## 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
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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.## 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