On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity
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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).
Key wordspolyanalytic function polyanalytic polynomial uniform approximation Schwartz function Vandermonde matrix
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