Eigenvalue bounds for Schrödinger operators with complex potentials
We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our ma...
| Published in: | Bulletin of the London Mathematical Society |
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| Main Author: | |
| Format: | Article in Journal/Newspaper |
| Language: | unknown |
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Wiley
2011
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| Subjects: | |
| Online Access: | https://doi.org/10.1112/blms/bdr008 |
| Summary: | We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz and Sogge. © 2011 London Mathematical Society. Received 17 May 2010; revised 20 January 2011; published online 6 April 2011. The author wishes to thank A. Laptev and O. Safronov for useful correspondence. Submitted - 1005.2785.pdf |
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