Eigenvalue bounds for Schrödinger operators with complex potentials

Rupert L. Frank

doi:10.1112/blms/bdr008

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arXiv · 1005.2785

Eigenvalue bounds for Schrödinger operators with complex potentials

Rupert L. Frank

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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.

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BibTeX RIS

Rupert L. Frank. 2010-05-17. Eigenvalue bounds for Schrödinger operators with complex potentials. https://doi.org/10.1112/blms%2Fbdr008

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