C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian
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Author(s)
Canzani, Yaiza
Hanin, Boris
Date Issued
May 2017
Journal
The Journal of Geometric Analysis
Publisher
Springer US
Citation
Canzani, Yaiza, and Boris Hanin. “C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian.” The Journal of Geometric Analysis, vol. 28, no. 1, Jan. 2018, pp. 111–22.
Version
Author's final manuscript
Abstract
This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non-self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n. Keywords: Spectral projector, Pointwise Weyl Law, Scaling limits, Laplace eigenfunctions, Non-self-focal points
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s12220-017-9812-5
