Lieb-Thirring Inequalities for Jacobi Matrices
Abstract
For a Jacobi matrix J on l2(Z+) with Ju(n)=an-1 u(n-1) + bn u(n) + an u(n+1), we prove that Σ|E|>2 (E2 -4)1/2 ≤ Σn |bn| + 4Σn |an -1|. We also prove bounds on higher moments and some related results in higher dimension.
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