Interpolation in the Nevanlinna class and harmonic majorants
Complex Variables
2007-05-23 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.math/0306093,
title = {Interpolation in the Nevanlinna class and harmonic majorants},
author = {A. Hartmann and X. Massaneda and A. Nicolau and P. Thomas},
journal= {arXiv preprint arXiv:math/0306093},
year = {2007}
}
Comments
27 pages