Band invariants and closed trajectories on \(S^ n\)

DOI10.1016/0001-8708(85)90120-3zbMath0587.58049OpenAlexW2058455192MaRDI QIDQ1072203

Alejandro Uribe

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0001-8708(85)90120-3

zbMATH Keywords

spectral analysiscorrespondence principleLaplace-Beltrami-Schrödinger operator

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds, Band asymptotics with nonsmooth potentials, On the pseudospectra of Schrödinger operators on Zoll manifolds, Semiclassical eigenvalues and shape problems on surfaces of revolution, Inverse spectral problem for the 2-sphere Schrödinger operators with zonal potentials, Quantized Neumann problem, separable potentials on S n and the Lamè equation, Band invariants for perturbations of the harmonic oscillator, Observability and quantum limits for the Schrödinger equation on 𝕊^{𝕕}, Multiparameter averaging and inverse spectral problem for anharmonic oscillators in \(\mathbb{R}{}^ n\), Nonselfadjoint Perturbations of Selfadjoint Operators in Two Dimensions II. Vanishing Averages, A symbol calculus for a class of pseudodifferential operators on \(S^ n\) and band asymptotics, Zonal Schrödinger operators on the \(n\)-sphere: Inverse spectral problem and rigidity, The Born approximation in the three-dimensional Calderón problem, Local \(L^p\) norms of Schrödinger eigenfunctions on \({\mathbb{S}}^2\)

Cites Work

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• Some spectral results for the Laplace operator with potential on the n- sphere
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Band asymptotics in two dimensions
• The spectrum of positive elliptic operators and periodic bicharacteristics
• The Radon transform on Zoll surfaces
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• A symbol calculus for a class of pseudodifferential operators on \(S^ n\) and band asymptotics
• The spectral function of an elliptic operator
• Regularization of kepler's problem and the averaging method on a manifold