# Traces of the Nevanlinna class on discrete sequences

## TL;DR

This paper characterizes when a discrete sequence in the unit disk can be covered by a finite union of Nevanlinna class interpolating sequences, using divided differences and harmonic control.

## Contribution

It provides a precise characterization of unions of Nevanlinna class interpolating sequences via divided differences and harmonic majorants.

## Key findings

- Characterization of unions of $n$ interpolating sequences for $N$
- Trace of $N$ on $ ext{Lambda}$ matches functions with controlled divided differences
- Conditions involving positive harmonic functions for sequence interpolation

## Abstract

We show that a discrete sequence $\Lambda$ of the unit disk is the union of $n$ interpolating sequences for the Nevanlinna class $N$ if and only if the trace of $N$ on $\Lambda$ coincides with the space of functions on $\Lambda$ for which the divided differences of order $n - 1$ are uniformly controlled by a positive harmonic function.