Abstract. We give an explicit relation between the Nevanlinna counting function of an analytic self-map of the unit disk and its pull-back measure. This gives a simple proof of the results of Lefévre, ...

Let φ be a holomorphic function taking the open unit disk U into itself. We show that the set of nonnegative powers of φ is orthogonal in L2(∂ U) if and only if the Nevanlinna counting function of φ, ...