Magnetic fields on resistance spaces

DOI10.4171/JFG/30zbMath1432.81063arXiv1501.01100OpenAlexW2963426335MaRDI QIDQ294290

F. Blanchet-Sadri, M. Dambrine

Publication date: 16 June 2016

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.01100

zbMATH Keywords

Dirichlet formsself-adjointnessmagnetic Laplaciansresistance forms

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Electromagnetic interaction; quantum electrodynamics (81V10) Fractals (28A80) Forms (bilinear, sesquilinear, multilinear) (47A07) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (11)

Fractal snowflake domain diffusion with boundary and interior drifts ⋮ Magnetic Laplacians of locally exact forms on the Sierpinski gasket ⋮ Power dissipation in fractal AC circuits ⋮ Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: solving the Hofstadter-Sierpinski butterfly ⋮ Approximation of fractals by discrete graphs: norm resolvent and spectral convergence ⋮ Spectral analysis on Barlow and Evans' projective limit fractals ⋮ Finite Energy Coordinates and Vector Analysis on Fractals ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ Approximation of partial differential equations on compact resistance spaces ⋮ On the viscous Burgers equation on metric graphs and fractals ⋮ Parabolic type equations associated with the Dirichlet form on the sierpinski gasket

Cites Work

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• On a spectral analysis for the Sierpiński gasket.
• Fredholm modules on P.C.F. self-similar fractals and their conformal geometry
• Uniqueness of Brownian motion on Sierpiński carpets
• What is not in the domain of the Laplacian on Sierpinski gasket type fractals
• 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
• Dirichlet forms and symmetric Markov processes
• Derivations as square roots of Dirichlet forms
• Harmonic analysis for resistance forms.
• Derivations and Dirichlet forms on fractals
• On singularity of energy measures on self-similar sets
• Dirac and magnetic Schrödinger operators on fractals
• Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces
• Resistance forms, quasisymmetric maps and heat kernel estimates
• ON SINGULARITY OF ENERGY MEASURES ON SELF-SIMILAR SETS II
• Brownian motion on nested fractals
• Fractafolds based on the Sierpinski gasket and their spectra
• Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals

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