关于Landau和Toeplitz的一个定理
On a theorem of Landau and Toeplitz
摘要：
现在规范证明施瓦茨引理出现在1907年的论文Carathéodory，谁归因于它的埃哈德施密特。从那时起，施瓦茨引理获得了相当大的声誉，有多个扩展和推广。鲜为人知的是，在同一年1907年，朗道和Toeplitz获得了类似的结果，直径的图像集接管的作用，最大模的功能。我们给出了一个简化的证明，这一结果，并将其扩展到包括最大模的增长界限。
英文摘要：
The now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carathéodory, who attributed it to Erhard Schmidt. Since then, Schwarz's Lemma has acquired considerable fame, with multiple extensions and generalizations. Much less known is that, in the same year 1907, Landau and Toeplitz obtained a similar result where the diameter of the image set takes over the role of the maximum modulus of the function. We give a streamlined proof of this result and also extend it to include bounds on the growth of the maximum modulus.
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。
