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


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.


Jacobi Matrix Real Axis Orthogonal Polynomial Jacobi Matrice Weyl Solution 
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© Springer-Verlag 2006

Authors and Affiliations

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

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