On the measure of the absolutely continuous spectrum for Jacobi matrices Original Research Article

We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support View the MathML sourceΣac of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure of View the MathML sourceΣac which takes into account the value distribution of the diagonal elements, and implies the bound due to Deift–Simon and Poltoratski–Remling. Second, we generalise the differential inequality of Deift–Simon for the integrated density of states associated with the absolutely continuous spectrum to general Jacobi matrices.