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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniqueness theorems for subharmonic functions in unbounded domains
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by S. J. Gardiner
Proc. Amer. Math. Soc. 99 (1987), 437-444
DOI: https://doi.org/10.1090/S0002-9939-1987-0875377-7

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.
References
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Bibliographic Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 437-444
  • MSC: Primary 31B05
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0875377-7
  • MathSciNet review: 875377