The behavior of the norm of an automorphism of the unit disk

Dennis Michael Girard

Vol. 47 (1973), No. 2, 443–456

DOI: 10.2140/pjm.1973.47.443

Abstract

For f(z) analytic on the closed unit disk,

let

In this paper the following result is obtained: Theorem. Let f(z) be an automorphism of the unit disk:

Then

as n →∞ where F = 2F₁ is the hypergeometric function and

Mathematical Subject Classification

Primary: 42A28

Secondary: 30A24

Milestones

Received: 8 May 1972

Revised: 2 January 1972

Published: 1 August 1973