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Quadrature formula and zeros of paraorthogonal polynomials on the unit circle
 Leonid Golinski
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Given a probability measure μ on the unit circle T, we study paraorthogonal polynomials B_{n}(^{.},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 paraorthogonal polynomials.
This revised version was published online in June 2006 with corrections to the Cover Date.
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 Title
 Quadrature formula and zeros of paraorthogonal polynomials on the unit circle
 Journal

Acta Mathematica Hungarica
Volume 96, Issue 3 , pp 169186
 Cover Date
 20020801
 DOI
 10.1023/A:1019765002077
 Print ISSN
 02365294
 Online ISSN
 15882632
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 measures on the unit circle
 paraorthogonal polynomials
 trigonometric moment problem
 Szegő quadrature formula
 Authors

 Leonid Golinski ^{(1)}
 Author Affiliations

 1. Mathematics Division B., Verkin Institute for Low Tempreture Physics and Engineering, 47 Lenin Avenue, 61164, Kharkov, Ukraine