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Arakelyan's theorem and relations between two harmonic functions

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  26 February 2010

J. M. Anderson  and
A. Hinkkanen
J. M. Anderson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K.
A. Hinkkanen
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, U.S.A.
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Abstract

It is shown that, if h and k are harmonic in ℝ2 and there exists a positive constant c so that

in ℝ2, where h+ = max {h, 0}, then it need not follow that h - k is identically a constant. The necessary counterexample is obtained by applying Arakelyan's theorem on approximation by an entire function in certain regions in ℝ2.

MSC classification

Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 301 - 304
Copyright
Copyright © University College London 2001

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References

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