On integrals of eigenfunctions over geodesics

DOI10.1090/S0002-9939-2014-12233-7zbMath1321.58023arXiv1302.5597OpenAlexW2964089088WikidataQ126027435 ScholiaQ126027435MaRDI QIDQ5496239

Xuehua Chen, Christopher D. Sogge

Publication date: 30 January 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5597

zbMATH Keywords

eigenfunctionsnegative curvature

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (15)

Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature ⋮ Averages of eigenfunctions over hypersurfaces ⋮ Explicit bounds on integrals of eigenfunctions over curves in surfaces of nonpositive curvature ⋮ EXTREME VALUES OF GEODESIC PERIODS ON ARITHMETIC HYPERBOLIC SURFACES ⋮ Looping directions and integrals of eigenfunctions over submanifolds ⋮ On the growth of generalized Fourier coefficients of restricted eigenfunctions ⋮ A two term Kuznecov sum formula ⋮ Improvements for eigenfunction averages: an application of geodesic beams ⋮ Geodesic biangles and Fourier coefficients of restrictions of eigenfunctions ⋮ Upper bounds for geodesic periods over hyperbolic manifolds ⋮ Eigenfunction concentration via geodesic beams ⋮ On the growth of eigenfunction averages: microlocalization and geometry ⋮ Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces ⋮ Expected values of eigenfunction periods ⋮ Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary

Cites Work

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• Local analysis of Selberg's trace formula
• Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• On the wave equation on a compact Riemannian manifold without conjugate points
• A few endpoint geodesic restriction estimates for eigenfunctions
• A uniform bound for geodesic periods of eigenfunctions on hyperbolic surfaces
• On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature
• Kuznecov Sum Formulae and Szegˇ Limit Formulae on Manifolds
• Hangzhou Lectures on Eigenfunctions of the Laplacian

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