Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line

Details Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line

2002-06-14

arxiv.org/abs/math-ph/0206023v1

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-003-0906-5

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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