Nonselfadjoint Perturbations of Selfadjoint Operators in Two Dimensions II. Vanishing Averages

DOI10.1081/PDE-200064447zbMath1096.47053arXivmath/0312222OpenAlexW2039434753MaRDI QIDQ5708002

Michael Hitrik, Johannes Sjöstrand

Publication date: 25 November 2005

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

Full work available at URL: https://arxiv.org/abs/math/0312222

zbMATH Keywords

eigenvalueaveraging methodperiodic flownon-selfadjoint operatorLagrangian torusodd perturbation

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Perturbation theory of linear operators (47A55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Lagrangian submanifolds; Maslov index (53D12) Perturbations of PDEs on manifolds; asymptotics (58J37) Pseudodifferential operators (47G30)

Related Items

Diophantine tori and Weyl laws for non-selfadjoint operators in dimension two, Spectral monodromy of non-self-adjoint operators, Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets

Cites Work

• Unnamed Item
• Applications harmoniques entre graphes finis et un théorème de superrigidité. (Harmonic maps between finite graphs and a theorem of superrigidity.)
• Band invariants and closed trajectories on \(S^ n\)
• Some spectral results for the Laplace operator with potential on the n- sphere
• Some spectral results on rank one symmetric spaces
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• The Radon transform on Zoll surfaces
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• The Radon transform.
• Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions. I
• Spectral statistics on Zoll surfaces
• On global action-angle coordinates
• The Spectrum of the Damped Wave Operator for a Bounded Domain inR²
• Asymptotic distribution of eigenfrequencies for damped wave equations
• Nonlinear wave equations and constrained harmonic motion