C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2018
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| Online Access: | http://hdl.handle.net/1721.1/115816 https://orcid.org/0000-0001-5911-1432 |
| Summary: | 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 |
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