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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	31-36
Revista	Mathematical Notes
Volum	83
Número	1-2
DOIs	https://doi.org/10.1134/S0001434608010045
Estat de la publicació	Publicada - 1 de febr. 2008

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10.1134/S0001434608010045

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https://www.scopus.com/pages/publications/48849084173

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title = "On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity",

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.",

keywords = "Polyanalytic function, Polyanalytic polynomial, Schwartz function, Uniform approximation, Vandermonde matrix",

author = "Carmona, \{J. J.\} and Fedorovskii, \{K. Yu\}",

year = "2008",

month = feb,

day = "1",

doi = "10.1134/S0001434608010045",

language = "English",

volume = "83",

pages = "31--36",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Springer Science + Business Media",

number = "1-2",

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TY - JOUR

T1 - On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity

AU - Carmona, J. J.

AU - Fedorovskii, K. Yu

PY - 2008/2/1

Y1 - 2008/2/1

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

UR - https://www.scopus.com/pages/publications/48849084173

U2 - 10.1134/S0001434608010045

DO - 10.1134/S0001434608010045

M3 - Article

SN - 0001-4346

VL - 83

SP - 31

EP - 36

JO - Mathematical Notes

JF - Mathematical Notes

IS - 1-2

ER -

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

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