On an Identity Theorem in the Nevanlinna Class [formula omitted

Abstract

We prove the following theorem: Let ƒ be in the Nevanlinna class N , and let z n be distinct points in the unit disk D with Σ ∞ n=1 (1 - | z n |) = ∞. Further let λ n > 0, λ n → ∞ as n → ∞ and ϵ n > 0, Σ ∞ n=1 ϵ n < ∞. If [formula] where [formula] then ƒ ≡ 0. This result is an extension of the classical theorem of Blaschke about the zeros of functions in the Nevanlinna class N , in the case when these zeros are distinct.