|
|||||
|
|
Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants |
|
| Authors: | Andreas Hartmann Pascal Thomas |
| Institution: | a Laboratoire de Mathématiques Pures de Bordeaux, Université Bordeaux I, 351 Cours de la Libération, 33405 Talence, France b Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain c Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain d Laboratoire de Mathématiques Emile Picard, UMR CNRS 5580, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France |
| 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 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. |
| Keywords: | 30E05 32A35 |
| 本文献已被 ScienceDirect 等数据库收录！ | |