On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity

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 2 n is already dense in C( X ).

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Bibliographic Details
Published in:Mathematical Notes 2008-02, Vol.83 (1-2), p.31-36
Main Authors: Carmona, J. J., Fedorovskii, K. Yu
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 2 n is already dense in C( X ).
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434608010045