The Spectrum of Schrödinger Operators with Positive Potentials in Riemannian Manifolds
نویسنده
چکیده
Let M be a noncompact complete Riemannian manifold. We consider the Schrödinger operator −∆ + V acting on L2(M), where V is a nonnegative, locally integrable function on M . We obtain some simple conditions which imply that inf Spec(−∆ + V ), the bottom of the spectrum of −∆ + V , is strictly positive. We also establish upper and lower bounds for the counting function N(λ).
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