Đề tài " Sum rules for Jacobi matrices and their applications to spectral theory "

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 − J0 is Hilbert-Schmidt, and a proof of Nevai’s conjecture that the Szeg˝ condition o holds if J − J0 is trace class.