The averaging method and ergodic theory for pseudo-differential operators on compact hyperbolic surfaces

DOI10.1016/0022-1236(89)90091-8zbMath0693.58025OpenAlexW1978513206WikidataQ125364947 ScholiaQ125364947MaRDI QIDQ908567

Steven Zelditch

Publication date: 1989

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(89)90091-8

zbMATH Keywords

geodesic flowpseudo-differential operatorergodicRiemannian manifold with Laplacian

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Ergodic theory (37A99) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items (8)

Mass equidistribution for automorphic forms of cohomological type on 𝐺𝐿₂ ⋮ Uniform distribution of eigenfunctions on compact hyperbolic surfaces ⋮ Patterson-Sullivan distributions in higher rank ⋮ Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series ⋮ Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras ⋮ Triple product \(L\)-functions and quantum chaos on \(\mathrm{SL}(2,\mathbb C)\) ⋮ Semiclassical limits for the hyperbolic plane ⋮ Ergodic properties of the quantum geodesic flow on tori

Cites Work

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• Eigenvalue distribution theorems for certain homogeneous spaces
• Pseudo-differential analysis on hyperbolic surfaces
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Band asymptotics in two dimensions
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential

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