Eigenvalue bounds for Schrodinger 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: | Text |
Language: | English |
Published: |
Oxford University Press
2011
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Subjects: | |
Online Access: | http://blms.oxfordjournals.org/cgi/content/short/bdr008v1 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. |
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