\(L^q\) bounds on restrictions of spectral clusters to submanifolds for low regularity metrics

DOI10.2140/apde.2013.6.1263zbMath1291.35154arXiv1202.6385OpenAlexW3099812192MaRDI QIDQ2441197

Matthew D. Blair

Publication date: 21 March 2014

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.6385

zbMATH Keywords

estimateseigenfunctionswave packetsfolding singularitiesquasimodes\(L^p\) estimatesspectral cluster

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Spectral theory and eigenvalue problems for partial differential equations (35P99) PDEs with low regular coefficients and/or low regular data (35R05) General harmonic expansions, frames (42C15) Initial value problems for second-order hyperbolic equations (35L15) Harmonic analysis and PDEs (42B37)

Related Items (6)

Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues ⋮ Concentration of Laplace eigenfunctions and stabilization of weakly damped wave equation ⋮ Eigenfunction restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature ⋮ Absolute continuity of the spectrum of the periodic Schrödinger operator in a cylinder with Robin boundary condition ⋮ Sharp norm estimates of layer potentials and operators at high frequency ⋮ Quantum ergodicity and \(L^{p}\) norms of restrictions of eigenfunctions

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