Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants
Hartmann, Andreas ; Massaneda, Xavier ; Nicolau, Artur ; Thomas, Pascal J.
HAL, hal-00128477 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  free interpolation,  Smirnov and Nevanlinna class,  harmonic majorants,  Poisson balayage,  AMS Subject Classification (2000): 30E05, 32A35,  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 
@article{hal-00128477,
     author = {Hartmann, Andreas and Massaneda, Xavier and Nicolau, Artur and Thomas, Pascal J.},
     title = {Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00128477}
}

Hartmann, Andreas; Massaneda, Xavier; Nicolau, Artur; Thomas, Pascal J. Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00128477/