Nonuniqueness Sequences for Weighted Algebras of Holomorphic Functions in the Unit Circle

摘要

Suppose that P is a system of continuous subharmonic functions in the unit disk D and A_P is the class of holomorphic functions f in ED such that log|f(z)| ≤ B_fp_f(z) +C_f, z ∈ D, where B_f and C_f are constants and p_f ∈ P. We obtain sufficient conditions for a given number sequence Λ = {λ_n} is contained in D to be a subsequence of zeros of some nonzero holomorphic function from A_P , i.e., Λ is a nonuniqueness sequence for A_P.