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On a positivity preservation property for Schrödinger operators on Riemannian manifolds


Author: Ognjen Milatovic
Journal: Proc. Amer. Math. Soc. 144 (2016), 301-313
MSC (2010): Primary 47B25, 58J50; Secondary 35P05, 60H30
Published electronically: May 28, 2015
MathSciNet review: 3415597
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Abstract: We study a positivity preservation property for Schrödinger operators with singular potential on geodesically complete Riemannian manifolds with non-negative Ricci curvature. We apply this property to the question of self-adjointness of the maximal realization of the corresponding operator.


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Additional Information

Ognjen Milatovic
Affiliation: Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida 32224
Email: omilatov@unf.edu

DOI: https://doi.org/10.1090/proc/12701
Keywords: Non-negative Ricci curvature, positivity preservation, Riemannian manifold, Schr\"odinger operator, self-adjoint, singular potential
Received by editor(s): November 16, 2014
Received by editor(s) in revised form: December 21, 2014
Published electronically: May 28, 2015
Communicated by: Varghese Mathai
Article copyright: © Copyright 2015 American Mathematical Society