Abstract
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.
Citation
Yaiza Canzani. Boris Hanin. "Scaling limit for the kernel of the spectral projector and remainder estimates in the pointwise Weyl law." Anal. PDE 8 (7) 1707 - 1731, 2015. https://doi.org/10.2140/apde.2015.8.1707
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