C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian

Yaiza Canzani; Boris Hanin

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arXiv · 1602.00730

C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian

Yaiza Canzani·Boris Hanin

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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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BibTeX RIS

Yaiza Canzani, Boris Hanin. 2016-02-01. C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian. https://arxiv.org/abs/1602.00730

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