角域上Bergman多项式的精细渐近性
Fine asymptotics for Bergman polynomials over domains with corners
AI总结：
研究边界含角点的Jordan曲线所围有界单连通区域上Bergman正交多项式的首项系数及其在区域补集中的精细渐近行为。
摘要：
我们考虑与复平面中有界单连通区域（其边界为Jordan曲线）相关的Bergman正交多项式级数。这些多项式是关于区域上的面积测度正交归一化的。本文旨在报告关于当边界包含角点时，首项系数和多项式在区域补集中的精细渐近行为的最新结果。这些结果补充了T. Carleman在1920年代开始的关于解析边界区域精细渐近性的研究，以及P.K. Suetin在1960年代对光滑边界区域建立的结论。
英文摘要：
We consider the series of the Bergman orthogonal polynomials associated with a bounded simply-connected domain in the complex plane, whose boundary is a Jordan curve. These are the polynomials that are orthonormal with respect to the area measure on the domain. The purpose of this note is to report on recent results regarding the fine asymptotic behaviour of the the leading coefficients and the polynomials in the complement of the domain, in cases when the boundary includes corners. These results complement an investigation started in the 1920's by T. Carleman, who obtained the fine asymptotics for domains with analytic boundaries and carried over by P.K. Suetin in the 1960's, who established them for domains with smooth boundaries.
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