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Decrease of bounded holomorphic functions along discrete sets

Jordi Pau·Pascal J. Thomas
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Abstract

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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Jordi Pau, Pascal J. Thomas. 2002-09-06. Decrease of bounded holomorphic functions along discrete sets. https://arxiv.org/abs/math/0106048

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