Lieb-Thirring Inequalities for Jacobi Matrices
数学物理
2007-05-23 v1 math.MP
摘要
For a Jacobi matrix J on l^2(Z_+) with Ju(n)=a_{n-1} u(n-1) + b_n u(n) + a_n u(n+1), we prove that \sum_{|E|>2} (E^2 -4)^{1/2} \leq \sum_n |b_n| + 4\sum_n |a_n -1|. We also prove bounds on higher moments and some related results in higher dimension.
引用
@article{arxiv.math-ph/0112027,
title = {Lieb-Thirring Inequalities for Jacobi Matrices},
author = {Dirk Hundertmark and Barry Simon},
journal= {arXiv preprint arXiv:math-ph/0112027},
year = {2007}
}
备注
21 pages, LaTeX2e