Bohr定理的一个bootstrap证明

中文摘要 AI 辅助

设$f$为单位圆盘上模被1界定的解析函数。我们给出Bohr定理的一个新证明，该定理断言其优函数$Mf(r)$在$0\leq r \leq 1/3$时有界为1，且$1/3$是最优的。该论证还给出了$Mf(r)$关于$\lvert f(0) \rvert$的锐上界，补充了Bombieri的一个结果。

英文摘要

Let $f$ be an analytic function in the unit disc whose modulus is bounded by $1$. We present a new proof of Bohr's theorem, which asserts that its majorant function $Mf(r)$ is bounded by $1$ for $0\leq r \leq 1/3$ and that $1/3$ is optimal. The argument also yields a sharp upper bound for $Mf(r)$ in terms of $\lvert f(0) \rvert$, complementing a result due to Bombieri.

发表机构

• Norwegian University of Science and Technology (NTNU)（挪威科技大学）

机构由 AI 辅助整理，请以论文原文为准。