Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds

Details Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds

2000-07-04

arxiv.org/abs/math/0007019v2

Mathematics

Spectral Theory

24 pages, revised version, to appear in Journal of Functional Analysis

Scientific paper

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.

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