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Communication Dans Un Congrès Année : 2017

Interpolation and peak functions for the Nevanlinna and Smirnov classes

Résumé

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.

Dates et versions

hal-00950111 , version 1 (20-02-2014)

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Xavier Massaneda, Pascal J. Thomas. Interpolation and peak functions for the Nevanlinna and Smirnov classes. conference on Harmonic Analysis, Function Theory, Operator Theory and Applications, Jun 2015, Bordeaux, France. p. 199-206. ⟨hal-00950111⟩
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