Semi‐classical resolvent estimates and regions free of resonances

DOI10.1002/mana.201300018zbMath1296.35034OpenAlexW1578570285MaRDI QIDQ5419517

Georgi Vodev

Publication date: 10 June 2014

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201300018

zbMATH Keywords

potentialresolventsemi-classical

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Second-order elliptic equations (35J15)

Related Items (16)

Semiclassical estimates for scattering on the real line ⋮ Low energy scattering asymptotics for planar obstacles ⋮ Exponential lower resolvent bounds far away from trapped sets ⋮ Semiclassical resolvent bound for compactly supporte \(L^\infty\) potentials ⋮ Semiclassical resolvent bounds for short range L ∞ potentials with singularities at the origin ⋮ Semiclassical resolvent bounds for compactly supported radial potentials ⋮ Exponential time‐decay for a one‐dimensional wave equation with coefficients of bounded variation ⋮ Local energy decay for Lipschitz wavespeeds ⋮ Semiclassical resolvent estimates for bounded potentials ⋮ Semiclassical resolvent bounds in dimension two ⋮ Sharp resolvent bounds and resonance-free regions ⋮ Mathematical study of scattering resonances ⋮ Semiclassical resolvent estimates for short-range \(L^\infty\) potentials ⋮ Quantitative limiting absorption principle in the semiclassical limit ⋮ High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis ⋮ Manifolds with cylindrical ends having a finite and positive number of embedded eigenvalues

Cites Work

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• Fractal upper bounds on the density of semiclassical resonances
• Semiclassical estimates in asymptotically Euclidean scattering
• Uniform estimates of the resolvent of the Laplace-Beltrami operator on infinite volume Riemannian manifolds. II
• Resonance free domains for non globally analytic potentials
• Semi-classical resolvent estimates for the Schrödinger operator on non-compact complete Riemannian manifolds
• Lower bounds for shape resonances widths of long range Schrodinger operators
• Semiclassical resolvent estimates for two and three–body schrödinger operators
• Extending Cutoff Resolvent Estimates via Propagation of Singularities
• Resolvent estimates for perturbations by large magnetic potentials

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