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15 February 2013 A positive density analogue of the Lieb–Thirring inequality
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Duke Math. J. 162(3): 435-495 (15 February 2013). DOI: 10.1215/00127094-2019477

Abstract

The Lieb–Thirring inequalities give a bound on the negative eigenvalues of a Schrödinger operator in terms of an Lp-norm of the potential. These are dual to bounds on the H1-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of the Fermi sea of noninteracting particles (i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials).

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Rupert L. Frank. Mathieu Lewin. Elliott H. Lieb. Robert Seiringer. "A positive density analogue of the Lieb–Thirring inequality." Duke Math. J. 162 (3) 435 - 495, 15 February 2013. https://doi.org/10.1215/00127094-2019477

Information

Published: 15 February 2013
First available in Project Euclid: 14 February 2013

zbMATH: 1260.35088
MathSciNet: MR3024090
Digital Object Identifier: 10.1215/00127094-2019477

Subjects:
Primary: 35P15
Secondary: 35J10 , 35Q40 , 81Q20

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 3 • 15 February 2013
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