On a theorem of Landau and Toeplitz

Simple item page
dc.creatorBurckel, Robert B.
dc.creatorMarshall, Donald E.
dc.creatorPoggi-Corradini, Pietro
dc.date2006-03-24
dc.date.accessioned2026-07-07T07:07:12Z
dc.date.available2026-07-07T07:07:12Z
dc.descriptionThe 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0603579
dc.identifierhttp://arxiv.org/abs/math/0603579
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110304
dc.subjectComplex Variables
dc.subjectHistory and Overview
dc.subject30C80
dc.titleOn a theorem of Landau and Toeplitz
dc.typetext

Files

Collections

arXiv