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Arakelyan's theorem and relations between two harmonic functions
Published online by Cambridge University Press: 26 February 2010
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.
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- Copyright © University College London 2001