Equidistribution of toral eigenfunctions along hypersurfaces
DOI10.4171/rmi/1135zbMath1446.58013arXiv1801.07858OpenAlexW2995483173MaRDI QIDQ2177527
Publication date: 6 May 2020
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.07858
lattice pointsharmonic analysis on the torusLaplace eigenfunctions\(L^2\)-restriction estimatesquantum ergodicity restriction
Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51) PDEs on manifolds (35R01)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Almost all eigenfunctions of a rational polygon are uniformly distributed
- Quantum ergodic restriction theorems. I: Interior hypersurfaces in domains with ergodic billiards
- Small scale equidistribution of eigenfunctions on the torus
- On the geometry of the nodal lines of eigenfunctions of the two-dimensional torus
- Restriction of toral eigenfunctions to hypersurfaces and nodal sets
- Upper bounds on the rate of quantum ergodicity
- \(L^{p}\) norms, nodal sets, and quantum ergodicity
- Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
- Ergodicity and eigenfunctions of the Laplacian
- Uniform distribution of eigenfunctions on compact hyperbolic surfaces
- Fourier transforms related to convex sets
- The spectrum of positive elliptic operators and periodic bicharacteristics
- On the rate of quantum ergodicity. I: Upper bounds
- Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
- Nodal intersections and geometric control
- The proof of the \(l^2\) decoupling conjecture
- Quantitative equidistribution properties of toral eigenfunctions
- Quantum ergodicity for point scatterers on arithmetic tori
- Quantum ergodic restriction theorems: manifolds without boundary
- On the distribution of matrix elements for the quantum cat map
- Planck-scale mass equidistribution of toral Laplace eigenfunctions
- Quadratic forms and semiclassical eigenfunction hypothesis for flat tori
- The spectral function of an elliptic operator
- Über Integrale auf konvexen Körpern. I, II
- Northcott's theorem on heights II. The quadratic case
- Kuznecov Sum Formulae and Szegˇ Limit Formulae on Manifolds
- Quantum ergodicity for restrictions to hypersurfaces
- Fourier transforms of surface-carried measures and differentiability of surface averages
- A Cantor-Lebesgue Theorem in Two Dimensions
- Almost-primes represented by quadratic polynomials
This page was built for publication: Equidistribution of toral eigenfunctions along hypersurfaces
