Paper detail

Interpolation and peak functions for the Nevanlinna and Smirnov classes

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.