Asymptotics for Christoffel functions of planar measures |
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Authors: | T Bloom N Levenberg |
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Institution: | (1) Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada;(2) Department of Mathematics, Indiana University, Bloomington, IN 47405, USA |
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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.
Supported in part by an NSERC of Canada grant |
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