Essential self-adjointness for semi-bounded magnetic Schr\"odinger operators on non-compact manifolds
Essential self-adjointness for semi-bounded magnetic Schr\"odinger operators on non-compact manifolds
复制标题
非紧流形上半有界磁薛定格算子的基本自伴性
DOI：
10.1006/jfan.2001.3778
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
M. Shubin
中科院分区：
文献类型：
--
作者：
M. Shubin
我们证明了完整黎曼流形上的半有界下磁薛定谔算子的基本自伴性，具有给定的正光滑测度，该测度与度量无关。允许标量势的一些奇点。
这是波夫兹纳-维恩霍尔茨-西马德定理的延伸。该证明使用 Wienholtz 方案，但需要通过零件技术进行精细的不变积分，以及使用由 Karcher 的非平凡平滑过程构造的一系列截止函数。
We prove essential self-adjointness for semi-bounded below magnetic Schr\"odinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed.
This is an extension of the Povzner--Wienholtz--Simader theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher.