Asymptotics for Christoffel functions of planar measures

Abstract

We prove a version of asymptotics of Christoffel functions with varying weights for a general class of sets E in, and measures μ on the complex plane ℂ. This class includes all regular measures μ in the sense of Stahl-Totik [18] on regular compact sets E in ℂ and even allows varying weights. Our main theorems cover some known results for subsets of the real line ℝ. In particular, we recover information in the case of E = ℝ with Lebesgue measure dx and weight w(x) = exp(−Q(x)) where Q(x) is a nonnegative even degree polynomial having positive leading coefficient.