The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds
Author:
Zhongwei Shen
Journal:
Proc. Amer. Math. Soc. 131 (2003), 34473456
MSC (2000):
Primary 35P20, 35J10
Published electronically:
February 20, 2003
MathSciNet review:
1990634
Fulltext PDF Free Access
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Abstract: Let be a noncompact complete Riemannian manifold. We consider the Schrödinger operator acting on , where is a nonnegative, locally integrable function on . We obtain some simple conditions which imply that , the bottom of the spectrum of , is strictly positive. We also establish upper and lower bounds for the counting function .
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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/S0002993903069685
PII:
S 00029939(03)069685
Received by editor(s):
May 27, 2002
Published electronically:
February 20, 2003
Communicated by:
Andreas Seeger
Article copyright:
© Copyright 2003
American Mathematical Society
