Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds


Author: Zhongwei Shen
Journal: Proc. Amer. Math. Soc. 131 (2003), 3447-3456
MSC (2000): Primary 35P20, 35J10
Published electronically: February 20, 2003
MathSciNet review: 1990634
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35P20, 35J10

Retrieve articles in all journals with MSC (2000): 35P20, 35J10


Additional Information

Zhongwei Shen
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: shenz@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06968-5
PII: S 0002-9939(03)06968-5
Received by editor(s): May 27, 2002
Published electronically: February 20, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society