Lieb-Thirring Inequalities for Jacobi Matrices
Abstract
Description
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.
21 pages, LaTeX2e
21 pages, LaTeX2e