Volume 19, pp. 29-36, 2005.

Asymptotics for extremal polynomials with varying measures

M. Bello Hernández and J. Mínguez Ceniceros

Abstract

In this paper, we give strong asymptotics of extremal polynomials with respect to varying measures of the form $d{\sigma }_n=\frac{d\sigma }{|Y_n{|}^p}$, where $\sigma$ is a positive measure on a closed analytic Jordan curve $C$, and $\{Y_n\}$ is a sequence of polynomials such that for each $n$, $Y_n$ has exactly degree $n$ and all its zeros $({\alpha }_{n,i})$, $i=1,2,\dots$, lie in the exterior of $C$.

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Key words

Rational Approximation, Orthogonal Polynomials, Varying Measures.

AMS subject classifications

30E10, 41A20, 42C05.