02-266 Barry Simon, Andrej Zlatos
Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line (80K, LaTeX 2e) Jun 14, 02
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Abstract. We study the Case sum rules, especially $C_0$, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theorem to cases with an infinite point spectrum and a proof that if $\lim n (a_n -1)=\alpha$ and $\lim nb_n =\beta$ exist and $2\alpha <\abs{\beta}$, then the Szeg\H{o} condition fails.

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