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Zeros of Non-Baxter Paraorthogonal Polynomials on the Unit Circle

Abstract

We provide leading-order asymptotics for the size of the gap in the zeros around 1 of paraorthogonal polynomials on the unit circle whose Verblunsky coefficients satisfy a slow decay condition and are inside the interval (−1,0). We also include related results that impose less restrictive conditions on the Verblunsky coefficients.

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Correspondence to Brian Simanek.

Additional information

Communicated by Serguei Denissov.

This research was partially supported by an NSF GRFP grant.

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Simanek, B. Zeros of Non-Baxter Paraorthogonal Polynomials on the Unit Circle. Constr Approx 35, 107–121 (2012). https://doi.org/10.1007/s00365-011-9127-x

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  • DOI: https://doi.org/10.1007/s00365-011-9127-x

Keywords

  • Zeros of paraorthogonal polynomials
  • Slow decay of Verblunsky coefficients
  • CMV matrix
  • Blaschke products
  • Approximate eigenvectors

Mathematics Subject Classification (2000)

  • 42C05
  • 26C10
  • 47B36