Strong asymptotics for Christoffel functions of planar measures

Details Strong asymptotics for Christoffel functions of planar measures Strong asymptotics for Christoffel functions of planar measures

2007-09-13

arxiv.org/abs/0709.2073v1

Mathematics

Complex Variables

Scientific paper

We prove a version of strong asymptotics of Christoffel functions with varying weights for a general class of sets E and measures in the complex plane. This class includes all regular measures in the sense of Stahl-Totik on regular compact sets E in the plane and even allows varying weights. Our main theorems cover some known results for subsets E 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.

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