Focal points and sup-norms of eigenfunctions

DOI10.4171/RMI/904zbMath1361.32011arXiv1311.3999OpenAlexW2963401810MaRDI QIDQ346658

Christopher D. Sogge, Steven Zelditch

Publication date: 29 November 2016

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3999

zbMATH Keywords

eigenfunctions\(L^\infty\) boundsself-focal dissipative points

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Real-analytic manifolds, real-analytic spaces (32C05)

Related Items (16)

Focal points and sup-norms of eigenfunctions II: the two-dimensional case ⋮ Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions ⋮ Completeness of boundary traces of eigenfunctions ⋮ Eigenfunction scarring and improvements in \(L^\infty\) bounds ⋮ A two term Kuznecov sum formula ⋮ Quantum entanglement and the growth of Laplacian eigenfunctions ⋮ Improvements for eigenfunction averages: an application of geodesic beams ⋮ Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière ⋮ \(C^\infty\) scaling asymptotics for the spectral projector of the Laplacian ⋮ Eigenfunction concentration via geodesic beams ⋮ On the growth of eigenfunction averages: microlocalization and geometry ⋮ Interface asymptotics of eigenspace Wigner distributions for the harmonic oscillator ⋮ Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature ⋮ Defect measures of eigenfunctions with maximal \(L^\infty\) growth ⋮ Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary ⋮ Local \(L^p\) norms of Schrödinger eigenfunctions on \({\mathbb{S}}^2\)

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