$$C^\infty $$C∞ Scaling Asymptotics for the Spectral Projector of the Laplacian
$$C^\infty $$C∞ Scaling Asymptotics for the Spectral Projector of the Laplacian
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$$C^infty $$C∞ 拉普拉斯谱投影的标度渐近
DOI：
10.1007/s12220-017-9812-5
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Hanin
中科院分区：
文献类型：
--
作者：
Y. Canzani;B. Hanin
本文研究了紧致n维黎曼流形上逐点Weyl律的余项及其导数的新的非对角估计。作为应用，我们证明了在任何非自聚焦点附近，拉普拉斯算子的谱投影到恒定大小的频率窗口上的缩放极限是仅依赖于n的归一化贝塞尔函数。
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.