Vol. 48, No. 1, 1973

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Angular limits of locally finitely valent holomorphic functions

David Charles Haddad

Vol. 48 (1973), No. 1, 107–112
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
Authors
David Charles Haddad