 01453 Rowan Killip, Barry Simon
 Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory
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Dec 6, 01

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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 $JJ_0$ is HilbertSchmidt, and a proof of Nevai's
conjecture that the Szeg\H{o} condition holds if $JJ_0$ is trace class.
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