Criteria for spectral gaps of Laplacians on fractals

DOI10.1007/s00041-009-9087-8zbMath1190.28005OpenAlexW1998704844MaRDI QIDQ2380393

Denglin Zhou

Publication date: 26 March 2010

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-009-9087-8

zbMATH Keywords

spectral gapLaplacianSierpinski gasketfractal

Mathematics Subject Classification ID

Dirichlet forms (31C25) Fractals (28A80) Nontrigonometric harmonic analysis (42C99)

Related Items (11)

EIGENVALUES OF LAPLACIANS ON HIGHER DIMENSIONAL VICSEK SET GRAPHS ⋮ Spectral analysis on infinite Sierpiński fractafolds ⋮ Spectral decimation on Hambly's homogeneous hierarchical gaskets ⋮ Gaps labeling theorem for the bubble-diamond self-similar graphs ⋮ Exact spectrum of the Laplacian on a domain in the Sierpinski gasket ⋮ Explicit spectral decimation for a class of self-similar fractals ⋮ The ``hot spots conjecture for the Sierpiński gasket ⋮ The resolvent kernel for PCF self-similar fractals ⋮ VIBRATION SPECTRA OF THE m-TREE FRACTAL ⋮ Laplacians on a family of quadratic Julia sets I ⋮ Spectral decimation for a graph-directed fractal pair

Cites Work

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• Plancherel-type estimates and sharp spectral multipliers
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• Spectral analysis of Laplacians on the Vicsek set
• Laplacians on fractals with spectral gaps have nicer Fourier series
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• Vibration modes of 3n-gaskets and other fractals
• Dynamics in One Complex Variable. (AM-160)
• The finite element method on the Sierpinski gasket

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