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Published August 2011 | Submitted
Journal Article Open

Eigenvalue bounds for Schrödinger operators with complex potentials

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.

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August 19, 2023
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