Decrease of bounded holomorphic functions along discrete sets

Details Decrease of bounded holomorphic functions along discrete sets Decrease of bounded holomorphic functions along discrete sets

2001-06-07

arxiv.org/abs/math/0106048v2

Mathematics

Complex Variables

13 pp ; rewritten introduction, proofs revised for clarity, a number of minor corrections

Scientific paper

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.

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