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

J. J. Carmona; K. Yu Fedorovskii

doi:10.1134/S0001434608010045

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

J. J. Carmona, K. Yu Fedorovskii

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

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). © 2008 Pleiades Publishing, Ltd.

Original language	English
Pages (from-to)	31-36
Journal	Mathematical Notes
Volume	83
Issue number	1-2
DOIs	https://doi.org/10.1134/S0001434608010045
Publication status	Published - 1 Feb 2008

Keywords

Polyanalytic function
Polyanalytic polynomial
Schwartz function
Uniform approximation
Vandermonde matrix

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10.1134/S0001434608010045

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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). {\textcopyright} 2008 Pleiades Publishing, Ltd.",

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N2 - 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). © 2008 Pleiades Publishing, Ltd.

AB - 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). © 2008 Pleiades Publishing, Ltd.

KW - Polyanalytic function

KW - Polyanalytic polynomial

KW - Schwartz function

KW - Uniform approximation

KW - Vandermonde matrix

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DO - 10.1134/S0001434608010045

M3 - Article

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JO - Mathematical Notes

JF - Mathematical Notes

IS - 1-2

ER -

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

Abstract

Keywords

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