Lieb-Thirring Inequalities for Finite and Infinite Gap Jacobi Matrices
  We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class perturbations under very general assumptions. Our results apply, in particular, to perturbations of reflectionless Jacobi operators with finite gap and Cantor-type essential spectrum. 
Jacob S. Christiansen and Maxim Zinchenko
math.SP math-ph math.MP