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


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.


Download Citation

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


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

zbMATH: 1055.31003
MathSciNet: MR1973984

Primary: 31B05
Secondary: 26E05 , 35C10

Keywords: domain of convergence , Harmonic function , Taylor expansion

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
Back to Top