2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56926We discuss the proof of and systematic application of Case's sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classification of the spectral measures of all Jacobi matrices J for which J-J_0 is Hilbert--Schmidt, and a proof of Nevai's conjecture that the Szego condition holds if J-J_0 is trace class.69 pages, published versionMathematical PhysicsClassical Analysis and ODEs34L05, 42C05, 47B36, 81Q10text