Geodesic
Criteria for the individual $C^m$-approximability of~functions on compact subsets of~$\mathbb R^N$ by solutions of second-order homogeneous elliptic equations
Sbornik. Mathematics, Tome 209 (2018) no. 6, pp. 857-870

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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. Bibliography: 11 titles.
Keywords: $C^m$-approximation by solutions of homogeneous elliptic equations, Vitushkin-type localization operator, $C^m$-invariance of Calderón-Zygmund operators, harmonic $C^m$-capacity
Mots-clés : $p$-dimensional Hausdorff content, $L$-oscillation. 
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     author = {P. V. Paramonov},
     title = {Criteria for the individual $C^m$-approximability of~functions on compact subsets of~$\mathbb R^N$ by solutions of second-order homogeneous elliptic equations},
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     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_6_a5/}
}
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P. V. Paramonov. Criteria for the individual $C^m$-approximability of~functions on compact subsets of~$\mathbb R^N$ by solutions of second-order homogeneous elliptic equations. Sbornik. Mathematics, Tome 209 (2018) no. 6, pp. 857-870. http://geodesic.mathdoc.fr/item/SM_2018_209_6_a5/