Failure of \(L^p\) symmetry of zonal spherical harmonics

DOI10.4171/jst/446zbMath1527.33009arXiv2209.00212OpenAlexW4385293017MaRDI QIDQ6062687

Gabriel Beiner, William Verreault

Publication date: 6 November 2023

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.00212

zbMATH Keywords

spherical harmonicsBessel functionsLegendre polynomialsLaplace eigenfunctionssymmetry conjecture

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spherical harmonics (33C55)

Cites Work

• Nodal sets of eigenfunctions on Riemannian manifolds
• Quasi-symmetry of \(L^ p\) norms of eigenfunctions.
• Distribution symmetry of toral eigenfunctions
• Regular and irregular semiclassical wavefunctions
• Inequalities for the Zeros of Legendre Polynomials and Related Functions
• Sign equidistribution of Legendre polynomials
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