A characterization of $F^{+}\cap N$

Abstract:

In this note we give a characterization of ${F^ + } \cap N$, where $N$ denotes the Nevanlinna class of functions of bounded characteristic and ${F^ + }$ denotes the containing Fréchet space of ${N^ + }$. We show that a holomorphic function $f \in {F^ + } \cap N$ if and only if $f(z) = g(z)/{S_\mu }(z)$, where $g \in {N^ + }$ and ${S_\mu }$ is a singular inner function with respect to a nonnegative continuous singular measure $\mu$.