Finitely generated ideals in the Nevanlinna class

Andreas Hartmann (1) , Xavier Massaneda (2) , Artur Nicolau (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 Departament de Matemàtica Aplicada i Anàlisi
3 UAB - Departament de Matemàtiques [Barcelona]

In this paper we investigate finitely generated ideals in the Nevanlinna class. We prove analogues to some known results for the algebra of bounded analytic functions $H^{\infty}$. We also show that, in contrast to the $H^ {\infty}$-case, the stable rank of the Nevanlinna class is strictly bigger than 1.

Mots clés: corona theorem; interpolation; harmonic measure; stable rank; ideals; Nevanlinna class

Domaines: Variables complexes [math.CV]; Analyse classique [math.CA]

Andreas Hartmann, Xavier Massaneda, Artur Nicolau. Finitely generated ideals in the Nevanlinna class. Israel Journal of Mathematics, 2019, 231 (1), pp.139-179. ⟨hal-01321488⟩