AI 中文总结
该研究描述平面解析若尔当弧上切比雪夫多项式的渐近行为，结合多种多项式与不等式证明，解决相关猜想并得到其Szegő-Widom渐近结果。
AI 中文摘要
我们描述平面上解析若尔当弧上切比雪夫多项式的渐近行为，这对Christiansen-Simon-Zinchenko的猜想给出肯定回答，该猜想基于Widom1969年的预测。证明结合了加权Faber多项式、极值符号、离散正交多项式及Marcinkiewicz-Zygmund采样不等式，得到切比雪夫多项式自身的Szegő-Widom渐近行为。
英文摘要
We describe the asymptotics of Chebyshev polynomials on an analytic Jordan arc in the plane. This gives an affirmative answer to a conjecture of Christiansen-Simon-Zinchenko, based on predictions of Widom from 1969. The proof combines weighted Faber polynomials with extremal signatures, discrete orthogonal polynomials and a Marcinkiewicz-Zygmund sampling inequality, and yields Szegő-Widom asymptotics for the Chebyshev polynomials themselves.
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