Subharmonic functions outside a compact set in $\textbf {R}^{n}$
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- by Victor Anandam PDF
- Proc. Amer. Math. Soc. 84 (1982), 52-54 Request permission
Abstract:
Let $u$ be a subharmonic function defined outside a compact set in ${{\mathbf {R}}^2}$. Then $u$ is of the form $u(x) = s(x) - \alpha \log \left | x \right |$ outside a disc where $s(x)$ is a nonconstant subharmonic function in ${{\mathbf {R}}^2}$ and $\alpha \geqslant 0$. Some applications and the analogues in ${{\mathbf {R}}^n}$, $n \geqslant 3$, are given.References
- M. Brelot, Sur le rôle du point à l’infini dans la théorie des fonctions harmoniques, Ann. Sci. École Norm. Sup. 61 (1944), 301–332 (French). MR 0013823, DOI 10.24033/asens.919 W. K. Hayman and P. B. Kennedy, Subharmonic functions, vol. 1, Academic Press, London, 1976.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 52-54
- MSC: Primary 31A05; Secondary 31B05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633276-5
- MathSciNet review: 633276