平面测度的Christoffel函数的强渐近性
Strong asymptotics for Christoffel functions of planar measures
摘要：
对于复平面上的一类集合E和测度，证明了变权Christoffel函数的强渐近性.这类测度包含平面上正则紧集E上Stahl-Totik意义下的所有正则测度，甚至允许变权。我们的主要定理涵盖了实数直线R的子集E的一些已知结果;特别地，我们恢复了E=R且具有勒贝格测度dx和权重w（x）= exp（-Q（x））的情况下的信息，其中Q（x）是具有正首项系数的非负偶数次多项式。
英文摘要：
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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