Lieb-thirring inequalities for Jacobi matrices

Abstract

For a Jacobi matrix J on ℓ2(ℤ+) with Ju(n) = an-1u(n-1) + bnu(n) + anu(n + 1), we prove that ∑E >2 (E2 - 4)1/2 ≤ ∑n bn + 4 ∑n an -1 . We also prove bounds on higher moments and some related results in higher dimension. © 2002 Elsevier Science (USA).