Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory
Mathematical Physics
2007-05-23 v2 Classical Analysis and ODEs
math.MP
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 Szego condition holds if J-J_0 is trace class.
Cite
@article{arxiv.math-ph/0112008,
title = {Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory},
author = {Rowan Killip and Barry Simon},
journal= {arXiv preprint arXiv:math-ph/0112008},
year = {2007}
}
Comments
69 pages, published version