Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds
Abstract
Description
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 a use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher.
24 pages, revised version, to appear in Journal of Functional Analysis
24 pages, revised version, to appear in Journal of Functional Analysis