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Schrödinger operators with a complex valued potential


Author: Sol Schwartzman
Journal: Proc. Amer. Math. Soc. 140 (2012), 4203-4204
MSC (2010): Primary 35J10
DOI: https://doi.org/10.1090/S0002-9939-2012-11367-X
Published electronically: April 4, 2012
MathSciNet review: 2957209
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Abstract: If $ M_n$ is a compact Riemannian manifold for which $ H^1(M_n,\mathbb{Z})=0$, $ V$ is a continuous complex valued function whose imaginary part is of constant sign, and $ -\Delta \psi +V\psi =0$ for some $ C^2$ complex valued function $ \psi $ on $ M_n$, then either $ \psi $ vanishes somewhere or there is a constant $ c$ and an everywhere positive function $ F$ such that $ \psi =cF$.


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

  • 1. Bochner, S. and Yano, K. Curvature and Betti Numbers, Princeton University Press, 1953 (p. 26). MR 0062505 (15:989f)
  • 2. Sol Schwartzman, Schrödinger Operators and the Zeroes of Their Eigenfunctions, Communications in Mathematical Physics 306 (2011), 187-191. MR 2819423 (2012e:81079)

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Additional Information

Sol Schwartzman
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
Email: solschwartzman@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2012-11367-X
Received by editor(s): May 19, 2011
Published electronically: April 4, 2012
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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