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

Mikhail Shubin
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Abstract

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.

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Mikhail Shubin. 2001-07-30. Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds. https://arxiv.org/abs/math/0007019

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