๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Orthogonal polynomials on the unit circle via a polynomial mapping on the real line

โœ Scribed by J. Petronilho

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
382 KB
Volume
216
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 OPUC whose sequence of Verblunsky coefficients is -

๐Ÿ“œ SIMILAR VOLUMES

Zeros of orthogonal polynomials on the r
Zeros of orthogonal polynomials on the real line
โœ Sergey A Denisov; Barry Simon ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 144 KB

Let p n รฐxรž be the orthonormal polynomials associated to a measure dm of compact support in R: If Eesuppรฐdmรž; we show there is a d40 so that for all n; either p n or p nรพ1 has no zeros in รฐE ร€ d; E รพ dรž: If E is an isolated point of suppรฐmรž; we show there is a d so that for all n; either p n or p nรพ

Classification Theorems for General Orth
Classification Theorems for General Orthogonal Polynomials on the Unit Circle
โœ S.V. Khrushchev ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 411 KB

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