A note on principal functions and multiply-valent canonical mappings

Paul Adrian Nickel

Vol. 20 (1967), No. 2, 283–288

DOI: 10.2140/pjm.1967.20.283

Abstract

L. Sario has constructed principal analytic functions on planar bordered Riemann surfaces by applying the method of linear operators to certain sets of singularity functions. Weakly λ-valent principal functions result from a similar construction, starting with singularity functions having flux equal to integral multiples of 2π. In fact, such λ-valent maps are characterized as integral powers of principal analytic functions already mentioned.

Mathematical Subject Classification

Primary: 30.42

Milestones

Received: 25 October 1965

Revised: 17 January 1966

Published: 1 February 1967