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

2016/02/01 by Yaiza Canzani, Boris Hanin, Canzani, Yaiza +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1602.00730

openalex publication_date 2016/02/01 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28

Abstract

This article concerns new off-diagonal estimates on the remainder and its\nderivatives in the pointwise Weyl law on a compact n-dimensional Riemannian\nmanifold. As an application, we prove that near any non self-focal point, the\nscaling limit of the spectral projector of the Laplacian onto frequency windows\nof constant size is a normalized Bessel function depending only on n.\n

Citations

• On the topology of the zero sets of monochromatic random waves

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• Anomalies in local Weyl laws and applications to random topology at critical dimension

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