AN IMPROVEMENT TO A BEREZIN-LI-YAU TYPE INEQUALITY

被引:16
|
作者
Yolcu, Selma Yildirim [1 ]
机构
[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
关键词
Fractional Laplacian; Weyl law; universal bounds; Klein-Gordon operator; Berezin-Li-Yau inequality; CAUCHY PROCESS; BOUNDS;
D O I
10.1090/S0002-9939-2010-10419-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article we improve a lower bound for Sigma(k)(j=1) beta(j) (a Berezin-Li-Yau type inequality) that appeared in an earlier paper of Harrell and Yolcu. Here beta(j) denotes the jth eigenvalue of the Klein Gordon Hamiltonian H-0,H-Omega = vertical bar p vertical bar when restricted to a bounded set Omega subset of R-n. H-0,H-Omega can also be described as the generator of the Cauchy stochastic process with a killing condition on partial derivative Omega. To do this, we adapt the proof of Melas, who improved the estimate for the bound of E-j=1(k) lambda(j), where lambda(j) denotes the jth eigenvalue of the Dirichlet; Laplacian on a bounded domain in R-d.
引用
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页码:4059 / 4066
页数:8
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