Non cyclic functions in the Hardy space of the bidisc with arbitrary decrease

Xavier Massaneda (1) , Pascal J. Thomas (2)

1 Departament de Matemàtica Aplicada i Anàlisi
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We construct an example to show that no condition of slow decrease of the modulus of a function is sufficient to make it cyclic in the Hardy space of the bidisc. This is similar to what is well known in the case of the Hardy space of the disc, but in contrast to the case of the Bergman space of the disc.

Mots clés: bidisk; cyclic functions; bergman spaces; hardy spaces

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Xavier Massaneda, Pascal J. Thomas. Non cyclic functions in the Hardy space of the bidisc with arbitrary decrease. 2013. ⟨hal-00950114⟩