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Abstract: We show that the absolute values of non-positive eigenvalues of Schr\-odingeroperators with complex potentials can be bounded in terms of L p-norms of thepotential. This extends an inequality of Abramov, Aslanyan, and Davies tohigher dimensions and proves a conjecture by Laptev and Safronov. Our mainingredient are the uniform Sobolev inequalities of Kenig, Ruiz, and Sogge.



Autor: Rupert L. Frank

Fuente: https://arxiv.org/







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