C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian
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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
Date issued
2017-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1050-6926
1559-002X