Spectral cluster estimates for Schrödinger operators of relativistic type

DOI10.1016/j.matpur.2021.08.004zbMath1477.35109OpenAlexW3196133146MaRDI QIDQ2246800

Yannick Sire, Cheng Zhang, Xiaoqi Huang

Publication date: 16 November 2021

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2021.08.004

zbMATH Keywords

clusters of eigenvaluesspectral geometryfractional operatorssingular potentialsquasi-modeseigenfunctions of relativistic operators

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Fractional partial differential equations (35R11) Harmonic analysis and PDEs (42B37)

Related Items (4)

Sharp pointwise Weyl laws for Schrödinger operators with singular potentials on flat tori ⋮ From spectral cluster to uniform resolvent estimates on compact manifolds ⋮ Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded domain ⋮ Pointwise Weyl laws for Schrödinger operators with singular potentials

Cites Work

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• Endpoint resolvent estimates for compact Riemannian manifolds
• Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions
• Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes
• On the parabolic kernel of the Schrödinger operator
• The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
• Heat kernel bounds on manifolds
• Pseudodifferential operators and nonlinear PDE
• The stability and instability of relativistic matter
• Fractional quantum mechanics and Lévy path integrals
• One-electron relativistic molecules with Coulomb interaction
• Conditional gauge theorem for non-local Feynman-Kac transforms
• Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators
• Heat kernel for fractional diffusion operators with perturbations
• Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value
• On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds
• Fractals and quantum mechanics
• Uniform Sobolev Resolvent Estimates for the Laplace–Beltrami Operator on Compact Manifolds
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
• On L^p resolvent estimates for Laplace–Beltrami operators on compact manifolds
• Global existence for energy critical waves in 3-d domains
• Slicing surfaces and the Fourier restriction conjecture
• Harnack inequality for stable processes on d-sets
• Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation

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