Abstract
I. In a previous paper [5], we have considered the question of interpolation on finite open Riemann surfaces; it is our intention to show in this note that the problem can be treated in an essentially simpler way. We shall suppose given a finite open Riemann surface, R. Such a surface is, by definition, the complement in some compact Riemann surface of a finite family of closed, pairwise disjoint discs each of which we may assume to have an analytic simple closed curve as boundary. A set ECR is called an interpolation set for R if given a bounded, complex valued function ax on E, there is a bounded holomorphic function f on R such that f I E = a. It is convenient to denote by H14[R] the collection of all functions which are bounded and holomorphic on R. For our characterization of interpolation sets in R we introduce a functional dR(z, E) as follows: If zEE, then
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
