New constants in discrete Lieb–Thirring inequalities for Jacobi matrices

Abstract

As is known, some results used for improving constants in the Lieb–Thirring inequalities for Schrödinger operators in L 2(−∞, ∞) can be translated to discrete Schrödinger operators and, more generally, to Jacobi matrices. We improve constants obtained earlier for Lieb–Thirring inequalities for the moments of eigenvalues larger than or equal to one. Bibliography: 9 titles.