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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| Veröffentlicht in: | Mathematical Notes 2008-02, Vol.83 (1-2), p.31-36 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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 |