A short proof of Weyl's law for fractional differential operators

被引：15

作者：

Geisinger, Leander ^{[1
]}

机构：

[1] Princeton Univ, Dept Phys, Princeton, NJ 08544 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2014年 / 55卷 / 01期

基金：

美国国家科学基金会;

关键词：

EIGENVALUES;

D O I：

10.1063/1.4861935

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study spectral asymptotics for a large class of differential operators on an open subset of R-d with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with non-homogeneous symbols. Based on a sharp estimate for the sum of the eigenvalues we establish the first term of the semiclassical asymptotics. This generalizes Weyl's law for the Laplace operator. (C) 2014 AIP Publishing LLC.

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页数：7

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