On the ideal structure of the Nevanlinna class

Abstract:

Let $N$ denote the Nevanlinna class, i.e. the algebra of holomorphic functions of bounded characteristic in the open unit disc. We study analytic conditions for a finitely generated ideal to be equal to the whole algebra $N$. Then we characterize the finitely generated prime ideals containing a nontangential interpolating Blaschke product. Further, we give an example of an ideal of $N$ whose closure in the natural metric on $N$ is not an ideal.