (28A80)

Related Items (4)

Spectral decimation on Hambly's homogeneous hierarchical gaskets ⋮ Explicit spectral decimation for a class of self-similar fractals ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces

Cites Work

• Unnamed Item
• On a spectral analysis for the Sierpiński gasket.
• Spectral analysis on infinite Sierpiński gaskets
• Self-similarity, operators and dynamics
• The homogenization problem for Vicsek set
• On eigenvalue problems for Laplacians on p.c.f. self-similar sets
• Spectral analysis of Laplacians on the Vicsek set
• Laplacians on fractals with spectral gaps have nicer Fourier series
• Partial differential equations on products of Sierpinski gaskets
• Vibration modes of 3n-gaskets and other fractals
• The finite element method on the Sierpinski gasket

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