Remarks on the Cwikel–Lieb–Rozenblum and Lieb–Thirring Estimates for Schrödinger Operators on Riemannian Manifolds

被引：0
|
作者：
El Maati Ouhabaz
César Poupaud
机构：
[1] Université Bordeaux 1,Institut de Mathématiques de Bordeaux (IMB), CNRS UMR 5251, Equipe d’Analyse et Géométrie
[2] MIP/CEREMATH,undefined
来源：
Acta Applicandae Mathematicae | 2010年 / 110卷
关键词：
Spectral theory; Schrödinger operator; Cwikel–Lieb–Rozenblum estimates; Lieb–Thirring estimates; Riemannian manifolds; 46B22; 46G10; 44A10; 42A38;
D O I：
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摘要：
Let M be a general complete Riemannian manifold and consider a Schrödinger operator −Δ+V on L2(M). We prove Cwikel–Lieb–Rozenblum as well as Lieb–Thirring type estimates for −Δ+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 Schrödinger operators with complex-valued potentials.
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页码：1449 / 1459
页数：10
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