Orthogonal polynomials on the unit circle: New results

@article{Simon2004OrthogonalPO,
  title={Orthogonal polynomials on the unit circle: New results},
  author={Barry Simon},
  journal={International Mathematics Research Notices},
  year={2004},
  volume={2004},
  pages={2837-2880}
}
  • B. Simon
  • Published 6 May 2004
  • Mathematics
  • International Mathematics Research Notices
We announce numerous new results in the theory of orthogonal polynomials on the unit circle, most of which involve the connection between a measure on the unit circle in the complex plane and the coefficients in the recursion relations for the polynomials known as Verblunsky coefficients. Included are several applications of the recently discovered matrix realization of Cantero, Moral, and Velazquez. In analogy with the spectral theory of Jacobi matrices, several classes of exotic Verblunsky… 
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