若尔当弧上的极值多项式

摘要：

设$Γ$是$C^{2+}$的一条若尔当弧，$Γ_0$是由$Γ$的内点组成的开弧。本文给出了文献[18]中给出的$Γ$上的$L_2(μ)$极值多项式的Widom因子极限的具体上、下界.此外，我们还证明了当格林函数的两个法向导数在一点$z\in Γ_0$不一致时，文[18]中得到的加权切比雪夫多项式的Widom因子的极限上确界的上界可以得到改进.我们还表明，如果$Γ_0$不是解析的，那么我们就改进了上界。

英文摘要：

Let $Γ$ be a $C^{2+}$ Jordan arc and let $Γ_0$ be the open arc which consists of interior points of $Γ$. We find concrete upper and lower bounds for the limit of Widom factors for $L_2(μ)$ extremal polynomials on $Γ$ which was given in [18]. In addition, we show that the upper bound for the limit supremum of Widom factors for the weighted Chebyshev polynomials which was obtained in [18] can be improved once two normal derivatives of the Green function do not agree at one point $z\in Γ_0$. We also show that if $Γ_0$ is not analytic then we have improved upper bounds.

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