Weyl remainders: an application of geodesic beams

DOI10.1007/s00222-023-01178-5zbMath1514.35294arXiv2010.03969WikidataQ125728352 ScholiaQ125728352MaRDI QIDQ6040624

Jeffrey Galkowski, Yaiza Canzani

Publication date: 19 May 2023

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.03969

zbMATH Keywords

asymptotics for the Schwartz kernel of the spectral projectornegative definite Laplace-Beltrami operator

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05)

Related Items

Sharp pointwise Weyl laws for Schrödinger operators with singular potentials on flat tori, A two term Kuznecov sum formula, Pointwise Weyl law for graphs from quantized interval maps, Real analysis, harmonic analysis and applications. Abstracts from the workshop held July 3--9, 2022, Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case, Improvements for eigenfunction averages: an application of geodesic beams, Fourier coefficients of restrictions of eigenfunctions, Semiclassical estimates for eigenvalue means of Laplacians on spheres

Cites Work

• Scaling limit for the kernel of the spectral projector and remainder estimates in the pointwise Weyl law
• Local analysis of Selberg's trace formula
• Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten
• Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
• Fourier coefficients of automorphic forms
• The spectrum of positive elliptic operators and periodic bicharacteristics
• On the wave equation on a compact Riemannian manifold without conjugate points
• The \(\Theta\) function and the Weyl law on manifolds without conjugate points
• \(C^\infty\) scaling asymptotics for the spectral projector of the Laplacian
• Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition
• Formule de Poisson pour les variétés riemanniennes
• When is a geodesic flow of Anosov type, I
• Riemannian manifolds with maximal eigenfunction growth
• Weyl law improvement for products of spheres
• Eigenfunction concentration via geodesic beams
• Riemannian manifolds with geodesic flow of Anosov type
• On the growth of eigenfunction averages: microlocalization and geometry
• Defect measures of eigenfunctions with maximal \(L^\infty\) growth
• Semiclassical \(L^p\) estimates
• The spectral function of an elliptic operator
• Verification of the Hamilton flow conditions associated with Weyl's conjecture
• Monochromatic Random Waves for General Riemannian Manifolds
• Kuznecov Sum Formulae and Szegˇ Limit Formulae on Manifolds
• Mathematical Theory of Scattering Resonances
• Microlocal limits of plane waves and Eisenstein functions
• Improved two–term asymptotics for the eigenvalue distribution function of an elliptic operator on a compact manifold
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
• On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item