## 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 $(\alpha_{n,i})$, $i=1,\,2,\ldots$, lie in the exterior of $C$.

Full Text (PDF) [98 KB], BibTeX

### Key words

Rational Approximation, Orthogonal Polynomials, Varying Measures.

### AMS subject classifications

30E10, 41A20, 42C05.

< Back