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2002-2003 A Taylor series condition for harmonic extension.
Adam Coffman, David Legg, Yifei Pan
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Real Anal. Exchange 28(1): 229-248 (2002-2003).

Abstract

For a harmonic function on an open subset of real $n$-space, we propose a condition on the Taylor expansion that implies harmonic extension to a larger set, by a result on the size of the domain of convergence of its Taylor series. The result in the $n=2$ case is due to M.\ B\^ocher (1909), and the generalization to $n>2$ is given a mostly elementary proof, using basic facts about multivariable power series.

Citation

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Adam Coffman. David Legg. Yifei Pan. "A Taylor series condition for harmonic extension.." Real Anal. Exchange 28 (1) 229 - 248, 2002-2003.

Information

Published: 2002-2003
First available in Project Euclid: 12 June 2006

zbMATH: 1055.31003
MathSciNet: MR1973984

Subjects:
Primary: 31B05
Secondary: 26E05, 35C10

Rights: Copyright © 2002 Michigan State University Press

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