Geodesic
$C^m$-approximations by harmonic polynomials on compact sets in~$\mathbb R^n$
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 231-251

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Conditions for approximation of functions by harmonic polynomials on compact sets $X$ in $\mathbb R^n$ $(n = 2,3,\dots)$ in Whitney type norms on the spaces $C_{\mathrm{jet}}^m(X)$ $(m\geqslant 0)$ are studied in this paper. 
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     author = {P. V. Paramonov},
     title = {$C^m$-approximations by harmonic polynomials on compact sets in~$\mathbb R^n$},
     journal = {Sbornik. Mathematics},
     pages = {231--251},
     publisher = {mathdoc},
     volume = {78},
     number = {1},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_1_a14/}
}
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P. V. Paramonov. $C^m$-approximations by harmonic polynomials on compact sets in~$\mathbb R^n$. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 231-251. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a14/