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Asymptotics of polynomials orthogonal with respect to varying measures

Authors:

Guillermo López Lagomasino

Institution:

1. Havana University, Havana, Cuba

Abstract:

Letd be a finite positive Borel measure on the interval 0, 2 pgr

] such that sgr

>0 almost everywhere; andW _n be a sequence of polynomials, degW _n=n, whose zeros (w _n,1, ctdot

,w _n,n lie in |z|

1]. Let

d _n

for each_n isin

N, whered _n=d/|W _n(e ⁱ)|². We consider the table of polynomials _n,m such that for each fixedn isin

N the system _n,m,m isin

N, is orthonormal with respect tod _n. If

$\mathop {\lim }\limits_n \sum\limits_{\iota = 1}^n {(1 - \|w_{n,\iota } \|) = + \infty }$

Keywords:	AMS classification" target="_blank">AMS classification 42C05 41A25
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