On a theorem of Landau and Toeplitz
Complex Variables
2007-05-23 v1 History and Overview
Abstract
The now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carath\'eodory, 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.
Cite
@article{arxiv.math/0603579,
title = {On a theorem of Landau and Toeplitz},
author = {Robert B. Burckel and Donald E. Marshall and Pietro Poggi-Corradini},
journal= {arXiv preprint arXiv:math/0603579},
year = {2007}
}
Comments
9 pages