Remarks on the Cwikel-Lieb-Rozenblum and Lieb-Thirring Estimates for Schrodinger Operators on Riemannian Manifolds

被引：3

作者：

Ouhabaz, El Maati ^{[1
]}

Poupaud, Cesar ^{[2
]}

机构：

[1] Univ Bordeaux 1, IMB, CNRS, Equipe Anal & Geometrie,UMR 5251, F-33405 Talence, France

[2] MIP CEREMATH, F-31000 Toulouse, France

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 03期

关键词：

Spectral theory; Schrodinger operator; Cwikel-Lieb-Rozenblum estimates; Lieb-Thirring estimates; Riemannian manifolds; ELLIPTIC-OPERATORS; INEQUALITIES; EIGENVALUES; KERNEL; BOUNDS;

D O I：

10.1007/s10440-009-9519-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a general complete Riemannian manifold and consider a Schrodinger operator -Delta+V on L (2)(M). We prove Cwikel-Lieb-Rozenblum as well as Lieb-Thirring type estimates for -Delta+V. These estimates are given in terms of the potential and the heat kernel of the Laplacian on the manifold. Some of our results hold also for Schrodinger operators with complex-valued potentials.

引用

页码：1449 / 1459

页数：11