Lieb-Thirring Inequalities for Jacobi Matrices

Details Lieb-Thirring Inequalities for Jacobi Matrices Lieb-Thirring Inequalities for Jacobi Matrices

2001-12-13

arxiv.org/abs/math-ph/0112027v1

Physics

Mathematical Physics

21 pages, LaTeX2e

Scientific paper

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.

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