Mathematical Proceedings of the Cambridge Philosophical Society



A generalization of the Schwarz–Carathéodory reflection principle and spaces of pseudo-metrics


RICHARD FOURNIER a1 1 and STEPHAN RUSCHEWEYH a2
a1 Centre de Recherches de Mathématiques, Université de Montréal, Montréal H3C 3J7, Canada; e-mail: fournier@DMS.UMontreal.CA
a2 Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany; e-mail: ruscheweyh@mathematik.uni-wuerzburg.de

Abstract

We generalize the Carathéodory version of the Schwarz reflection principle for pseudo-metrics

formula here

where w is analytic in some domain of the complex plane, [mid R:] w [mid R:] < 1 and use a unit disk version of the new result to study certain homeomorphisms of the unit ball in [script H]([open face D]) onto itself.

(Received June 14 1999)
(Revised January 13 2000)



Footnotes

1 The first author acknowledges support of FCAR (Quebec).