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Inventiones mathematicae

, Volume 165, Issue 1, pp 1–50 | Cite as

Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics

  • David Damanik
  • Barry Simon
Article

Abstract

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Weyl solution. We also prove L2 convergence of Szegő asymptotics on the spectrum.

Keywords

Jacobi Matrix Real Axis Orthogonal Polynomial Jacobi Matrice Weyl Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Mathematics 253-37California Institute of TechnologyPasadenaUSA

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