Interpolation in the Nevanlinna class and harmonic majorants

Details Interpolation in the Nevanlinna class and harmonic majorants Interpolation in the Nevanlinna class and harmonic majorants

2003-06-05

arxiv.org/abs/math/0306093v1

Mathematics

Complex Variables

27 pages

Scientific paper

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.

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