Let p n ðxÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppðdmÞ; we show there is a d40 so that for all n; either p n or p nþ1 has no zeros in ðE À d; E þ dÞ: If E is an isolated point of suppðmÞ; we show there is a d so that for all n; either p n or p nþ
Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line
✍ Scribed by Barry Simon; Andrej Zlatoš
- Publisher
- Springer
- Year
- 2003
- Tongue
- English
- Weight
- 289 KB
- Volume
- 242
- Category
- Article
- ISSN
- 0010-3616
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let { n } n 0 be a sequence of monic orthogonal polynomials on the unit circle (OPUC) with respect to a symmetric and finite positive Borel measure d on [0, 2 ] and let -1, 0 , 1 , 2 , . . . be the associated sequence of Verblunsky coefficients. In this paper we study the sequence { n } n 0 of monic
We investigate the properties of extremal point systems on the real line consisting of two interlaced sets of points solving a modified minimum energy problem. We show that these extremal points for the intervals [-1, 1], [0, ∞) and (-∞, ∞), which are analogues of Menke points for a closed curve, ar