Sum Rules for Jacobi Matrices and Divergent Lieb-Thirring Sums

Details Sum Rules for Jacobi Matrices and Divergent Lieb-Thirring Sums Sum Rules for Jacobi Matrices and Divergent Lieb-Thirring Sums

2004-06-03

arxiv.org/abs/math-ph/0406007v1

Physics

Mathematical Physics

Scientific paper

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.

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