Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory

Details Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory

2001-12-06

arxiv.org/abs/math-ph/0112008v2

Ann. of Math. (2), Vol. 158 (2003), no. 1, 253--321

Physics

Mathematical Physics

69 pages, published version

Scientific paper

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.

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