Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]
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Rocky Mt Math Consortium
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Abstract
We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through the transformation x = (z1/2+z1/2)/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal polynomials on [-1, 1]. In the case of any symmetric quadrature rule on [-1, 1], its associated quadrature rule on the unit circle is also given.
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English
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Rocky Mountain Journal of Mathematics, v. 33, n. 2, p. 567-584, 2003.
