C∞ Scaling Asymptotics for the Spectral Projector of the Laplacian

Yaiza Canzani; Boris Hanin

doi:10.1007/s12220-017-9812-5

C^∞ Scaling Asymptotics for the Spectral Projector of the Laplacian

Yaiza Canzani
, Boris Hanin

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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.

Original language	English (US)
Pages (from-to)	111-122
Number of pages	12
Journal	Journal of Geometric Analysis
Volume	28
Issue number	1
DOIs	https://doi.org/10.1007/s12220-017-9812-5
State	Published - Jan 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Laplace eigenfunctions
Non-self-focal points
Pointwise Weyl Law
Scaling limits
Spectral projector

Access to Document

10.1007/s12220-017-9812-5

Cite this

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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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KW - Scaling limits

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