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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Uniqueness theorems for subharmonic functions in unbounded domains


Author: S. J. Gardiner
Journal: Proc. Amer. Math. Soc. 99 (1987), 437-444
MSC: Primary 31B05
MathSciNet review: 875377
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Abstract: A theorem of Carlson says that a holomorphic function of exponential growth in the half-plane cannot approach zero exponentially along the boundary unless it vanishes identically. This paper presents a generalization of this result for subharmonic functions in a Greenian domain $ \Omega $, using the Martin boundary, minimal fine topology and PWB solution to the $ h$-Dirichlet problem. Applications of the general theorem to specific choices of $ \Omega $, such as the half-space and strip, are presented in later sections.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875377-7
PII: S 0002-9939(1987)0875377-7
Article copyright: © Copyright 1987 American Mathematical Society