A Taylor series condition for harmonic extension.
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.
Permanent link to this document: http://projecteuclid.org/euclid.rae/1150118743
Mathematical Reviews number (MathSciNet): MR1973984