C Scaling Asymptotics for the Spectral Projector of the Laplacian

Yaiza Canzani, Boris Hanin

Research output: Contribution to journalArticlepeer-review

5 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 languageEnglish (US)
Pages (from-to)111-122
Number of pages12
JournalJournal of Geometric Analysis
Volume28
Issue number1
DOIs
StatePublished - Jan 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

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

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