## Real Analysis Exchange

### A Taylor series condition for harmonic extension.

#### 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.

#### Article information

Source
Real Anal. Exchange Volume 28, Number 1 (2002), 229-248.

Dates
First available in Project Euclid: 12 June 2006

Permanent link to this document
http://projecteuclid.org/euclid.rae/1150118743

Mathematical Reviews number (MathSciNet)
MR1973984

#### Citation

Coffman, Adam; Legg, David; Pan, Yifei. A Taylor series condition for harmonic extension. Real Anal. Exchange 28 (2002), no. 1, 229--248. http://projecteuclid.org/euclid.rae/1150118743.