Coefficients of Orthogonal Polynomials on the Unit Circle and Higher-Order Szego Theorems
✍ Scribed by Leonid Golinskii; Andrej Zlatos
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 263 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0176-4276
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📜 SIMILAR VOLUMES
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.
The set P of all probability measures s on the unit circle T splits into three disjoint subsets depending on properties of the derived set of {|j n | 2 ds} n \ 0 , denoted by Lim(s). Here {j n } n \ 0 are orthogonal polynomials in L 2 (ds). The first subset is the set of Rakhmanov measures, i.e., of
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.