On self-adjointness of a Schroedinger operator

1996/07/28 by Maxim Braverman, Braverman, Maxim
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #dg-ga #funct-an #math.DG #math.FA

paper · pdf · doi:10.48550/arxiv.funct-an/9607002

AMS-TeX, 7 pages; some minor misprints were corrected

arxiv created 1996/08/28 · arxiv updated 2009/11/30

Abstract

Let M be a complete Riemannian manifold and let Ω^*(M) denote the space of differential forms on M. Let d:Ω^*(M) → Ω^*+1(M) be the exterior differential operator and let \Del=dd^*+d^*d be the Laplacian. We establish a sufficient condition for the Schroedinger operator H=\Del+V(x) (where the potential V(x):Ω^*(M)→ Ω^*(M) is a zero order differential operator) to be self-adjoint. Our result generalizes a theorem by Igor Oleinik about self-adjointness of a Schroedinger operator which acts on the space of scalar valued functions.

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