Band asymptotics in two dimensions

DOI10.1016/0001-8708(81)90042-6zbMath0478.58029OpenAlexW2035370714MaRDI QIDQ1161191

Victor W. Guillemin

Publication date: 1981

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(81)90042-6

zbMATH Keywords

spectral asymptoticsaveraging lemmaband asymptoticsband invariantfunctional operations in the ring of pseudodifferential operatorsmeasures on the bands of spectral valuesMorse lemma for volume preserving mapsperturbing the Laplace-Beltrami operator on the 2-sphere or the projective plane by zero order selfadjoint pseudodifferential operators

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Global Riemannian geometry, including pinching (53C20) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items

Transverse Morse lemma for powers of volume forms, Spectral statistics on Zoll surfaces, Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds, Band asymptotics with nonsmooth potentials, Band Asymptotics for Operators of Dirac Type onSⁿ, Spectral Properties of a Certain Class of Complex Potentials, Bernstein inequalities and applications to analytic geometry and differential equations, Regularized trace of the perturbed Laplace-Beltrami operator on two-dimensional manifolds with closed geodesics, On the pseudospectra of Schrödinger operators on Zoll manifolds, The averaging method and ergodic theory for pseudo-differential operators on compact hyperbolic surfaces, Semiclassical approximation for Schrödinger operators on a two-sphere at high energy, Band invariants for perturbations of the harmonic oscillator, Constants of motion of the harmonic oscillator, Diophantine tori and Weyl laws for non-selfadjoint operators in dimension two, The regularized trace of the perturbed Laplace-Beltrami operator on a certain family of manifolds, Rigid motions: Action-angles, relative cohomology and polynomials with roots on the unit circle, Quantum ergodicity on the sphere, A symbol calculus for a class of pseudodifferential operators on \(S^ n\) and band asymptotics, Toeplitz operators in \(n\)-dimensions, Inverse Spectral Results on Two-Dimensional Tori, Schrödinger trace invariants for homogeneous perturbations of the harmonic oscillator, Singular Bohr–Sommerfeld rules for 2D integrable systems, Circular symmetry and the trace formula, Maximally degenerate Laplacians, On the convergence of the trace of a power of the Laplace-Beltrami operator with a potential on the sphere \(S^n\), On Limiting Eigenvalue Distribution Theorems in Semiclassical Analysis, Band invariants and closed trajectories on \(S^ n\), Clustering theorems with twisted spectra, Local \(L^p\) norms of Schrödinger eigenfunctions on \({\mathbb{S}}^2\)

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