Rowan Killip, Barry Simon
Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory
(159K, AMS-LaTeX)

ABSTRACT.  We 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 Szeg\H{o} condition holds if $J-J_0$ is trace class.