Real Analysis Exchange

The Determination of a Harmonic Function by Its Sign

D. H. Armitage

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Abstract

We give an improvement of the result that if $hP\ge0$ on $\R^n$, where $h$ is a harmonic function and $P$ a non-trivial harmonic polynomial, then $h$ is proportional to $P$.

Article information

Source
Real Anal. Exchange, Volume 33, Number 2 (2007), 275-278.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1229619405

Mathematical Reviews number (MathSciNet)
MR2458244

Zentralblatt MATH identifier
1165.31001

Subjects
Primary: 31A05: Harmonic, subharmonic, superharmonic functions

Keywords
harmonic function Liouville theorem

Citation

Armitage, D. H. The Determination of a Harmonic Function by Its Sign. Real Anal. Exchange 33 (2007), no. 2, 275--278. https://projecteuclid.org/euclid.rae/1229619405


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References

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