Constructing a Laplacian on the Diamond Fractal

DOI10.1080/10586458.2001.10504461zbMath0999.31007OpenAlexW1990398631MaRDI QIDQ2775770

Robert S. Strichartz, Katharine C. Walker, Jun Kigami

Publication date: 23 November 2002

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1069786349

zbMATH Keywords

Laplace operatornonlinear eigenvalue problemfractals

Mathematics Subject Classification ID

Fractals (28A80) Discrete potential theory (31C20)

Related Items (18)

Duality questions for operators, spectrum and measures ⋮ Resistance forms on self-similar sets with finite ramification of finite type ⋮ Analysis of orthogonality and of orbits in affine iterated function systems ⋮ The spectra of Cantor-type measures with consecutive digits ⋮ Fourier bases of a class of planar self-affine measures ⋮ Fourier bases of the planar self‐affine measures with three digits ⋮ Free probability on the limit \(C^\ast\)-algebra induced by a chain of graphs ⋮ On Semicircular Elements Induced by Connected Finite Graphs ⋮ Harmonic analysis for resistance forms. ⋮ The short-cut test ⋮ Applications of automata and graphs: Labeling operators in Hilbert space. II. ⋮ Axiomatic regularity on metric spaces ⋮ The semicircular law of free probability as noncommutative multivariable operator theory ⋮ Wave propagation speed on fractals ⋮ Applications of automata and graphs: Labeling-operators in Hilbert space. I ⋮ Probability and Fourier duality for affine iterated function systems ⋮ Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals ⋮ From Sobolev inequality to doubling

Cites Work

• Harmonic Calculus on P.C.F. Self-Similar Sets
• A harmonic calculus on the Sierpinski spaces
• Brownian motion on nested fractals
• Densities of Self-Similar Measures on the Line

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