Criteria for the individual $C^m$-approximability of functions on compact subsets of $\mathbb R^N$ by solutions of second-order homogeneous elliptic equations

Criteria for the individual approximability of functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients in the norms of Whitney-type $C^m$-spaces on compact subsets of $\mathbb R^N$, $N\in\{2,3,\dots\}$, are obtained for $m \in (0, 1) \cup (0,2)$. These results, which are analogues of Vitushkin's celebrated criteria for uniform rational approximation, were previously established by Mazalov for harmonic approximations (for $m \in (0, 1)$ and $N \geqslant 3$) and by Mazalov and Paramonov for bi-analytic approximation.
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