Angular limits of locally finitely valent holomorphic functions

David Charles Haddad

Vol. 48 (1973), No. 1, 107–112

DOI: 10.2140/pjm.1973.48.107

Abstract

A function f defined in a domain D is n-valent in D if f(z) − w₀ has at most n zeros in D for each complex number w₀. The purpose of this paper is to show that a sufficient condition for a holomorphic function f in |z| < 1 to have angular limits almost everywhere on |z| = 1 is that there exist a positive integer n and a positive number r₀ such that f is n-valent in each component of the set {z : |f(z)| > r₀}.

Mathematical Subject Classification

Primary: 30A72

Milestones

Received: 22 June 1972

Published: 1 September 1973