Traces of the Nevanlinna class on discrete sequences

Abstract

We show that a discrete sequence $\Lambda$ of the unit disk is the union of $n$ interpolating sequences for the Nevanlinna class $\mathcal{N}$ if and only if the trace of $\mathcal{N}$ 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.