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DECREASE OF BOUNDED HOLOMORPHIC FUNCTIONS ALONG DISCRETE SETS

Published online by Cambridge University Press:  10 December 2003

Jordi Pau  and
Pascal J. Thomas
Jordi Pau
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain ([email protected])
Pascal J. Thomas
Affiliation:
Laboratoire de Mathématiques Emile Picard, UMR CNRS 5580, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France ([email protected])
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Abstract

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We provide uniqueness results for holomorphic functions in the Nevanlinna class which bridge those previously obtained by Hayman and by Lyubarskii and Seip. In particular, we propose certain classes of hyperbolically separated sequences in the disc, in terms of the rate of non-tangential accumulation to the boundary (the outer limits of this spectrum of classes being, respectively, the sequences with a non-tangential cluster set of positive measure, and the sequences satisfying the Blaschke condition). 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.

AMS 2000 Mathematics subject classification: Primary 30D50; 30D55

Keywords

uniqueness theoremsessential minorantspositive harmonic functionsmaximal functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 3 , October 2003 , pp. 703 - 718
Copyright
Copyright © Edinburgh Mathematical Society 2003