Pseudo-differential operators on fractals and other metric measure spaces

DOI10.4171/RMI/752zbMath1287.35111arXiv1108.2246MaRDI QIDQ2436054

Marius V. Ionescu, Robert S. Strichartz, Luke G. Rogers

Publication date: 21 February 2014

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2246

zbMATH Keywords

Laplacianfractalsmicrolocal analysispseudo-differential operatorsmetric measure spacesfractafoldssub-Gaussian estimates

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Integral transforms in distribution spaces (46F12) Multipliers for harmonic analysis in several variables (42B15) Fractals (28A80) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)

Related Items (13)

A trace theorem for Sobolev spaces on the Sierpinski gasket ⋮ From Strichartz Estimates to Differential Equations on Fractals ⋮ Some spectral properties of pseudo-differential operators on the Sierpiński gasket ⋮ Einstein field equations extended to fractal manifolds: a fractal perspective ⋮ Unexpected spectral asymptotics for wave equations on certain compact spacetimes ⋮ Pseudodifferential operators associated with a semigroup of operators ⋮ Spectral analysis on Barlow and Evans' projective limit fractals ⋮ Spectral analysis beyond \(\ell^2\) on Sierpinski lattices ⋮ Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ The Mathieu differential equation and generalizations to infinite fractafolds ⋮ Sobolev spaces on p.c.f. self-similar sets I: critical orders and atomic decompositions

Cites Work

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• Complex powers of the Laplacian on affine nested fractals as Calderón-Zygmund operators
• The construction of Brownian motion on the Sierpinski carpet
• Spectral decimation on Hambly's homogeneous hierarchical gaskets
• Distribution theory on p.c.f. fractals
• Analysis of the Laplacian and spectral operators on the Vicsek set
• On a spectral analysis for the Sierpiński gasket.
• Brownian motion on the Sierpinski gasket
• What is not in the domain of the Laplacian on Sierpinski gasket type fractals
• Transition density estimates for Brownian motion on affine nested fractals
• Diffusion processes on fractal fields: Heat kernel estimates and large deviations
• Pure point spectrum for the Laplacian on unbounded nested fractals
• Plancherel-type estimates and sharp spectral multipliers
• Calculus on the Sierpinski gasket. I: Polynomials, exponentials and power series
• Uniformly elliptic operators with measurable coefficients
• Estimates for the resolvent kernel of the Laplacian on p.c.f. self-similar fractals and blowups
• Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups
• The resolvent kernel for PCF self-similar fractals
• Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals
• Multivariable spectral multipliers and analysis of quasielliptic operators on fractals
• Brownian motion on nested fractals
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Partial differential equations on products of Sierpinski gaskets
• Spectral operators on the Sierpinski gasket I

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