Abstract
In this paper, we construct, for each n ∈ ℕ, a compact set X ⊂ ℂ (depending on n) such that the set of all polyanalytic polynomials of order n is not dense in C(X), but the set of all polyanalytic polynomials of order 2n is already dense in C(X).
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Original Russian Text © J. J. Carmona, K. Yu. Fedorovskii, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 1, pp. 32–38.
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Carmona, J.J., Fedorovskii, K.Y. On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity. Math Notes 83, 31–36 (2008). https://doi.org/10.1134/S0001434608010045
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DOI: https://doi.org/10.1134/S0001434608010045