有边界紧凑流形上薛定谔算子的韦尔定律

arXiv - MATH - Spectral Theory Pub Date : 2024-09-09 DOI:arxiv-2409.05252

Xiaoqi Huang, Xing Wang, Cheng Zhang

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引用次数: 0

摘要

我们证明了在有边界的紧凑流形上具有临界奇异势的薛定谔算子的韦尔定律。我们还改进了在所有周期性大地台球集合的度量为 0 的条件下的韦尔残差估计。证明使用了短时间的高斯热核边界和涉及波方程的扰动论证。

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Weyl laws for Schrödinger operators on compact manifolds with boundary

We prove Weyl laws for Schr\"odinger 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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arXiv - MATH - Spectral Theory

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