Decrease of bounded holomorphic functions along discrete sets
复变函数
2007-05-23 v2 经典分析与常微分方程
摘要
We provide results of uniqueness for holomorphic functions in the Nevanlinna class bridging those previously obtained by Hayman and Lyubarskii-Seip. Namely, we propose certain classes of hyperbolically separated sequences in the disk, in terms of the rate of non-tangential accumulation to the boundary (the endpoints of this spectrum of classes being respectively the sequences with a non-tangential cluster set of positive measure, and the sequences violating the Blaschke condition); and for each of those classes, we give a critical condition of radial decrease on the modulus which will force a Nevanlinna class function to vanish identically.
引用
@article{arxiv.math/0106048,
title = {Decrease of bounded holomorphic functions along discrete sets},
author = {Jordi Pau and Pascal J. Thomas},
journal= {arXiv preprint arXiv:math/0106048},
year = {2007}
}
备注
13 pp ; rewritten introduction, proofs revised for clarity, a number of minor corrections