Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants
Language
en
Article de revue
This item was published in
J. Funct. Anal. 217. 2004, vol. 217, p. 1-37
English 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 ...Read more >
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 disk having a harmonic majorant. An answer is given in terms of a dual relation which involves positive measures in the disk with bounded Poisson balayage. We deduce necessary and sufficient geometric conditions, both expressed in terms of certain maximal functions.Read less <
English Keywords
free interpolation
Smirnov and Nevanlinna class
harmonic majorants
Poisson balayage
Origin
Hal imported