On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals

DOI10.1007/s00440-012-0420-9zbMath1277.28011OpenAlexW2082895208MaRDI QIDQ1955834

Naotaka Kajino

Publication date: 19 June 2013

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-012-0420-9

zbMATH Keywords

oscillationheat kernelDirichlet formshort time asymptoticsaffine nested fractalspost-critically finite self-similar fractals

Mathematics Subject Classification ID

Dirichlet forms (31C25) Fractals (28A80) Transition functions, generators and resolvents (60J35) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (7)

Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022 ⋮ Oscillations of BV measures on unbounded nested fractals ⋮ Heat Kernel Fluctuations for Stochastic Processes on Fractals and Random Media ⋮ Log-periodic asymptotic expansion of the spectral partition function for self-similar sets ⋮ Poincaré Functional Equations, Harmonic Measures on Julia Sets, and Fractal Zeta Functions ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities

Cites Work

• Dirichlet forms and symmetric Markov processes.
• Comparison inequalities for heat semigroups and heat kernels on metric measure spaces
• Electrical resistance of \(n\)-gasket fractal networks
• Local limit theorems for sequences of simple random walks on graphs
• Dominated variation and related concepts and Tauberian theorems for Laplace transforms
• Brownian motion on the Sierpinski gasket
• Functional iterations and periodic oscillations for simple random walk on the Sierpiński graph
• Transition density estimates for Brownian motion on affine nested fractals
• Harmonic analysis for resistance forms.
• On the asymptotic behaviour of analytic solutions of linear iterative functional equations
• Resistance forms, quasisymmetric maps and heat kernel estimates
• Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet
• Localized Eigenfunctions of the Laplacian on p.c.f. Self-Similar Sets
• Asymptotics of the transition probabilities of the simple random walk on self-similar graphs
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
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