Product Manifolds with Improved Spectral Cluster and Weyl Remainder Estimates

DOI10.1007/978-3-031-37800-3_6arXiv2205.04489OpenAlexW4387916313MaRDI QIDQ6194485

Xiaoqi Huang, Christopher D. Sogge, Michael E. Taylor

Publication date: 19 March 2024

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.04489

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) PDEs on manifolds (35R01)

Cites Work

• Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten
• Oscillatory integrals and spherical harmonics
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• On the convergence of Riesz means on compact manifolds
• The spectrum of positive elliptic operators and periodic bicharacteristics
• On the wave equation on a compact Riemannian manifold without conjugate points
• Concerning Toponogov's theorem and logarithmic improvement of estimates of eigenfunctions
• Weyl law improvement for products of spheres
• Eigenfunction concentration via geodesic beams
• Uniform \(L^p\) resolvent estimates on the torus
• Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature
• Improvement of eigenfunction estimates on manifolds of nonpositive curvature
• The proof of the \(l^2\) decoupling conjecture
• The spectral function of an elliptic operator
• On Fourier coefficients and transforms of functions of two variables
• Hangzhou Lectures on Eigenfunctions of the Laplacian
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