POSITIVE PERTURBATIONS OF SELF-ADJOINT SCHRÖDINGER OPERATORS ON RIEMANNIAN MANIFOLDS

We consider a Schrödinger differential expression L0 = ΔM + V0 on a Riemannian manifold (M,g) with metric g, where ΔM is the scalar Laplacian on M and V0 is a real-valued locally square integrable function on M. We consider a perturbation L0 + V, where V is a non-negative locally square-integrable function on M, and give sufficient conditions for L0 + V to be essentially self-adjoint on [Formula: see text]. This is an extension of a result of T. Kappeler.