Published August 2011
| Submitted
Journal Article
Open
Eigenvalue bounds for Schrödinger operators with complex potentials
- Creators
- Frank, Rupert L.
Abstract
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.
Additional Information
© 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.Attached Files
Submitted - 1005.2785.pdf
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1005.2785.pdf
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Additional details
- Eprint ID
- 77079
- DOI
- 10.1112/blms/bdr008
- Resolver ID
- CaltechAUTHORS:20170501-065723391
- Created
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2017-05-01Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field