TheL2behavior of eigenfunctions near the glancing set

DOI10.1080/03605302.2016.1227339zbMath1362.53046arXiv1604.01699OpenAlexW3105232632MaRDI QIDQ2955371

Jeffrey Galkowski

Publication date: 25 January 2017

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

Full work available at URL: https://arxiv.org/abs/1604.01699

zbMATH Keywords

pseudodifferential operatorssemiclassical analysiseigenfunction estimatesrestriction to hypersurfacesspectral weight

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Second-order elliptic equations (35J15) Pseudodifferential and Fourier integral operators on manifolds (58J40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (5)

Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues ⋮ The quantization of normal velocity does not concentrate on hypersurfaces ⋮ Nodal intersections and geometric control ⋮ Control from an interior hypersurface ⋮ Lower bounds for Cauchy data on curves in a negatively curved surface

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Quantum ergodic restriction theorems. I: Interior hypersurfaces in domains with ergodic billiards
• Semiclassical \(L^p\) estimates of quasimodes on curved hypersurfaces
• Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions
• Fractal upper bounds on the density of semiclassical resonances
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Equivalence of glancing hyper-surfaces
• Asymptotic distribution of resonances for convex obstacles
• Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues
• Ergodicity of eigenfunctions for ergodic billiards
• Erratum to: ``Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions
• Quantum ergodic restriction theorems: manifolds without boundary
• Semiclassical \(L^p\) estimates
• Stochastic stability of Pollicott–Ruelle resonances
• Quantum ergodicity for restrictions to hypersurfaces
• SemiclassicalL^pEstimates of Quasimodes on Submanifolds

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