Interpolation and peak functions for the Nevanlinna and Smirnov classes

zbMATH Open1438.30172arXiv1212.6268MaRDI QIDQ4631963

Xavier Massaneda, Pascal J. Thomas

Publication date: 24 April 2019

Abstract: It is known (implicit in [HMNT]) that when $Lambda$ is an interpolating sequence for the Nevanlinna or the Smirnov class then there exist functions $f_{l}ambda$ in these spaces, with uniform control of their growth and attaining values 1 on $lambda$ and 0 in all other $lambd{a}^{\prime }eqlambda$. We provide an example showing that, contrary to what happens in other algebras of holomorphic functions, the existence of such functions does not imply that $Lambda$ is an interpolating sequence.

Full work available at URL: https://arxiv.org/abs/1212.6268

zbMATH Keywords

Nevanlinna classSmirnov classpeak functionsinterpolation sequence

Mathematics Subject Classification ID

Nevanlinna spaces and Smirnov spaces (30H15)

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