Weak limits of the measures of maximal entropy for Orthogonal polynomials

Abstract

In this paper we study the sequence of orthonormal polynomials $\{P_n(\mu ;z)\}$ defined by a probability measure $\mu$ with non-polar compact support $S(\mu )\subset \mathbb{C}$. We show that the support of any weak* limit of the sequence of measures of maximal entropy ${\omega }_n$ for $P_n$ is contained in the polynomial-convex hull of $S(\mu )$. And for $n$-th root regular measures the ${\omega }_n$ converge weak* to the equilibrium measure on $S(\mu )$.

8 pages