Estimates for the resolvent kernel of the Laplacian on p.c.f. self-similar fractals and blowups

DOI10.1090/S0002-9947-2011-05551-0zbMath1267.28012arXiv1009.5334MaRDI QIDQ2880692

Luke G. Rogers

Publication date: 13 April 2012

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

Full work available at URL: https://arxiv.org/abs/1009.5334

zbMATH Keywords

resolvent kernelblowupheat operatorLaplacianpost-critically finite self-similar set

Mathematics Subject Classification ID

Fractals (28A80) Transition functions, generators and resolvents (60J35)

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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 ⋮ Power dissipation in fractal AC circuits ⋮ Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs ⋮ Pseudo-differential operators on fractals and other metric measure spaces ⋮ Complex powers of the Laplacian on affine nested fractals as Calderón-Zygmund operators ⋮ Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials ⋮ Derivations and Dirichlet forms on fractals ⋮ Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces ⋮ Higher order Laplacians on p.c.f. fractals with three boundary points and dihedral symmetry ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ The strong maximum principle for Schrödinger operators on fractals

Cites Work

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• Complex powers of the Laplacian on affine nested fractals as Calderón-Zygmund operators
• Distribution theory on p.c.f. fractals
• Brownian motion on the Sierpinski gasket
• Spectral analysis on infinite Sierpiński gaskets
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Estimates of transition densities for Brownian motion of nested fractals
• Transition density estimates for Brownian motion on affine nested fractals
• Harmonic analysis for resistance forms.
• Calculus on the Sierpinski gasket. I: Polynomials, exponentials and power series
• The resolvent kernel for PCF self-similar fractals
• Volume doubling measures and heat kernel estimates on self-similar sets
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Fractals in the Large
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Analysis on products of fractals
• Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem