This article is cited in 11 papers

On the Dependence of Uniform Polyanalytic Polynomial Approximations on the Order of Polyanalyticity

J. J. Carmona^a, K. Yu. Fedorovskiy<sup>b

a</sup> Universitat Autònoma de Barcelona
^b Institute of Information Systems in Management at the State University of Management

Abstract: In this paper, we construct, for each $n\in\mathbb N$, a compact set $X\subset\mathbb C$ (depending on $n$) such that the set of all polyanalytic polynomials of order $n$ is not dense in $\mathrm C(X)$, but the set of all polyanalytic polynomials of order $2n$ is already dense in $\mathrm C(X)$.

Keywords: polyanalytic function, polyanalytic polynomial, uniform approximation, holomorphic function, Schwartz function, Borel measure, Vandermonde matrix.

UDC: 517.583.5+517.956.2

Received: 26.02.2007

DOI: 10.4213/mzm3768

 English version: Mathematical Notes, 2008, 83:1, 31–36

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