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

2000/07/04 by Mikhail Shubin, Shubin, Mikhail · 2 citations
Mathematics · #35P05 #58G25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P05 #msc:58G25

paper · pdf · doi:10.48550/arxiv.math/0007019

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

arxiv created 2001/07/30 · arxiv updated 2009/11/30

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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• Uniqueness problem for accretive Schrödinger operators with complex singular coefficients
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