On 𝒞^{𝓂}-approximability of functions by polynomial solutions of elliptic equations on plane compact sets

Fedorovskiĭ, K.

doi:10.1090/S1061-0022-2013-01260-X

On $\mathcal {C}^m$-approximability of functions by polynomial solutions of elliptic equations on plane compact sets
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by K. Yu. Fedorovskiĭ
Translated by: the author

St. Petersburg Math. J. 24 (2013), 677-689

DOI: https://doi.org/10.1090/S1061-0022-2013-01260-X

Published electronically: May 24, 2013

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Abstract:

Conditions of $\mathcal {C}^m$-approximability of functions by polynomial solutions of homogeneous elliptic equations of order $n$ on plane compact sets are studied. For positive integers $m$ and $n$ such that $m\geq n-1$, new necessary and sufficient approximability conditions of a topological and metrical nature are obtained.

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