✦ LIBER ✦
Essential Self-Adjointness for Semi-bounded Magnetic Schrödinger Operators on Non-compact Manifolds
✍ Scribed by Mikhail Shubin
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 182 KB
- Volume
- 186
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
We prove essential self-adjointness for semi-bounded below magnetic Schrödinger 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 the use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher.