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.