Orthogonal polynomials on the unit circle: distribution of zeros
✍ Scribed by F. Marcellán; E. Godoy
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 724 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0377-0427
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## Abstract We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a qu
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