In this paper we analyze the Stieltjes functions defined by the Szegő inverse transformation of a nontrivial probability measure supported on the unit circle such that the corresponding sequence of orthogonal polynomials is defined by either backward or forward shifts in their Verblunsky parameters.
Szegö polynomials and quadrature formulas on the unit circle
✍ Scribed by Leyla Daruis; Pablo González-Vera
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 354 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0168-9274
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✦ Synopsis
In this paper, computation of the so-called Szegö quadrature formulas is considered for some special weight functions on the unit circle. The case of the Lebesgue measure is more deeply analyzed. Illustrative numerical examples are also given.
📜 SIMILAR VOLUMES
Properties of second kind polynomials, and, in particular, conditions for second kind measures to be absolutely continuous are investigated. The asymptotic representation for second kind polynomials is obtained. Examples of generalized Jacobi weighted functions are considered. 1995 Academic Press. I
The main object of this paper is to construct a new quadrature formula based on the zeros of the polynomial (1 -x2)P(a'f~)(x)P(a'B)' (x), where P(a'f~)(x) is the Jacobi polynomial of degree n. It is interesting to mention that this quadrature formula is closely related to the wellknown Gaussian Quad