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April, 2008 Sampling Sets for the Nevanlinna class
Xavier Massaneda , Pascal J. Thomas
Rev. Mat. Iberoamericana 24(1): 353-385 (April, 2008).


We propose a definition of sampling set for the Nevanlinna and Smirnov classes in the disk and show its equivalence with the notion of determination set for the same classes. We also show the relationship with determination sets for related classes of functions and deduce a characterization of Smirnov sampling sets. For Nevanlinna sampling we give general conditions (necessary or sufficient), from which we obtain precise geometric descriptions in several regular cases.


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Xavier Massaneda . Pascal J. Thomas . "Sampling Sets for the Nevanlinna class." Rev. Mat. Iberoamericana 24 (1) 353 - 385, April, 2008.


Published: April, 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1160.30020
MathSciNet: MR2435975

Primary: 30C80 , 30D50 , 30E05

Keywords: determination sets , Nevanlinna class , sampling sets , Smirnov class

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 1 • April, 2008
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