The resolvent kernel for PCF self-similar fractals

DOI10.1090/S0002-9947-10-05098-1zbMath1204.28013arXiv0811.4203MaRDI QIDQ3581147

Erin P. J. Pearse, Robert S. Strichartz, Luke G. Rogers, Huo-Jun Ruan, Marius V. Ionescu

Publication date: 16 August 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.4203

zbMATH Keywords

eigenvalueDirichlet formfractalself-similarpost-critically finitediscrete potential theorygraph Laplaciangraph energydiscrete Laplace operatorresolvent formula

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Eigenvalue problems for linear operators (47A75) Discrete version of topics in analysis (39A12) Difference operators (39A70) Fractals (28A80) Linear difference operators (47B39)

Related Items (20)

Estimates for the resolvent kernel of the Laplacian on p.c.f. self-similar fractals and blowups ⋮ Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Sobolev spaces on p.c.f. self-similar sets. II: Boundary behavior and interpolation theorems ⋮ Spectral analysis on infinite Sierpiński fractafolds ⋮ Some properties of the derivatives on Sierpinski gasket type fractals ⋮ Power dissipation in fractal AC circuits ⋮ Distribution theory on p.c.f. fractals ⋮ Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs ⋮ The ``hot spots conjecture on higher dimensional Sierpinski gaskets ⋮ A counterexample to the ``hot spots conjecture on nested fractals ⋮ Pseudo-differential operators on fractals and other metric measure spaces ⋮ The ``hot spots conjecture for the Sierpiński gasket ⋮ Extensions and their minimizations on the Sierpinski gasket ⋮ Approximation of fractals by discrete graphs: norm resolvent and spectral convergence ⋮ Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials ⋮ Derivations and Dirichlet forms on fractals ⋮ Gradients of Laplacian eigenfunctions on the Sierpinski gasket ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ The Kusuoka measure and the energy Laplacian on level-\(k\) Sierpiński gaskets

Cites Work

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• Spectral decimation on Hambly's homogeneous hierarchical gaskets
• Spectral analysis on infinite Sierpiński gaskets
• Transition density estimates for Brownian motion on affine nested fractals
• Harmonic analysis for resistance forms.
• Spectral analysis of Laplacians on the Vicsek set
• Criteria for spectral gaps of Laplacians on fractals
• Gradients of Laplacian eigenfunctions on the Sierpinski gasket
• Existence and uniqueness of diffusions on finitely ramified self-similar fractals
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Vibration modes of 3n-gaskets and other fractals
• The Resolvent of an Elliptic Boundary Problem

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