Analysis & PDE
- Anal. PDE
- Volume 8, Number 7 (2015), 1707-1731.
Scaling limit for the kernel of the spectral projector and remainder estimates in the pointwise Weyl law
Let be a compact, smooth, Riemannian manifold. We obtain new off-diagonal estimates as for the remainder in the pointwise Weyl law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most . A corollary is that, when rescaled around a non-self-focal point, the kernel of the spectral projector onto the frequency interval has a universal scaling limit as (depending only on the dimension of ). Our results also imply that, if has no conjugate points, then immersions of into Euclidean space by an orthonormal basis of eigenfunctions with frequencies in are embeddings for all sufficiently large.
Anal. PDE, Volume 8, Number 7 (2015), 1707-1731.
Received: 3 February 2015
Revised: 2 June 2015
Accepted: 31 July 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions
Secondary: 58J40: Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx] 35L05: Wave equation
Canzani, Yaiza; Hanin, Boris. Scaling limit for the kernel of the spectral projector and remainder estimates in the pointwise Weyl law. Anal. PDE 8 (2015), no. 7, 1707--1731. doi:10.2140/apde.2015.8.1707. https://projecteuclid.org/euclid.apde/1510843169