Interpolation in the Nevanlinna class and harmonic majorants

TL;DR

This paper characterizes interpolating sequences in Nevanlinna and Smirnov classes using harmonic majorants, providing geometric conditions and dual measure relations for positive functions in the disc.

Contribution

It offers a new characterization of interpolation sequences in Nevanlinna and Smirnov classes through harmonic majorants and dual measure conditions.

Findings

Characterization of interpolating sequences via harmonic majorants.

Dual relation involving positive measures with bounded Poisson balayage.

Necessary and sufficient geometric conditions for harmonic majorants.

Abstract

We consider a free interpolation problem in Nevanlinna and Smirnov classes and find a characterization of the corresponding interpolating sequences in terms of the existence of harmonic majorants of certain functions. We also consider the related problem of characterizing positive functions in the disc having a harmonic majorant. An answer is given in terms of a dual relation which involves positive measures in the disc with bounded Poisson balayage. We deduce necessary and sufficient geometric conditions, both expressed in terms of certain maximal functions.