A positive density analogue of the Lieb-Thirring inequality

@article{Frank2011APD,
  title={A positive density analogue of the Lieb-Thirring inequality},
  author={Rupert L. Frank and Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
  journal={arXiv: Mathematical Physics},
  year={2011}
}
The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr\"odinger operator in terms of an $L^p$ norm of the potential. This is dual to a bound on the $H^1$-norms of a system of orthonormal functions. Here we extend these to analogous inequalities for perturbations of the Fermi sea of non-interacting particles, i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials. 
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