01-456 Dirk Hundertmark, Barry Simon
Lieb-Thirring Inequalities for Jacobi Matrices (55K, LaTeX 2e) Dec 6, 01
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Abstract. For a Jacobi matrix J on l^2(N_0) with Ju(n)=a_{n-1} u(n-1) + b_n u(n) + a_n u(n+1)$, we prove that \sum_{\abs{E}>2} (E^2 -4)^{1/2} <= \sum_n \abs{b_n} + 4\sum_n \abs{a_n -1}. We also prove bounds on higher moments and some related results in higher dimension.

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