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 mai...
| Published in: | Bulletin of the London Mathematical Society |
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| Main Author: | |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Wiley
2011
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| Subjects: | |
| Online Access: | https://authors.library.caltech.edu/77079/ https://authors.library.caltech.edu/77079/1/1005.2785.pdf https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391 |
| 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. |
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