We study the strong asymptotics of orthogonal polynomials with
respect to a measure of the type ${d\mu }/{2\pi }+\sum_{j=1}^{\infty }A_{j}\delta (z-z_{k})$ , where $\mu $ is a
positive measure on the unit circle $\Gamma $ satisfying the
Szegö condition and $\{ z_{j}\} _{j=1}^{\infty }$ are fixed points outside $\Gamma $ . The masses $\{ A_{j}\}_{j=1}^{\infty }$ are positive numbers such that $\sum_{j=1}^{\infty }A_{j}<+\infty $ . Our main result is the explicit strong asymptotic formulas for the corresponding
orthogonal polynomials.
Publié le : 2004-05-16
Classification:
30C40,
30D50,
30E10,
30E15,
42C05
@article{1086103879,
author = {Khaldi, R. and Benzine, R.},
title = {Asymptotics for orthogonal polynomials off the circle},
journal = {J. Appl. Math.},
volume = {2004},
number = {1},
year = {2004},
pages = { 37-53},
language = {en},
url = {http://dml.mathdoc.fr/item/1086103879}
}
Khaldi, R.; Benzine, R. Asymptotics for orthogonal polynomials off the circle. J. Appl. Math., Tome 2004 (2004) no. 1, pp. 37-53. http://gdmltest.u-ga.fr/item/1086103879/