Existence of self-similar energies on finitely ramified fractals

DOI10.1007/s11854-014-013-xzbMath1298.28021OpenAlexW2035401131MaRDI QIDQ464284

Roberto Peirone

Publication date: 17 October 2014

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-014-013-x

zbMATH Keywords

renormalization operator\(r\)-eigenformG-eigenformself-similar discrete Dirichlet form

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractals (28A80) Discrete potential theory (31C20)

Related Items (11)

\(p\)-energies on p.c.f. self-similar sets ⋮ Uniqueness of eigenforms on fractals - II ⋮ On a recursive construction of Dirichlet form on the Sierpiński gasket ⋮ Fixed points of anti‐attracting maps and eigenforms on fractals ⋮ Homogeneous Dirichlet forms on p.c.f. fractals and their spectral asymptotics ⋮ Degenerate limits for one-parameter families of non-fixed-point diffusions on fractals ⋮ Uniqueness of eigenforms on fractals ⋮ Another point of view on Kusuoka's measure ⋮ EIGENFORMS ON FRACTALS WITH CONNECTED INTERIOR AND THREE VERTICES ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ Dirichlet forms and critical exponents on fractals

Cites Work

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• The short-cut test
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Brownian motion on nested fractals
• Existence and uniqueness of diffusions on finitely ramified self-similar fractals
• Existence of eigenforms on fractals with three vertices
• SELF-SIMILAR ENERGIES ON POST-CRITICALLY FINITE SELF-SIMILAR FRACTALS

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