$C^m$-approximations by harmonic polynomials on compact sets in $\mathbb R^n$

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.