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

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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)=α and lim nb n =β exist and 2α<|β|, then the Szegő condition fails.

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Authors and Affiliations

  1. Mathematics 253-37, California Institute of Technology, Pasadena, CA, 91125, USA

    Barry Simon & Andrej Zlatoš

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  1. Barry Simon
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  2. Andrej Zlatoš
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Correspondence to Barry Simon.

Additional information

Communicated by M. Aizenman

Supported in part by NSF grant DMS-9707661.

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Simon, B., Zlatoš, A. Sum Rules and the Szegő Condition for Orthogonal Polynomials on the Real Line. Commun. Math. Phys. 242, 393–423 (2003). https://doi.org/10.1007/s00220-003-0906-5

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