Sampling and Weyl's Law on compact Riemannian manifolds
Sampling and Weyl's Law on compact Riemannian manifolds
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紧黎曼流形上的采样和韦尔定律
DOI：
10.1109/sampta.2017.8024469
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
I. Pesenson
中科院分区：
文献类型：
--
作者：
I. Pesenson
紧致黎曼流形上Laplace-Beltrami算子在区间[0，ω]上的特征值个数N_ω的逼近公式是著名的Weyl渐近公式。本文从紧致黎曼流形上的Shannon抽样的角度讨论了这一问题。也就是说，对于M上的ω带限函数的子空间，我们证明了Nω相当于某些采样集的基数。
The well known Weyl's asymptotic formula gives an approximation to the number Nω of eigenvalues (counted with multiplicities) on an interval [0, ω] of the Laplace-Beltrami operator on a compact Riemannian manifold M. In this paper we approach this question from the point of view of Shannon-type sampling on compact Riemannian manifolds. Namely, we show that Nω is comparable to cardinality of certain sampling sets for the subspace of ω-bandlimited functions on M.