Sampling Sets for the Nevanlinna class

Abstract

We propose a definition of sampling set for the Nevanlinna and Smirnov classes in the disk and show its equivalence with the notion of determination set for the same classes. We also show the relationship with determination sets for related classes of functions and deduce a characterization of Smirnov sampling sets. For Nevanlinna sampling we give general conditions (necessary or sufficient), from which we obtain precise geometric descriptions in several regular cases.