Let K be the closure of a bounded region in the complex plane with simply connected complement whose boundary is a piecewise analytic curve with at least one outward cusp. The asymptotics of zeros of Faber polynomials for K are not understood in this general setting. Joukowski airfoils provide a particular class of such sets. We determine the (unique) weak-* limit of the full sequence of normalized counting measures of the Faber polynomials for Joukowski airfoils; it is never equal to the potential-theoretic equilibrium measure of K . This implies that these airfoils admit an electrostatic skeleton and also explains an interesting class of examples of Ullman (Mich Math J 13:417–423, 1966) related to Chebyshev quadrature.

中文翻译：

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Joukowski 翼型的 Faber 多项式的零点

令 K 是复平面中一个有界区域的闭包，其边界是具有至少一个向外尖点的分段解析曲线。在这种一般设置中，无法理解 K 的 Faber 多项式的零点渐近性。Joukowski 翼型提供了一类特殊的此类装置。我们确定了 Joukowski 翼型的 Faber 多项式的完整标准化计数测量序列的（唯一）弱*极限；它永远不等于 K 的潜在理论平衡测度。这意味着这些翼型具有静电骨架，并且还解释了与切比雪夫正交相关的一类有趣的 Ullman (Mich Math J 13:417–423, 1966) 示例。