Interpolation and peak functions for the Nevanlinna and Smirnov classes

Xavier Massaneda; Pascal J. Thomas

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arXiv · 1212.6268

Interpolation and peak functions for the Nevanlinna and Smirnov classes

Xavier Massaneda·Pascal J. Thomas

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Abstract

It is known (implicit in [HMNT]) that when $Λ$ is an interpolating sequence for the Nevanlinna or the Smirnov class then there exist functions $f_λ$ in these spaces, with uniform control of their growth and attaining values 1 on $λ$ and 0 in all other $λ'\neqλ$. 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 $Λ$ is an interpolating sequence.

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Xavier Massaneda, Pascal J. Thomas. 2012-12-26. Interpolation and peak functions for the Nevanlinna and Smirnov classes. https://arxiv.org/abs/1212.6268

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