On the Zeros of Analytic Functions in the Disk with a Given Majorant near Its Boundary

摘要

Suppose that λ is an arbitrary positive function from C[0,1) such that λ(r) → ∞ as r → 1-0 and satisfying some growth regularity conditions, A(λ) is the set of all holomorphic functions f in the unit disk for which ln|f(z)| ≤ c· λ(|z|), |z| < 1. In this paper, we establish that there exists a function f ∈ A(λ) with root set {z_k)_(k=1)~(+∞) such that the sequence {|z_k|}_(k=1)~(+∞) is the uniqueness set for the class A(λ).