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Proceedings of the American Mathematical Society

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

 

 

Subharmonic functions outside a compact set in $ {\bf R}\sp{n}$


Author: Victor Anandam
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
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Abstract | References | Similar Articles | Additional Information

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\vert x \right\vert$ 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 [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] W. K. Hayman and P. B. Kennedy, Subharmonic functions, vol. 1, Academic Press, London, 1976.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0633276-5
Keywords: Subharmonic extension, representation, order
Article copyright: © Copyright 1982 American Mathematical Society