Geodesic
On the Dependence of Uniform Polyanalytic Polynomial Approximations on the Order of Polyanalyticity
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 32-38

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In this paper, we construct, for each $n\in\mathbb N$, a compact set $X\subset\mathbb C$ (depending on $n$) such that the set of all polyanalytic polynomials of order $n$ is not dense in $\mathrm C(X)$, but the set of all polyanalytic polynomials of order $2n$ is already dense in $\mathrm C(X)$.
Keywords: polyanalytic function, uniform approximation, holomorphic function, Schwartz function, Borel measure
Mots-clés : polyanalytic polynomial, Vandermonde matrix. 
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J. J. Carmona; K. Yu. Fedorovskiy. On the Dependence of Uniform Polyanalytic Polynomial Approximations on the Order of Polyanalyticity. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 32-38. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a3/