Two-Dimensional Berezin-Li-Yau Inequalities with a Correction Term

被引：0

作者：

Hynek Kovařík

Semjon Vugalter

Timo Weidl

机构：

[1] Universität Stuttgart,Institute of Analysis, Dynamics and Modeling

来源：

Communications in Mathematical Physics | 2009年 / 287卷

关键词：

Correction Term; General Domain; Extended Domain; Spectral Asymptotics; Discrete Laplace Operator;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas, [11].

引用

页码：959 / 981

页数：22

共 12 条

[1]

Berezin F.A.(1972)Covariant and contravariant symbols of operators Izv. Akad. Nauk SSSR Ser. Mat. 36 1134-1167

[2]

Freericks J.K.(2002)Segregation in the Falicov-Kimball model Commun. Math. Phys. 227 243-279

[3]

Lieb E.H.(2003)Lower bound for the segregation in the Falicov-Kimball model J. Phys. A. 36 2227-2234

[4]

Ueltschi D.(1994)Estimates for sums of eigenvalues of the Laplacian J. Funct. Anal. 126 217-227

[5]

Goldbaum P.(1997)Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces J. Funct. Anal. 151 531-545

[6]

Kröger P.(1983)On the Schrödinger equation and the eigenvalue problem, Comm Math. Phys. 88 309-318

[7]

Laptev A.(2003)A lower bound for sums of eigenvalues of the Laplacian Proc. Amer. Math. Soc. 131 631-636

[8]

Li P.(1961)On the eigenvalues of vibrating membranes Proc. London Math. Soc. 11 419-433

[9]

Yau S.T.(1912)Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen Math. Ann. 71 441-479

[10]

Melas A.D.(undefined)undefined undefined undefined undefined-undefined

← 1 2 →