Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique

A. Zeriahi

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 1, page 35-50
  • ISSN: 0066-2216

Abstract

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We first give a general growth version of the theorem of Bernstein-Walsh-Siciak concerning the rate of convergence of the best polynomial approximation of holomorphic functions on a polynomially convex compact subset of an affine algebraic manifold. This can be considered as a quantitative version of the well known approximation theorem of Oka-Weil. Then we give two applications of this theorem. The first one is a generalization to several variables of Winiarski's theorem relating the growth of an entire function to the rate of convergence of its best polynomial approximation; the second application concerns the extension with growth of an entire function from an algebraic submanifold to the whole space.

How to cite

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A. Zeriahi. "Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique." Annales Polonici Mathematici 63.1 (1996): 35-50. <http://eudml.org/doc/262537>.

@article{A1996,
author = {A. Zeriahi},
journal = {Annales Polonici Mathematici},
keywords = {Green function; L² estimation; approximation; growth; extension; best polynomial approximation; holomorphic functions; algebraic manifold; entire function; convergence},
language = {fre},
number = {1},
pages = {35-50},
title = {Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique},
url = {http://eudml.org/doc/262537},
volume = {63},
year = {1996},
}

TY - JOUR
AU - A. Zeriahi
TI - Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 1
SP - 35
EP - 50
LA - fre
KW - Green function; L² estimation; approximation; growth; extension; best polynomial approximation; holomorphic functions; algebraic manifold; entire function; convergence
UR - http://eudml.org/doc/262537
ER -

References

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