Interpolation and peak functions for the Nevanlinna and Smirnov classes

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 $f_\lambda$ in these spaces, with uniform control of their growth and attaining values 1 on $\lambda$ and 0 in all other $\lambda'\neq\lambda$. 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.