2011/08/31 by Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb +1
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Inequality #Laplace operator #Mathematical functions and polynomials #Operator (biology) #Orthonormal basis #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #cond-mat.quant-gas #math-ph #math.MP #math.SP
paper · pdf · doi:10.1215/00127094-2019477
published as Duke Math. J. 162, no. 3 (2013), 435-495 · 48 pages; revised version including a new result (Thm. 2.6); to appear in Duke Mathematical Journal
arxiv created 2012/05/16 · openalex publication_date 2013/02/14 · openalex created_date 2016/06/24 · arxiv updated 2019/12/19 · openalex updated_date 2026/08/05
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).