On generalized Schr枚dinger semigroups

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• 作者：Batu Gü ; neysu ^{gueneysu@math.hu-berlin.de}
• 关键词：Schr&ouml ; dinger operator ; Feynman&ndash ; Kac formula ; Riemannian geometry ; Lp smoothing
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 June, 2012
• 卷：262
• 期：11
• 页码：4639-4674
• 文件大小：265 K

摘要

We prove a Feynman-Kac formula for Schr枚dinger type operators on vector bundles over arbitrary Riemannian manifolds, where the potentials are allowed to have strong singularities, like those that typically appear in atomic quantum mechanical problems. This path integral formula is then used to prove several -type results, like bounds on the ground state energy and smoothing properties of the corresponding Schr枚dinger semigroups. As another main result, we will prove that with a little control on the Riemannian structure, the latter semigroups are also smoothing for Kato decomposable potentials.