Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential
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Abstract:
We study a family of Schrödinger operators $-{\Delta }+\alpha V$. We find conditions on $V$ that guarantee that the a.c. spectrum of the operator covers the interval $[0,\infty )$ for almost every $\alpha$.References
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Additional Information
- Oleg Safronov
- Affiliation: Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223
- MR Author ID: 607478
- Received by editor(s): March 16, 2012
- Published electronically: October 11, 2013
- Communicated by: James E. Colliander
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 639-649
- MSC (2010): Primary 81U05, 47F05
- DOI: https://doi.org/10.1090/S0002-9939-2013-12186-6
- MathSciNet review: 3134004