High-frequency resolvent estimates on asymptotically Euclidean warped products

DOI10.1080/03605302.2018.1517786zbMath1421.35010arXiv1303.6172OpenAlexW2963875046MaRDI QIDQ4628869

Hans Christianson

Publication date: 25 March 2019

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6172

zbMATH Keywords

local smoothingdamped wave equationone dimensional Schrödinger operatorsmicrolocal resolvent behaviorpartially rectangular billiards

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectrum, resolvent (47A10) Schrödinger operator, Schrödinger equation (35J10) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Resonance in context of PDEs (35B34)

Related Items

Smoothness of the fundamental solution of Schrödinger equations with mild trapping, Local smoothing for the Schrödinger equation on a multi-warped product manifold with inflection-transmission trapping, Quantitative limiting absorption principle in the semiclassical limit, Unique continuation for quasimodes on surfaces of revolution: rotationally invariant neighbourhoods, High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis

Cites Work

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• From resolvent estimates to damped waves
• Fractal upper bounds on the density of semiclassical resonances
• Semiclassical non-concentration near hyperbolic orbits
• From quasimodes to resonances
• Semiclassical estimates in asymptotically Euclidean scattering
• Smoothing effects of Schrödinger evolution groups on Riemannian manifolds
• Imperfect geometric control and overdamping for the damped wave equation
• On the existence and the regularity of solutions of linear pseudo- differential equations
• Sharp local smoothing for manifolds with smooth inflection transmission
• Spreading of quasimodes in the Bunimovich stadium
• Dispersive Estimates for Manifolds with One Trapped Orbit
• Decay of solutions to nondissipative hyperbolic systems on compact manifolds
• Geometric control in the presence of a black box
• Gluing Semiclassical Resolvent Estimates via Propagation of Singularities
• Local Smoothing with a Prescribed Loss for the Schrödinger Equation
• Quantum Monodromy and nonconcentration near a closed semi-hyperbolic orbit
• A Non-Concentration Estimate for Partially Rectangular Billiards
• Unique continuation for quasimodes on surfaces of revolution: rotationally invariant neighbourhoods