Laplacians on a family of quadratic Julia sets I

DOI10.1090/S0002-9947-2012-05398-0zbMath1290.28011OpenAlexW1973137520WikidataQ121816383 ScholiaQ121816383MaRDI QIDQ2841339

Taryn C. Flock, Robert S. Strichartz

Publication date: 25 July 2013

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05398-0

zbMATH Keywords

Julia setsLaplacians

Mathematics Subject Classification ID

Fractals (28A80)

Related Items (9)

``Graph paper trace characterizations of functions of finite energy ⋮ Resistance forms on self-similar sets with finite ramification of finite type ⋮ Exact spectrum of the Laplacian on a domain in the Sierpinski gasket ⋮ Computing eigenvalues of the Laplacian on rough domains ⋮ From Strichartz Estimates to Differential Equations on Fractals ⋮ Convergence of energy forms on Sierpinski gaskets with added rotated triangle ⋮ Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps ⋮ SPECTRUM OF THE LAPLACIAN ON THE VICSEK SET “WITH NO LOOSE ENDS” ⋮ The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain

Cites Work

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• Uniqueness of extremizers for an endpoint inequality of the \(k\)-plane transform
• Analysis of the Laplacian and spectral operators on the Vicsek set
• On a spectral analysis for the Sierpiński gasket.
• Laplacians on the basilica Julia set
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Laplacians on a family of quadratic Julia sets. II.
• Spectral analysis of Laplacians on the Vicsek set
• Criteria for spectral gaps of Laplacians on fractals

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