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

 

Growth properties of superharmonic functions along rays


Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 128 (2000), 1963-1970
MSC (2000): Primary 31B05
Published electronically: November 1, 1999
MathSciNet review: 1646303
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Abstract: This paper gives a precise topological description of the set of rays along which a superharmonic function on $\mathbb{R}^n$ may grow quickly. The corollary that arbitrary growth cannot occur along all rays answers a question posed by Armitage.


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Additional Information

Stephen J. Gardiner
Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
Email: stephen.gardiner@ucd.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05197-7
PII: S 0002-9939(99)05197-7
Received by editor(s): April 1, 1998
Received by editor(s) in revised form: August 13, 1998
Published electronically: November 1, 1999
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society