Sum Rules for Jacobi Matrices and Divergent Lieb-Thirring Sums
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
Extending earlier work of Killip-Simon and Simon-Zlatos, we obtain sum rules for Jacobi matrices in which the a.c. part of the spectral measure and the eigenvalues of the matrix appear on opposite sides of the equation. We use these to obtain various results on divergence of certain Lieb-Thirring sums of eigenvalues and Szego-type integrals of the a.c. part of the spectral measure.
Keywords
Cite
@article{arxiv.math-ph/0406007,
title = {Sum Rules for Jacobi Matrices and Divergent Lieb-Thirring Sums},
author = {Andrej Zlatos},
journal= {arXiv preprint arXiv:math-ph/0406007},
year = {2007}
}