$$C^\infty $$ Scaling Asymptotics for the Spectral Projector of the Laplacian |
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Authors: | Yaiza Canzani Boris Hanin |
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Institution: | 1.University of North Carolina at Chapel Hill,Chapel Hill,USA;2.Department of Mathematics,MIT,Cambridge,USA |
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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. |
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