Acta Mathematica Hungarica

, Volume 96, Issue 3, pp 169–186

Quadrature formula and zeros of para-orthogonal polynomials on the unit circle

  • Leonid Golinski
Article

DOI: 10.1023/A:1019765002077

Cite this article as:
Golinski, L. Acta Mathematica Hungarica (2002) 96: 169. doi:10.1023/A:1019765002077

Abstract

Given a probability measure μ on the unit circle T, we study para-orthogonal polynomials Bn(.,w) (with fixed w ∈ T) and their zeros which are known to lie on the unit circle. We focus on the properties of zeros akin to the well known properties of zeros of orthogonal polynomials on the real line, such as alternation, separation and asymptotic distribution. We also estimate the distance between the consecutive zeros and examine the property of the support of μ to attract zeros of para-orthogonal polynomials.

measures on the unit circlepara-orthogonal polynomialstrigonometric moment problemSzegő quadrature formula

Copyright information

© Kluwer Academic Publishers/Akadémiai Kiadó 2002

Authors and Affiliations

  • Leonid Golinski
    • 1
  1. 1.Mathematics Division B.Verkin Institute for Low Tempreture Physics and EngineeringKharkovUkraine