On self-adjointness of a Schroedinger operator

Details On self-adjointness of a Schroedinger operator On self-adjointness of a Schroedinger operator

1996-07-28

arxiv.org/abs/funct-an/9607002v2

Mathematics

Differential Geometry

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

Scientific paper

Let $M$ be a complete Riemannian manifold and let $\Omega^*(M)$ denote the space of differential forms on $M$. Let $d:\Omega^*(M) \to \Omega^{*+1}(M)$ 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 $V(x):\Omega^*(M)\to \Omega^*(M)$ 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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