A remark on a paper of E. B. Davies

DOI10.1090/S0002-9939-01-05909-3zbMath0981.35107MaRDI QIDQ2723492

Maciej Zworski

Publication date: 5 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

semi-classical pseudodifferential operatorscomplex quasi-modesHörmander's commutator conditionsemi-classical symbols

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27)

Related Items (24)

Pseudomodes for non-self-adjoint Dirac operators ⋮ Pseudospectra in non-Hermitian quantum mechanics ⋮ Semiclassical Analysis for the Kramers–Fokker–Planck Equation ⋮ The semiclassical regime for ablation front models ⋮ Almost sure Weyl law for quantized tori ⋮ Eight Perspectives on the Exponentially Ill-Conditioned Equation $\varepsilon y - x y' + y = 0$ ⋮ Resolvent estimates for one-dimensional Schrödinger operators with complex potentials ⋮ Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds ⋮ On the pseudospectrum of the harmonic oscillator with imaginary cubic potential ⋮ Almost sure Weyl law for a differential system in dimension 1 ⋮ Pseudo-modes for Schrödinger operators with complex potentials ⋮ Semiclassical spectral instability for non-self-adjoint operators. I: A model ⋮ Two point eigenvalue correlation for a class of non-selfadjoint operators under random perturbations ⋮ On the pseudospectrum of elliptic quadratic differential operators ⋮ Nonlinear instability in a semiclassical problem ⋮ Semiclassical spectral instability for non-self-adjoint operators. I: A model ⋮ Wave packet pseudomodes of variable coefficient differential operators ⋮ Resolvent Estimates for Non-Selfadjoint Operators via Semigroups ⋮ Perturbations of Gibbs semigroups and the non-selfadjoint harmonic oscillator ⋮ Pseudospectra of semiclassical (pseudo-) differential operators ⋮ Pseudospectra of semiclassical boundary value problems ⋮ Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets ⋮ Semi-classical analysis and pseudo-spectra ⋮ Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators

Cites Work

• Unnamed Item
• Semi-classical states for non-self-adjoint Schrödinger operators
• A global construction for pseudo-differential operators with non- involutive characteristics
• Scattering metrics and geodesic flow at infinity
• Differential equations without solutions

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