A Taylor series condition for harmonic extension.
Coffman, Adam ; Legg, David ; Pan, Yifei
Real Anal. Exchange, Tome 28 (2002) no. 1, p. 229-248 / Harvested from Project Euclid
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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.
Publié le : 2002-05-14
Classification:  Harmonic function,  Taylor expansion,  domain of convergence,  31B05,  26E05,  35C10 
@article{1150118743,
     author = {Coffman, Adam and Legg, David and Pan, Yifei},
     title = {A Taylor series condition for harmonic extension.},
     journal = {Real Anal. Exchange},
     volume = {28},
     number = {1},
     year = {2002},
     pages = { 229-248},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150118743}
}

Coffman, Adam; Legg, David; Pan, Yifei. A Taylor series condition for harmonic extension.. Real Anal. Exchange, Tome 28 (2002) no. 1, pp.  229-248. http://gdmltest.u-ga.fr/item/1150118743/