Weyl laws for Schrödinger operators on compact manifolds with boundary

2024/09/09 by Xiaoqi Huang, Xing Wang, Huang, Xiaoqi +3
Mathematics · #35P20 #47A75 #58C40 #58J32 #58J50 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.05252

openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Weyl laws for Schrödinger operators with critically singular potentials on compact manifolds with boundary. We also improve the Weyl remainder estimates under the condition that the set of all periodic geodesic billiards has measure 0. These extend the classical results by Seeley, Ivrii and Melrose. The proof uses the Gaussian heat kernel bounds for short times and a perturbation argument involving the wave equation.

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