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On Completeness With Respect to the Carathéodory Metric*
Published online by Cambridge University Press: 20 November 2018
Extract
Let X be a bounded region in the plane. Define
where f is an analytic function on X bounded in modulus by 1. We call d the Carathéodory metric.
In this note we give necessary and sufficient conditions to ensure that this metric be complete.
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- Copyright © Canadian Mathematical Society 1974
Footnotes
This is partly taken from the author’s Ph.D dissertation at Cornell University. Preparation of this paper was supported in part by the National Research Council. Grant No. A8088.
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