Real Analysis Exchange

A Taylor series condition for harmonic extension.

Adam Coffman, David Legg, and Yifei Pan

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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

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

First available in Project Euclid: 12 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31B05: Harmonic, subharmonic, superharmonic functions
Secondary: 26E05: Real-analytic functions [See also 32B05, 32C05] 35C10: Series solutions

Harmonic function Taylor expansion domain of convergence


Coffman, Adam; Legg, David; Pan, Yifei. A Taylor series condition for harmonic extension. Real Anal. Exchange 28 (2002), no. 1, 229--248.

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