有界解析函数三阶导数的变分区域
Variability regions for the third derivative of bounded analytic functions
摘要：
设$z_0$和$w_0$是开单位圆盘$\mathbb{D}$中的给定点，其中$|w_0| < |z_0|$，$\mathcal{H}_0$是$f(0)=0$归一化的$\mathbb{D}$的所有解析自映射$f$的类。本文建立了三阶Dieudonne引理，并应用它明确地确定了给定$z_0,w_0,w_1$的变域$\{f'''(z_0): f\in \mathcal{H}_0,f(z_0) =w_0, f'(z_0)=w_1\}$，给出了所有极值函数的形式.
英文摘要：
Let $z_0$ and $w_0$ be given points in the open unit disk $\mathbb{D}$ with $|w_0| < |z_0|$, and $\mathcal{H}_0$ be the class of all analytic self-maps $f$ of $\mathbb{D}$ normalized by $f(0)=0$. In this paper, we establish the third order Dieudonné Lemma, and apply it to explicitly determine the variability region $\{f'''(z_0): f\in \mathcal{H}_0,f(z_0) =w_0, f'(z_0)=w_1\}$ for given $z_0,w_0,w_1$ and give the form of all the extremal functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
