A necessary condition on the extreme points of a class of holomorphic functions

Frank John Forelli, Jr.

Vol. 73 (1977), No. 1, 81–86

DOI: 10.2140/pjm.1977.73.81

Abstract

We prove that if f is an extreme point of the class N(G,p) of all holomorphic functions g on the region G in Cⁿ such that Re g > 0 on G and g(p) = 1, and if three conditions on G hold, then the Cayley transform (f − 1)∕(f + 1) is irreducible.

Mathematical Subject Classification 2000

Primary: 32E30

Milestones

Received: 2 August 1976

Revised: 23 June 1977

Published: 1 November 1977