Spectral estimates around a critical level
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Publication:1902022
DOI10.1215/S0012-7094-95-07823-5zbMath0849.58067OpenAlexW1978163459WikidataQ125743190 ScholiaQ125743190MaRDI QIDQ1902022
Alejandro Uribe, Thierry Paul, R. G. M. Brummelhuis
Publication date: 10 November 1996
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1215/s0012-7094-95-07823-5
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)
Related Items (30)
Equilibrium and eigenfunctions estimates in the semiclassical regime ⋮ Spectral statistics on Zoll surfaces ⋮ Towards a semiclassical theory of the quantum Baker's map ⋮ Sharp semiclassical estimates for the number of eigenvalues below a totally degenerate critical level ⋮ Singular equivariant asymptotics and Weyl's law. On the distribution of eigenvalues of an invariant elliptic operator ⋮ \(L^{2}\)-restriction bounds for eigenfunctions along curves in the quantum completely integrable case ⋮ Inverse spectral problems for Schrödinger operators ⋮ On the semi-classical spectrum of an integrable system of dymension 1 around a hyperbolic singularity ⋮ Symplectic inverse spectral theory for pseudodifferential operators ⋮ A semi-classical trace formula for Schrödinger operators in the case of a critical energy level ⋮ On the pointwise behavior of semi-classical measures ⋮ Koszul complexes, Birkhoff normal form and the magnetic Dirac operator ⋮ Spectral rigidity for spherically symmetric manifolds with boundary ⋮ On the Poisson relation for compact Lie groups ⋮ Semiclassical asymptotic expansions for functions of the Bochner-Schrödinger operator ⋮ Eigenvalues of the reference operator and semiclassical resonances ⋮ Spectral fluctuations of Schrödinger operators generated by critical points of the potential ⋮ The Berry–Keating operator on a lattice ⋮ Unnamed Item ⋮ A semi-classical trace formula at a non-degenerate critical level. ⋮ A semi-classical study of the Jaynes–Cummings model ⋮ Quantum ergodicity and symmetry reduction ⋮ Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate minimum of the potential ⋮ Higher dimensional nonclassical eigenvalue asymptotics ⋮ Contributions of non-extremum critical points to the semi-classical trace formula ⋮ Asymptotic approximation of degenerate fiber integrals ⋮ Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential ⋮ Unnamed Item ⋮ A semi-classical trace formula for several commuting operators ⋮ Local scaling asymptotics in phase space and time in Berezin–Toeplitz quantization
Cites Work
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- Regular singular asymptotics
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- Uniform distribution of eigenfunctions on compact hyperbolic surfaces
- Oscillatory integrals with singular symbols
- The spectrum of positive elliptic operators and periodic bicharacteristics
- Newton polyhedra and estimation of oscillating integrals
- Circular symmetry and the trace formula
- The semi-classical trace formula and propagation of wave packets
- Distributions Invariant under an Orthogonal Group of Arbitrary Signature.
- Singular asymptotics approach to partial differential equations with isolated singularities in the coefficients
- Intégrales asymptotiques et monodromie
- Lagrangian Intersection and the Cauchy Problem
- On the semiclassical localization of the quantum probability
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