On the rate of Quantum Ergodicity, II: Lower bounds

DOI10.1080/03605309408821064zbMath0814.58042OpenAlexW2330114301MaRDI QIDQ4309996

Steven Zelditch

Publication date: 3 January 1995

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

Full work available at URL: https://doi.org/10.1080/03605309408821064

zbMATH Keywords

eigenfunctionpseudo-differential operatorremainder estimates

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Pseudodifferential and Fourier integral operators on manifolds (58J40)

Related Items (3)

Eigenfunction statistics on quantum graphs ⋮ On the rate of quantum ergodicity on hyperbolic surfaces and for billiards ⋮ Monochromatic Random Waves for General Riemannian Manifolds

Cites Work

• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Some inverse spectral results for negatively curved 2-manifolds
• Quantum ergodicity on the sphere
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Quantum transition amplitudes for ergodic and for completely integrable systems
• Selberg trace formulae and equidistribution theorems for closed geodesics and Laplace eigenfunctions: finite area surfaces
• Kuznecov Sum Formulae and Szegˇ Limit Formulae on Manifolds

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