2007/09/13 by Tom Bloom, Bloom, Tom, N. Levenberg +2 · 1 citation
Mathematics · Physics and Astronomy · #42C05 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.CA #math.CV #msc:42C05
paper · pdf · doi:10.48550/arxiv.0709.2073
arxiv created 2007/09/13 · openalex publication_date 2007/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.