## The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

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- by Zhongwei Shen
- Proc. Amer. Math. Soc.
**131**(2003), 3447-3456 - DOI: https://doi.org/10.1090/S0002-9939-03-06968-5
- Published electronically: February 20, 2003
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## Abstract:

Let $M$ be a noncompact complete Riemannian manifold. We consider the Schrödinger operator $-\Delta +V$ acting on $L^{2}(M)$, where $V$ is a nonnegative, locally integrable function on $M$. We obtain some simple conditions which imply that $\inf \text {Spec} (-\Delta +V)$, the bottom of the spectrum of $-\Delta +V$, is strictly positive. We also establish upper and lower bounds for the counting function $N(\lambda )$.## References

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## Bibliographic Information

**Zhongwei Shen**- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
- MR Author ID: 227185
- Email: shenz@ms.uky.edu
- Received by editor(s): May 27, 2002
- Published electronically: February 20, 2003
- Communicated by: Andreas Seeger
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 3447-3456 - MSC (2000): Primary 35P20, 35J10
- DOI: https://doi.org/10.1090/S0002-9939-03-06968-5
- MathSciNet review: 1990634